Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 79.8%

Time: 36.1s

Alternatives: 33

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 79.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_2 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b + \left(\frac{\mathsf{fma}\left(c, t \cdot j - z \cdot b, t\_1\right)}{i} - y \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (+ t_1 (* b (- (* a i) (* z c)))) (* j (- (* t c) (* y i))))))
   (if (<= t_2 5e+295)
     t_2
     (* i (+ (* a b) (- (/ (fma c (- (* t j) (* z b)) t_1) i) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= 5e+295) {
		tmp = t_2;
	} else {
		tmp = i * ((a * b) + ((fma(c, ((t * j) - (z * b)), t_1) / i) - (y * j)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= 5e+295)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(Float64(a * b) + Float64(Float64(fma(c, Float64(Float64(t * j) - Float64(z * b)), t_1) / i) - Float64(y * j))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 5e+295], t$95$2, N[(i * N[(N[(a * b), $MachinePrecision] + N[(N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / i), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 4.99999999999999991e295

   1. Initial program 91.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   if 4.99999999999999991e295 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 38.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 38.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 42.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 42.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 42.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 42.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 42.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 42.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 42.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 42.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 42.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 42.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 42.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 42.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 42.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 42.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 42.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 69.7%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b + \left(\frac{\mathsf{fma}\left(c, t \cdot j - z \cdot b, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i} - y \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* z (* c (- (/ (* x y) c) b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (c * (((x * y) / c) - b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (c * (((x * y) / c) - b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (c * (((x * y) / c) - b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(c * Float64(Float64(Float64(x * y) / c) - b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (c * (((x * y) / c) - b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(c * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 89.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 0.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 7.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 7.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 7.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 7.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 7.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 7.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 7.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 7.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 7.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 7.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 7.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 7.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 7.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 7.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 7.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 32.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 30.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 30.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 30.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 34.0%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 37.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 37.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 37.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 37.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 37.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 37.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 51.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 51.0%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in c around inf 52.7%

       \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -10600000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -1.6e+102)
     t_3
     (if (<= z -5e+40)
       t_1
       (if (<= z -10600000000000.0)
         t_3
         (if (<= z -4.9e-119)
           (* y (- (* x z) (* i j)))
           (if (<= z -4.1e-206)
             t_2
             (if (<= z 5e-260)
               t_1
               (if (<= z 1.5e-211)
                 (* a (- (* b i) (* x t)))
                 (if (<= z 1.45e-174)
                   (* i (- (* a b) (* y j)))
                   (if (<= z 2.2e+16)
                     (* t (- (* c j) (* x a)))
                     (if (<= z 3.8e+147) t_2 t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.6e+102) {
		tmp = t_3;
	} else if (z <= -5e+40) {
		tmp = t_1;
	} else if (z <= -10600000000000.0) {
		tmp = t_3;
	} else if (z <= -4.9e-119) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -4.1e-206) {
		tmp = t_2;
	} else if (z <= 5e-260) {
		tmp = t_1;
	} else if (z <= 1.5e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.45e-174) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.2e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-1.6d+102)) then
        tmp = t_3
    else if (z <= (-5d+40)) then
        tmp = t_1
    else if (z <= (-10600000000000.0d0)) then
        tmp = t_3
    else if (z <= (-4.9d-119)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-4.1d-206)) then
        tmp = t_2
    else if (z <= 5d-260) then
        tmp = t_1
    else if (z <= 1.5d-211) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.45d-174) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 2.2d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.8d+147) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.6e+102) {
		tmp = t_3;
	} else if (z <= -5e+40) {
		tmp = t_1;
	} else if (z <= -10600000000000.0) {
		tmp = t_3;
	} else if (z <= -4.9e-119) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -4.1e-206) {
		tmp = t_2;
	} else if (z <= 5e-260) {
		tmp = t_1;
	} else if (z <= 1.5e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.45e-174) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.2e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.6e+102:
		tmp = t_3
	elif z <= -5e+40:
		tmp = t_1
	elif z <= -10600000000000.0:
		tmp = t_3
	elif z <= -4.9e-119:
		tmp = y * ((x * z) - (i * j))
	elif z <= -4.1e-206:
		tmp = t_2
	elif z <= 5e-260:
		tmp = t_1
	elif z <= 1.5e-211:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.45e-174:
		tmp = i * ((a * b) - (y * j))
	elif z <= 2.2e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.8e+147:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.6e+102)
		tmp = t_3;
	elseif (z <= -5e+40)
		tmp = t_1;
	elseif (z <= -10600000000000.0)
		tmp = t_3;
	elseif (z <= -4.9e-119)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -4.1e-206)
		tmp = t_2;
	elseif (z <= 5e-260)
		tmp = t_1;
	elseif (z <= 1.5e-211)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.45e-174)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 2.2e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.8e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.6e+102)
		tmp = t_3;
	elseif (z <= -5e+40)
		tmp = t_1;
	elseif (z <= -10600000000000.0)
		tmp = t_3;
	elseif (z <= -4.9e-119)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -4.1e-206)
		tmp = t_2;
	elseif (z <= 5e-260)
		tmp = t_1;
	elseif (z <= 1.5e-211)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.45e-174)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 2.2e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.8e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+102], t$95$3, If[LessEqual[z, -5e+40], t$95$1, If[LessEqual[z, -10600000000000.0], t$95$3, If[LessEqual[z, -4.9e-119], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-206], t$95$2, If[LessEqual[z, 5e-260], t$95$1, If[LessEqual[z, 1.5e-211], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-174], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+147], t$95$2, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.6e102 or -5.00000000000000003e40 < z < -1.06e13 or 3.7999999999999997e147 < z

   1. Initial program 56.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 48.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 48.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 52.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 52.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 52.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 52.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.3%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -1.6e102 < z < -5.00000000000000003e40 or -4.10000000000000016e-206 < z < 5.0000000000000003e-260

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 66.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -1.06e13 < z < -4.9e-119

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 61.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -4.9e-119 < z < -4.10000000000000016e-206 or 2.2e16 < z < 3.7999999999999997e147

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 74.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 74.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 74.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 74.7%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 76.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 76.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 76.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 76.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 76.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 76.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 76.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 64.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 64.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 5.0000000000000003e-260 < z < 1.50000000000000002e-211

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 76.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 76.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      4. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 1.50000000000000002e-211 < z < 1.45000000000000005e-174

   1. Initial program 30.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 86.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 85.6%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 85.6%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 85.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 85.8%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 85.8%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 85.8%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 85.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if 1.45000000000000005e-174 < z < 2.2e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -10600000000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-206}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-260}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -5900000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -5.1e+101)
     t_2
     (if (<= z -6.8e+39)
       (* j (- (* t c) (* y i)))
       (if (<= z -5900000000000.0)
         t_2
         (if (<= z -1.75e-118)
           (* y (- (* x z) (* i j)))
           (if (<= z -1.1e-206)
             t_1
             (if (<= z 3e-261)
               (* j (* i (- (/ (* t c) i) y)))
               (if (<= z 1.55e-211)
                 (* a (- (* b i) (* x t)))
                 (if (<= z 1.9e-175)
                   (* i (- (* a b) (* y j)))
                   (if (<= z 2.4e+16)
                     (* t (- (* c j) (* x a)))
                     (if (<= z 3.8e+147) t_1 t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.1e+101) {
		tmp = t_2;
	} else if (z <= -6.8e+39) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -5900000000000.0) {
		tmp = t_2;
	} else if (z <= -1.75e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.1e-206) {
		tmp = t_1;
	} else if (z <= 3e-261) {
		tmp = j * (i * (((t * c) / i) - y));
	} else if (z <= 1.55e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.9e-175) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.4e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-5.1d+101)) then
        tmp = t_2
    else if (z <= (-6.8d+39)) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= (-5900000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.75d-118)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-1.1d-206)) then
        tmp = t_1
    else if (z <= 3d-261) then
        tmp = j * (i * (((t * c) / i) - y))
    else if (z <= 1.55d-211) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.9d-175) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 2.4d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.8d+147) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.1e+101) {
		tmp = t_2;
	} else if (z <= -6.8e+39) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -5900000000000.0) {
		tmp = t_2;
	} else if (z <= -1.75e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.1e-206) {
		tmp = t_1;
	} else if (z <= 3e-261) {
		tmp = j * (i * (((t * c) / i) - y));
	} else if (z <= 1.55e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.9e-175) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.4e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -5.1e+101:
		tmp = t_2
	elif z <= -6.8e+39:
		tmp = j * ((t * c) - (y * i))
	elif z <= -5900000000000.0:
		tmp = t_2
	elif z <= -1.75e-118:
		tmp = y * ((x * z) - (i * j))
	elif z <= -1.1e-206:
		tmp = t_1
	elif z <= 3e-261:
		tmp = j * (i * (((t * c) / i) - y))
	elif z <= 1.55e-211:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.9e-175:
		tmp = i * ((a * b) - (y * j))
	elif z <= 2.4e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.8e+147:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -5.1e+101)
		tmp = t_2;
	elseif (z <= -6.8e+39)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= -5900000000000.0)
		tmp = t_2;
	elseif (z <= -1.75e-118)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -1.1e-206)
		tmp = t_1;
	elseif (z <= 3e-261)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(t * c) / i) - y)));
	elseif (z <= 1.55e-211)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.9e-175)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 2.4e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.8e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -5.1e+101)
		tmp = t_2;
	elseif (z <= -6.8e+39)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= -5900000000000.0)
		tmp = t_2;
	elseif (z <= -1.75e-118)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -1.1e-206)
		tmp = t_1;
	elseif (z <= 3e-261)
		tmp = j * (i * (((t * c) / i) - y));
	elseif (z <= 1.55e-211)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.9e-175)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 2.4e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.8e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+101], t$95$2, If[LessEqual[z, -6.8e+39], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5900000000000.0], t$95$2, If[LessEqual[z, -1.75e-118], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-206], t$95$1, If[LessEqual[z, 3e-261], N[(j * N[(i * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-211], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-175], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+147], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -5.09999999999999995e101 or -6.7999999999999998e39 < z < -5.9e12 or 3.7999999999999997e147 < z

   1. Initial program 56.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 48.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 48.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 52.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 52.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 52.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 52.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.3%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -5.09999999999999995e101 < z < -6.7999999999999998e39

   1. Initial program 37.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 87.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 75.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -5.9e12 < z < -1.75e-118

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 61.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.75e-118 < z < -1.0999999999999999e-206 or 2.4e16 < z < 3.7999999999999997e147

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 74.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 74.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 74.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 74.7%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 76.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 76.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 76.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 76.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 76.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 76.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 76.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 64.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 64.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if -1.0999999999999999e-206 < z < 3.0000000000000001e-261

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 64.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in i around inf 64.5%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(\frac{c \cdot t}{i} - y\right)\right)} \]

   if 3.0000000000000001e-261 < z < 1.54999999999999998e-211

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 76.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 76.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      4. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 1.54999999999999998e-211 < z < 1.9e-175

   1. Initial program 30.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 86.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 85.6%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 85.6%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 85.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 85.8%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 85.8%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 85.8%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 85.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if 1.9e-175 < z < 2.4e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -5900000000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-206}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -9000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-206}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - \frac{z \cdot c}{i}\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-168}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -2.25e+102)
     t_1
     (if (<= z -1.65e+43)
       (* j (- (* t c) (* y i)))
       (if (<= z -9000000000000.0)
         t_1
         (if (<= z -4e-118)
           (* y (- (* x z) (* i j)))
           (if (<= z -1.02e-206)
             (* (* b i) (- a (/ (* z c) i)))
             (if (<= z 8.5e-261)
               (* j (* i (- (/ (* t c) i) y)))
               (if (<= z 1.5e-211)
                 (* a (- (* b i) (* x t)))
                 (if (<= z 4.2e-168)
                   (* i (- (* a b) (* y j)))
                   (if (<= z 2.55e+16)
                     (* t (- (* c j) (* x a)))
                     (if (<= z 3.8e+147)
                       (* b (- (* a i) (* z c)))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.25e+102) {
		tmp = t_1;
	} else if (z <= -1.65e+43) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -9000000000000.0) {
		tmp = t_1;
	} else if (z <= -4e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.02e-206) {
		tmp = (b * i) * (a - ((z * c) / i));
	} else if (z <= 8.5e-261) {
		tmp = j * (i * (((t * c) / i) - y));
	} else if (z <= 1.5e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 4.2e-168) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.55e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-2.25d+102)) then
        tmp = t_1
    else if (z <= (-1.65d+43)) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= (-9000000000000.0d0)) then
        tmp = t_1
    else if (z <= (-4d-118)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-1.02d-206)) then
        tmp = (b * i) * (a - ((z * c) / i))
    else if (z <= 8.5d-261) then
        tmp = j * (i * (((t * c) / i) - y))
    else if (z <= 1.5d-211) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 4.2d-168) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 2.55d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.8d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.25e+102) {
		tmp = t_1;
	} else if (z <= -1.65e+43) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -9000000000000.0) {
		tmp = t_1;
	} else if (z <= -4e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.02e-206) {
		tmp = (b * i) * (a - ((z * c) / i));
	} else if (z <= 8.5e-261) {
		tmp = j * (i * (((t * c) / i) - y));
	} else if (z <= 1.5e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 4.2e-168) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.55e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.25e+102:
		tmp = t_1
	elif z <= -1.65e+43:
		tmp = j * ((t * c) - (y * i))
	elif z <= -9000000000000.0:
		tmp = t_1
	elif z <= -4e-118:
		tmp = y * ((x * z) - (i * j))
	elif z <= -1.02e-206:
		tmp = (b * i) * (a - ((z * c) / i))
	elif z <= 8.5e-261:
		tmp = j * (i * (((t * c) / i) - y))
	elif z <= 1.5e-211:
		tmp = a * ((b * i) - (x * t))
	elif z <= 4.2e-168:
		tmp = i * ((a * b) - (y * j))
	elif z <= 2.55e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.8e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.25e+102)
		tmp = t_1;
	elseif (z <= -1.65e+43)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= -9000000000000.0)
		tmp = t_1;
	elseif (z <= -4e-118)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -1.02e-206)
		tmp = Float64(Float64(b * i) * Float64(a - Float64(Float64(z * c) / i)));
	elseif (z <= 8.5e-261)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(t * c) / i) - y)));
	elseif (z <= 1.5e-211)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 4.2e-168)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 2.55e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.8e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.25e+102)
		tmp = t_1;
	elseif (z <= -1.65e+43)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= -9000000000000.0)
		tmp = t_1;
	elseif (z <= -4e-118)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -1.02e-206)
		tmp = (b * i) * (a - ((z * c) / i));
	elseif (z <= 8.5e-261)
		tmp = j * (i * (((t * c) / i) - y));
	elseif (z <= 1.5e-211)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 4.2e-168)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 2.55e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.8e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+102], t$95$1, If[LessEqual[z, -1.65e+43], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9000000000000.0], t$95$1, If[LessEqual[z, -4e-118], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-206], N[(N[(b * i), $MachinePrecision] * N[(a - N[(N[(z * c), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-261], N[(j * N[(i * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-211], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-168], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -2.2500000000000001e102 or -1.6500000000000001e43 < z < -9e12 or 3.7999999999999997e147 < z

   1. Initial program 56.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 48.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 48.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 52.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 52.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 52.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 52.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.3%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -2.2500000000000001e102 < z < -1.6500000000000001e43

   1. Initial program 37.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 87.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 75.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -9e12 < z < -3.99999999999999994e-118

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 61.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -3.99999999999999994e-118 < z < -1.0200000000000001e-206

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 73.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in b around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 51.2%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right)} \]

      2. *-commutative 51.2%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right) \]

      3. mul-1-neg 51.2%

         \[\leadsto \left(i \cdot b\right) \cdot \left(a + \color{blue}{\left(-\frac{c \cdot z}{i}\right)}\right) \]

      4. unsub-neg 51.2%

         \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{\left(a - \frac{c \cdot z}{i}\right)} \]

      5. *-commutative 51.2%

         \[\leadsto \left(i \cdot b\right) \cdot \left(a - \frac{\color{blue}{z \cdot c}}{i}\right) \]

   10. Simplified 51.2%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(a - \frac{z \cdot c}{i}\right)} \]

   if -1.0200000000000001e-206 < z < 8.4999999999999996e-261

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 64.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in i around inf 64.5%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(\frac{c \cdot t}{i} - y\right)\right)} \]

   if 8.4999999999999996e-261 < z < 1.50000000000000002e-211

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 76.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 76.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      4. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 1.50000000000000002e-211 < z < 4.19999999999999988e-168

   1. Initial program 30.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 86.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 85.6%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 85.6%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 85.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 85.8%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 85.8%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 85.8%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 85.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if 4.19999999999999988e-168 < z < 2.55e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if 2.55e16 < z < 3.7999999999999997e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+102}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -9000000000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-206}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - \frac{z \cdot c}{i}\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-168}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -11200000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-206}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - \frac{z \cdot c}{i}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-260}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -1.55e+101)
     t_1
     (if (<= z -6.6e+40)
       (* j (- (* t c) (* y i)))
       (if (<= z -11200000000000.0)
         (- (* x (* y z)) (* b (* z c)))
         (if (<= z -4.6e-118)
           (* y (- (* x z) (* i j)))
           (if (<= z -3e-206)
             (* (* b i) (- a (/ (* z c) i)))
             (if (<= z 1.6e-260)
               (* j (* i (- (/ (* t c) i) y)))
               (if (<= z 1.75e-211)
                 (* a (- (* b i) (* x t)))
                 (if (<= z 1.9e-162)
                   (* i (- (* a b) (* y j)))
                   (if (<= z 2.2e+16)
                     (* t (- (* c j) (* x a)))
                     (if (<= z 4.4e+147)
                       (* b (- (* a i) (* z c)))
                       t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.55e+101) {
		tmp = t_1;
	} else if (z <= -6.6e+40) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -11200000000000.0) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (z <= -4.6e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -3e-206) {
		tmp = (b * i) * (a - ((z * c) / i));
	} else if (z <= 1.6e-260) {
		tmp = j * (i * (((t * c) / i) - y));
	} else if (z <= 1.75e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.9e-162) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.2e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 4.4e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-1.55d+101)) then
        tmp = t_1
    else if (z <= (-6.6d+40)) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= (-11200000000000.0d0)) then
        tmp = (x * (y * z)) - (b * (z * c))
    else if (z <= (-4.6d-118)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-3d-206)) then
        tmp = (b * i) * (a - ((z * c) / i))
    else if (z <= 1.6d-260) then
        tmp = j * (i * (((t * c) / i) - y))
    else if (z <= 1.75d-211) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.9d-162) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 2.2d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 4.4d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.55e+101) {
		tmp = t_1;
	} else if (z <= -6.6e+40) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= -11200000000000.0) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (z <= -4.6e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -3e-206) {
		tmp = (b * i) * (a - ((z * c) / i));
	} else if (z <= 1.6e-260) {
		tmp = j * (i * (((t * c) / i) - y));
	} else if (z <= 1.75e-211) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.9e-162) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.2e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 4.4e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.55e+101:
		tmp = t_1
	elif z <= -6.6e+40:
		tmp = j * ((t * c) - (y * i))
	elif z <= -11200000000000.0:
		tmp = (x * (y * z)) - (b * (z * c))
	elif z <= -4.6e-118:
		tmp = y * ((x * z) - (i * j))
	elif z <= -3e-206:
		tmp = (b * i) * (a - ((z * c) / i))
	elif z <= 1.6e-260:
		tmp = j * (i * (((t * c) / i) - y))
	elif z <= 1.75e-211:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.9e-162:
		tmp = i * ((a * b) - (y * j))
	elif z <= 2.2e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 4.4e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.55e+101)
		tmp = t_1;
	elseif (z <= -6.6e+40)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= -11200000000000.0)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c)));
	elseif (z <= -4.6e-118)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -3e-206)
		tmp = Float64(Float64(b * i) * Float64(a - Float64(Float64(z * c) / i)));
	elseif (z <= 1.6e-260)
		tmp = Float64(j * Float64(i * Float64(Float64(Float64(t * c) / i) - y)));
	elseif (z <= 1.75e-211)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.9e-162)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 2.2e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 4.4e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.55e+101)
		tmp = t_1;
	elseif (z <= -6.6e+40)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= -11200000000000.0)
		tmp = (x * (y * z)) - (b * (z * c));
	elseif (z <= -4.6e-118)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -3e-206)
		tmp = (b * i) * (a - ((z * c) / i));
	elseif (z <= 1.6e-260)
		tmp = j * (i * (((t * c) / i) - y));
	elseif (z <= 1.75e-211)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.9e-162)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 2.2e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 4.4e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+101], t$95$1, If[LessEqual[z, -6.6e+40], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -11200000000000.0], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-118], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-206], N[(N[(b * i), $MachinePrecision] * N[(a - N[(N[(z * c), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-260], N[(j * N[(i * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-211], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-162], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if z < -1.55e101 or 4.4000000000000003e147 < z

   1. Initial program 51.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 56.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 56.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 56.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 56.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 56.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 56.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 56.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 56.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 56.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 56.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 56.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 56.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 56.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 56.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 56.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 45.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 45.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 47.9%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 49.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 49.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 49.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 49.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 49.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 49.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 49.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 74.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 74.1%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -1.55e101 < z < -6.5999999999999997e40

   1. Initial program 37.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 87.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 75.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -6.5999999999999997e40 < z < -1.12e13

   1. Initial program 88.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 88.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 88.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 88.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 88.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 88.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 88.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 88.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 88.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 88.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 88.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 88.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 88.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 78.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 78.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 78.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 78.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 78.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 78.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 78.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 78.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 78.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 78.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 78.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in i around 0 67.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)} \]

   if -1.12e13 < z < -4.60000000000000042e-118

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 61.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -4.60000000000000042e-118 < z < -3.0000000000000002e-206

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 72.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 73.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in b around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 51.2%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right)} \]

      2. *-commutative 51.2%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot \left(a + -1 \cdot \frac{c \cdot z}{i}\right) \]

      3. mul-1-neg 51.2%

         \[\leadsto \left(i \cdot b\right) \cdot \left(a + \color{blue}{\left(-\frac{c \cdot z}{i}\right)}\right) \]

      4. unsub-neg 51.2%

         \[\leadsto \left(i \cdot b\right) \cdot \color{blue}{\left(a - \frac{c \cdot z}{i}\right)} \]

      5. *-commutative 51.2%

         \[\leadsto \left(i \cdot b\right) \cdot \left(a - \frac{\color{blue}{z \cdot c}}{i}\right) \]

   10. Simplified 51.2%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(a - \frac{z \cdot c}{i}\right)} \]

   if -3.0000000000000002e-206 < z < 1.59999999999999997e-260

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 64.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in i around inf 64.5%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(\frac{c \cdot t}{i} - y\right)\right)} \]

   if 1.59999999999999997e-260 < z < 1.75e-211

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 76.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.5%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 76.5%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      4. *-commutative 76.5%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 1.75e-211 < z < 1.90000000000000002e-162

   1. Initial program 30.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 86.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 85.6%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 85.6%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 85.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 85.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 85.8%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 85.8%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 85.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 85.8%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 85.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if 1.90000000000000002e-162 < z < 2.2e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if 2.2e16 < z < 4.4000000000000003e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -11200000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-206}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - \frac{z \cdot c}{i}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-260}:\\ \;\;\;\;j \cdot \left(i \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(t \cdot \left(j - b \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -7.7 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-172}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 10^{-6}:\\ \;\;\;\;i \cdot \left(y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= c -8.5e+100)
     (* c (* t (- j (* b (/ z t)))))
     (if (<= c -1.05e-91)
       t_2
       (if (<= c -7.7e-112)
         t_1
         (if (<= c -6e-172)
           (* a (- (* b i) (* x t)))
           (if (<= c -1.3e-243)
             t_1
             (if (<= c 4.8e-261)
               (* i (- (* a b) (* y j)))
               (if (<= c 8.8e-184)
                 t_1
                 (if (<= c 7.6e-153)
                   t_2
                   (if (<= c 1e-6)
                     (* i (* y (- (* x (/ z i)) j)))
                     (* c (- (* t j) (* z b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (c <= -8.5e+100) {
		tmp = c * (t * (j - (b * (z / t))));
	} else if (c <= -1.05e-91) {
		tmp = t_2;
	} else if (c <= -7.7e-112) {
		tmp = t_1;
	} else if (c <= -6e-172) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -1.3e-243) {
		tmp = t_1;
	} else if (c <= 4.8e-261) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 8.8e-184) {
		tmp = t_1;
	} else if (c <= 7.6e-153) {
		tmp = t_2;
	} else if (c <= 1e-6) {
		tmp = i * (y * ((x * (z / i)) - j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = b * ((a * i) - (z * c))
    if (c <= (-8.5d+100)) then
        tmp = c * (t * (j - (b * (z / t))))
    else if (c <= (-1.05d-91)) then
        tmp = t_2
    else if (c <= (-7.7d-112)) then
        tmp = t_1
    else if (c <= (-6d-172)) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= (-1.3d-243)) then
        tmp = t_1
    else if (c <= 4.8d-261) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 8.8d-184) then
        tmp = t_1
    else if (c <= 7.6d-153) then
        tmp = t_2
    else if (c <= 1d-6) then
        tmp = i * (y * ((x * (z / i)) - j))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (c <= -8.5e+100) {
		tmp = c * (t * (j - (b * (z / t))));
	} else if (c <= -1.05e-91) {
		tmp = t_2;
	} else if (c <= -7.7e-112) {
		tmp = t_1;
	} else if (c <= -6e-172) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -1.3e-243) {
		tmp = t_1;
	} else if (c <= 4.8e-261) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 8.8e-184) {
		tmp = t_1;
	} else if (c <= 7.6e-153) {
		tmp = t_2;
	} else if (c <= 1e-6) {
		tmp = i * (y * ((x * (z / i)) - j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if c <= -8.5e+100:
		tmp = c * (t * (j - (b * (z / t))))
	elif c <= -1.05e-91:
		tmp = t_2
	elif c <= -7.7e-112:
		tmp = t_1
	elif c <= -6e-172:
		tmp = a * ((b * i) - (x * t))
	elif c <= -1.3e-243:
		tmp = t_1
	elif c <= 4.8e-261:
		tmp = i * ((a * b) - (y * j))
	elif c <= 8.8e-184:
		tmp = t_1
	elif c <= 7.6e-153:
		tmp = t_2
	elif c <= 1e-6:
		tmp = i * (y * ((x * (z / i)) - j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (c <= -8.5e+100)
		tmp = Float64(c * Float64(t * Float64(j - Float64(b * Float64(z / t)))));
	elseif (c <= -1.05e-91)
		tmp = t_2;
	elseif (c <= -7.7e-112)
		tmp = t_1;
	elseif (c <= -6e-172)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= -1.3e-243)
		tmp = t_1;
	elseif (c <= 4.8e-261)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 8.8e-184)
		tmp = t_1;
	elseif (c <= 7.6e-153)
		tmp = t_2;
	elseif (c <= 1e-6)
		tmp = Float64(i * Float64(y * Float64(Float64(x * Float64(z / i)) - j)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (c <= -8.5e+100)
		tmp = c * (t * (j - (b * (z / t))));
	elseif (c <= -1.05e-91)
		tmp = t_2;
	elseif (c <= -7.7e-112)
		tmp = t_1;
	elseif (c <= -6e-172)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= -1.3e-243)
		tmp = t_1;
	elseif (c <= 4.8e-261)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 8.8e-184)
		tmp = t_1;
	elseif (c <= 7.6e-153)
		tmp = t_2;
	elseif (c <= 1e-6)
		tmp = i * (y * ((x * (z / i)) - j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+100], N[(c * N[(t * N[(j - N[(b * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e-91], t$95$2, If[LessEqual[c, -7.7e-112], t$95$1, If[LessEqual[c, -6e-172], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-243], t$95$1, If[LessEqual[c, 4.8e-261], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e-184], t$95$1, If[LessEqual[c, 7.6e-153], t$95$2, If[LessEqual[c, 1e-6], N[(i * N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -8.50000000000000043e100

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 64.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 69.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in t around inf 69.8%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(j + -1 \cdot \frac{b \cdot z}{t}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 69.8%

         \[\leadsto c \cdot \left(t \cdot \left(j + \color{blue}{\left(-\frac{b \cdot z}{t}\right)}\right)\right) \]

      2. unsub-neg 69.8%

         \[\leadsto c \cdot \left(t \cdot \color{blue}{\left(j - \frac{b \cdot z}{t}\right)}\right) \]

      3. associate-/l* 69.7%

         \[\leadsto c \cdot \left(t \cdot \left(j - \color{blue}{b \cdot \frac{z}{t}}\right)\right) \]

   8. Simplified 69.7%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(j - b \cdot \frac{z}{t}\right)\right)} \]

   if -8.50000000000000043e100 < c < -1.05e-91 or 8.79999999999999967e-184 < c < 7.60000000000000046e-153

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 58.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 60.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 60.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 65.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 65.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 65.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 65.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 65.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 65.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 65.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 65.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 62.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 62.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 62.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 62.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if -1.05e-91 < c < -7.69999999999999959e-112 or -5.99999999999999967e-172 < c < -1.2999999999999999e-243 or 4.80000000000000028e-261 < c < 8.79999999999999967e-184

   1. Initial program 84.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 69.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 69.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 69.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 69.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -7.69999999999999959e-112 < c < -5.99999999999999967e-172

   1. Initial program 63.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 84.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 92.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 92.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 92.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 92.3%

         \[\leadsto \left(-a\right) \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      4. *-commutative 92.3%

         \[\leadsto \left(-a\right) \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 92.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t - i \cdot b\right)} \]

   if -1.2999999999999999e-243 < c < 4.80000000000000028e-261

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 70.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 57.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.8%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 57.8%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 57.8%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 57.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 64.1%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 64.1%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 64.1%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 64.1%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 64.1%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 64.1%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 64.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if 7.60000000000000046e-153 < c < 9.99999999999999955e-7

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 73.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 73.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 73.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 73.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 73.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 73.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 73.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 74.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in y around inf 65.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot \left(j - \frac{x \cdot z}{i}\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 65.1%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(y \cdot \left(j - \frac{x \cdot z}{i}\right)\right)} \]

      2. neg-mul-1 65.1%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(y \cdot \left(j - \frac{x \cdot z}{i}\right)\right) \]

      3. associate-/l* 69.4%

         \[\leadsto \left(-i\right) \cdot \left(y \cdot \left(j - \color{blue}{x \cdot \frac{z}{i}}\right)\right) \]

   10. Simplified 69.4%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot \left(j - x \cdot \frac{z}{i}\right)\right)} \]

   if 9.99999999999999955e-7 < c

   1. Initial program 60.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 61.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 61.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 61.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 61.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 61.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 61.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 61.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 64.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(t \cdot \left(j - b \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-91}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -7.7 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-172}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-261}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 10^{-6}:\\ \;\;\;\;i \cdot \left(y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9600000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-172}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -3.4e+101)
     t_3
     (if (<= z -2e+41)
       t_1
       (if (<= z -9600000000000.0)
         t_3
         (if (<= z -2.85e-117)
           (* y (- (* x z) (* i j)))
           (if (<= z -1.1e-206)
             t_2
             (if (<= z 9.6e-285)
               t_1
               (if (<= z 4.4e-172)
                 (* i (- (* a b) (* y j)))
                 (if (<= z 2.8e+16)
                   (* t (- (* c j) (* x a)))
                   (if (<= z 3.9e+147) t_2 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.4e+101) {
		tmp = t_3;
	} else if (z <= -2e+41) {
		tmp = t_1;
	} else if (z <= -9600000000000.0) {
		tmp = t_3;
	} else if (z <= -2.85e-117) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.1e-206) {
		tmp = t_2;
	} else if (z <= 9.6e-285) {
		tmp = t_1;
	} else if (z <= 4.4e-172) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.8e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.9e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-3.4d+101)) then
        tmp = t_3
    else if (z <= (-2d+41)) then
        tmp = t_1
    else if (z <= (-9600000000000.0d0)) then
        tmp = t_3
    else if (z <= (-2.85d-117)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-1.1d-206)) then
        tmp = t_2
    else if (z <= 9.6d-285) then
        tmp = t_1
    else if (z <= 4.4d-172) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 2.8d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.9d+147) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -3.4e+101) {
		tmp = t_3;
	} else if (z <= -2e+41) {
		tmp = t_1;
	} else if (z <= -9600000000000.0) {
		tmp = t_3;
	} else if (z <= -2.85e-117) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -1.1e-206) {
		tmp = t_2;
	} else if (z <= 9.6e-285) {
		tmp = t_1;
	} else if (z <= 4.4e-172) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 2.8e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.9e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -3.4e+101:
		tmp = t_3
	elif z <= -2e+41:
		tmp = t_1
	elif z <= -9600000000000.0:
		tmp = t_3
	elif z <= -2.85e-117:
		tmp = y * ((x * z) - (i * j))
	elif z <= -1.1e-206:
		tmp = t_2
	elif z <= 9.6e-285:
		tmp = t_1
	elif z <= 4.4e-172:
		tmp = i * ((a * b) - (y * j))
	elif z <= 2.8e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.9e+147:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -3.4e+101)
		tmp = t_3;
	elseif (z <= -2e+41)
		tmp = t_1;
	elseif (z <= -9600000000000.0)
		tmp = t_3;
	elseif (z <= -2.85e-117)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -1.1e-206)
		tmp = t_2;
	elseif (z <= 9.6e-285)
		tmp = t_1;
	elseif (z <= 4.4e-172)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 2.8e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.9e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -3.4e+101)
		tmp = t_3;
	elseif (z <= -2e+41)
		tmp = t_1;
	elseif (z <= -9600000000000.0)
		tmp = t_3;
	elseif (z <= -2.85e-117)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -1.1e-206)
		tmp = t_2;
	elseif (z <= 9.6e-285)
		tmp = t_1;
	elseif (z <= 4.4e-172)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 2.8e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.9e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+101], t$95$3, If[LessEqual[z, -2e+41], t$95$1, If[LessEqual[z, -9600000000000.0], t$95$3, If[LessEqual[z, -2.85e-117], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-206], t$95$2, If[LessEqual[z, 9.6e-285], t$95$1, If[LessEqual[z, 4.4e-172], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+147], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.40000000000000017e101 or -2.00000000000000001e41 < z < -9.6e12 or 3.90000000000000016e147 < z

   1. Initial program 56.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 59.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 48.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 48.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 52.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 52.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 52.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 52.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 52.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.3%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -3.40000000000000017e101 < z < -2.00000000000000001e41 or -1.0999999999999999e-206 < z < 9.6000000000000001e-285

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 68.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -9.6e12 < z < -2.85e-117

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 61.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 61.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2.85e-117 < z < -1.0999999999999999e-206 or 2.8e16 < z < 3.90000000000000016e147

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 74.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 74.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 74.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 74.7%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 76.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 76.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 76.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 76.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 76.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 76.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 76.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 64.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 64.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 64.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 9.6000000000000001e-285 < z < 4.40000000000000018e-172

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 95.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 70.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 70.0%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 70.0%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 70.0%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 70.0%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 70.0%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 70.0%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 70.0%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 70.0%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 70.0%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 70.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if 4.40000000000000018e-172 < z < 2.8e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -9600000000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-206}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-172}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 - a \cdot \left(x \cdot t\right)\\ t_4 := x \cdot y - b \cdot c\\ \mathbf{if}\;z \leq -9 \cdot 10^{+103}:\\ \;\;\;\;z \cdot t\_4\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-263}:\\ \;\;\;\;t\_2 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-183}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-155}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_4}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- t_2 (* a (* x t))))
        (t_4 (- (* x y) (* b c))))
   (if (<= z -9e+103)
     (* z t_4)
     (if (<= z -9.2e+39)
       t_3
       (if (<= z -8.1e+15)
         (- (* x (* y z)) (* b (* z c)))
         (if (<= z 7.5e-263)
           (+ t_2 (* b (* a i)))
           (if (<= z 1.22e-183)
             (+ (* c (* t j)) t_1)
             (if (<= z 3.7e-155)
               (- t_1 (* i (* y j)))
               (if (<= z 3.5e+16)
                 t_3
                 (if (<= z 3.9e+147)
                   (* b (- (* a i) (* z c)))
                   (* (* z i) (/ t_4 i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - (a * (x * t));
	double t_4 = (x * y) - (b * c);
	double tmp;
	if (z <= -9e+103) {
		tmp = z * t_4;
	} else if (z <= -9.2e+39) {
		tmp = t_3;
	} else if (z <= -8.1e+15) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (z <= 7.5e-263) {
		tmp = t_2 + (b * (a * i));
	} else if (z <= 1.22e-183) {
		tmp = (c * (t * j)) + t_1;
	} else if (z <= 3.7e-155) {
		tmp = t_1 - (i * (y * j));
	} else if (z <= 3.5e+16) {
		tmp = t_3;
	} else if (z <= 3.9e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_4 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 - (a * (x * t))
    t_4 = (x * y) - (b * c)
    if (z <= (-9d+103)) then
        tmp = z * t_4
    else if (z <= (-9.2d+39)) then
        tmp = t_3
    else if (z <= (-8.1d+15)) then
        tmp = (x * (y * z)) - (b * (z * c))
    else if (z <= 7.5d-263) then
        tmp = t_2 + (b * (a * i))
    else if (z <= 1.22d-183) then
        tmp = (c * (t * j)) + t_1
    else if (z <= 3.7d-155) then
        tmp = t_1 - (i * (y * j))
    else if (z <= 3.5d+16) then
        tmp = t_3
    else if (z <= 3.9d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * i) * (t_4 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - (a * (x * t));
	double t_4 = (x * y) - (b * c);
	double tmp;
	if (z <= -9e+103) {
		tmp = z * t_4;
	} else if (z <= -9.2e+39) {
		tmp = t_3;
	} else if (z <= -8.1e+15) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (z <= 7.5e-263) {
		tmp = t_2 + (b * (a * i));
	} else if (z <= 1.22e-183) {
		tmp = (c * (t * j)) + t_1;
	} else if (z <= 3.7e-155) {
		tmp = t_1 - (i * (y * j));
	} else if (z <= 3.5e+16) {
		tmp = t_3;
	} else if (z <= 3.9e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_4 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 - (a * (x * t))
	t_4 = (x * y) - (b * c)
	tmp = 0
	if z <= -9e+103:
		tmp = z * t_4
	elif z <= -9.2e+39:
		tmp = t_3
	elif z <= -8.1e+15:
		tmp = (x * (y * z)) - (b * (z * c))
	elif z <= 7.5e-263:
		tmp = t_2 + (b * (a * i))
	elif z <= 1.22e-183:
		tmp = (c * (t * j)) + t_1
	elif z <= 3.7e-155:
		tmp = t_1 - (i * (y * j))
	elif z <= 3.5e+16:
		tmp = t_3
	elif z <= 3.9e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * i) * (t_4 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 - Float64(a * Float64(x * t)))
	t_4 = Float64(Float64(x * y) - Float64(b * c))
	tmp = 0.0
	if (z <= -9e+103)
		tmp = Float64(z * t_4);
	elseif (z <= -9.2e+39)
		tmp = t_3;
	elseif (z <= -8.1e+15)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c)));
	elseif (z <= 7.5e-263)
		tmp = Float64(t_2 + Float64(b * Float64(a * i)));
	elseif (z <= 1.22e-183)
		tmp = Float64(Float64(c * Float64(t * j)) + t_1);
	elseif (z <= 3.7e-155)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (z <= 3.5e+16)
		tmp = t_3;
	elseif (z <= 3.9e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * i) * Float64(t_4 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 - (a * (x * t));
	t_4 = (x * y) - (b * c);
	tmp = 0.0;
	if (z <= -9e+103)
		tmp = z * t_4;
	elseif (z <= -9.2e+39)
		tmp = t_3;
	elseif (z <= -8.1e+15)
		tmp = (x * (y * z)) - (b * (z * c));
	elseif (z <= 7.5e-263)
		tmp = t_2 + (b * (a * i));
	elseif (z <= 1.22e-183)
		tmp = (c * (t * j)) + t_1;
	elseif (z <= 3.7e-155)
		tmp = t_1 - (i * (y * j));
	elseif (z <= 3.5e+16)
		tmp = t_3;
	elseif (z <= 3.9e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * i) * (t_4 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+103], N[(z * t$95$4), $MachinePrecision], If[LessEqual[z, -9.2e+39], t$95$3, If[LessEqual[z, -8.1e+15], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-263], N[(t$95$2 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-183], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 3.7e-155], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+16], t$95$3, If[LessEqual[z, 3.9e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(t$95$4 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -9.00000000000000002e103

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 61.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 61.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 61.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 61.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 61.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 61.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 61.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 61.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 61.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 61.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 46.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 46.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 46.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 49.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 49.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 49.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 49.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 49.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 49.0%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 49.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.3%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -9.00000000000000002e103 < z < -9.20000000000000047e39 or 3.7e-155 < z < 3.5e16

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -9.20000000000000047e39 < z < -8.1e15

   1. Initial program 87.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 87.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 87.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 87.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 87.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 87.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 87.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 87.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 87.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 87.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 87.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 87.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 87.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 87.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 87.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 87.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 87.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 87.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 87.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 87.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 87.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 87.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in i around 0 75.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)} \]

   if -8.1e15 < z < 7.50000000000000044e-263

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 67.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 69.8%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 7.50000000000000044e-263 < z < 1.21999999999999992e-183

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 93.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in y around 0 93.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + c \cdot \left(j \cdot t\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 93.0%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} + c \cdot \left(j \cdot t\right) \]

      2. +-commutative 93.0%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) + \left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      3. unsub-neg 93.0%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - a \cdot \left(t \cdot x - b \cdot i\right)} \]

      4. *-commutative 93.0%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      5. *-commutative 93.0%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      6. *-commutative 93.0%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 93.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 1.21999999999999992e-183 < z < 3.7e-155

   1. Initial program 40.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in c around 0 80.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 80.0%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) \]

      2. +-commutative 80.0%

         \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      3. unsub-neg 80.0%

         \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - a \cdot \left(t \cdot x - b \cdot i\right)} \]

      4. mul-1-neg 80.0%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      5. distribute-rgt-neg-in 80.0%

         \[\leadsto \color{blue}{i \cdot \left(-j \cdot y\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      6. distribute-rgt-neg-in 80.0%

         \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      7. *-commutative 80.0%

         \[\leadsto i \cdot \left(j \cdot \left(-y\right)\right) - a \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      8. *-commutative 80.0%

         \[\leadsto i \cdot \left(j \cdot \left(-y\right)\right) - a \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 80.0%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right) - a \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 3.5e16 < z < 3.90000000000000016e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 3.90000000000000016e147 < z

   1. Initial program 40.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 47.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 67.9%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 67.9%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 71.0%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 74.3%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 74.4%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 74.4%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 74.4%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-263}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-183}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + a \cdot \left(b \cdot i\right)\\ t_3 := x \cdot y - b \cdot c\\ t_4 := z \cdot t\_3\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-192}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_3}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* a (* b i))))
        (t_3 (- (* x y) (* b c)))
        (t_4 (* z t_3)))
   (if (<= z -2.2e+101)
     t_4
     (if (<= z -3.6e+24)
       t_2
       (if (<= z -1.15e+16)
         t_4
         (if (<= z -4e-192)
           (+ t_1 (* b (* a i)))
           (if (<= z 1.45e-162)
             t_2
             (if (<= z 3.3e+16)
               (* t (- (* c j) (* x a)))
               (if (<= z 3.9e+147)
                 (* b (- (* a i) (* z c)))
                 (* (* z i) (/ t_3 i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (a * (b * i));
	double t_3 = (x * y) - (b * c);
	double t_4 = z * t_3;
	double tmp;
	if (z <= -2.2e+101) {
		tmp = t_4;
	} else if (z <= -3.6e+24) {
		tmp = t_2;
	} else if (z <= -1.15e+16) {
		tmp = t_4;
	} else if (z <= -4e-192) {
		tmp = t_1 + (b * (a * i));
	} else if (z <= 1.45e-162) {
		tmp = t_2;
	} else if (z <= 3.3e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.9e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_3 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (a * (b * i))
    t_3 = (x * y) - (b * c)
    t_4 = z * t_3
    if (z <= (-2.2d+101)) then
        tmp = t_4
    else if (z <= (-3.6d+24)) then
        tmp = t_2
    else if (z <= (-1.15d+16)) then
        tmp = t_4
    else if (z <= (-4d-192)) then
        tmp = t_1 + (b * (a * i))
    else if (z <= 1.45d-162) then
        tmp = t_2
    else if (z <= 3.3d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.9d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * i) * (t_3 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (a * (b * i));
	double t_3 = (x * y) - (b * c);
	double t_4 = z * t_3;
	double tmp;
	if (z <= -2.2e+101) {
		tmp = t_4;
	} else if (z <= -3.6e+24) {
		tmp = t_2;
	} else if (z <= -1.15e+16) {
		tmp = t_4;
	} else if (z <= -4e-192) {
		tmp = t_1 + (b * (a * i));
	} else if (z <= 1.45e-162) {
		tmp = t_2;
	} else if (z <= 3.3e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.9e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_3 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (a * (b * i))
	t_3 = (x * y) - (b * c)
	t_4 = z * t_3
	tmp = 0
	if z <= -2.2e+101:
		tmp = t_4
	elif z <= -3.6e+24:
		tmp = t_2
	elif z <= -1.15e+16:
		tmp = t_4
	elif z <= -4e-192:
		tmp = t_1 + (b * (a * i))
	elif z <= 1.45e-162:
		tmp = t_2
	elif z <= 3.3e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.9e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * i) * (t_3 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(a * Float64(b * i)))
	t_3 = Float64(Float64(x * y) - Float64(b * c))
	t_4 = Float64(z * t_3)
	tmp = 0.0
	if (z <= -2.2e+101)
		tmp = t_4;
	elseif (z <= -3.6e+24)
		tmp = t_2;
	elseif (z <= -1.15e+16)
		tmp = t_4;
	elseif (z <= -4e-192)
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	elseif (z <= 1.45e-162)
		tmp = t_2;
	elseif (z <= 3.3e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.9e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * i) * Float64(t_3 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 + (a * (b * i));
	t_3 = (x * y) - (b * c);
	t_4 = z * t_3;
	tmp = 0.0;
	if (z <= -2.2e+101)
		tmp = t_4;
	elseif (z <= -3.6e+24)
		tmp = t_2;
	elseif (z <= -1.15e+16)
		tmp = t_4;
	elseif (z <= -4e-192)
		tmp = t_1 + (b * (a * i));
	elseif (z <= 1.45e-162)
		tmp = t_2;
	elseif (z <= 3.3e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.9e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * i) * (t_3 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * t$95$3), $MachinePrecision]}, If[LessEqual[z, -2.2e+101], t$95$4, If[LessEqual[z, -3.6e+24], t$95$2, If[LessEqual[z, -1.15e+16], t$95$4, If[LessEqual[z, -4e-192], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-162], t$95$2, If[LessEqual[z, 3.3e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(t$95$3 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.2000000000000001e101 or -3.59999999999999983e24 < z < -1.15e16

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 54.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 52.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 52.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 52.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 54.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 54.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 54.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 54.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 54.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 54.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 54.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 76.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 76.2%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -2.2000000000000001e101 < z < -3.59999999999999983e24 or -4.0000000000000004e-192 < z < 1.4500000000000001e-162

   1. Initial program 70.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -1.15e16 < z < -4.0000000000000004e-192

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 67.5%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 1.4500000000000001e-162 < z < 3.3e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if 3.3e16 < z < 3.90000000000000016e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 3.90000000000000016e147 < z

   1. Initial program 40.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 47.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 67.9%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 67.9%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 71.0%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 74.3%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 74.4%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 74.4%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 74.4%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-162}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot y - b \cdot c\\ t_3 := z \cdot t\_2\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -66000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-263}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_2}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- (* x y) (* b c)))
        (t_3 (* z t_2)))
   (if (<= z -1.25e+103)
     t_3
     (if (<= z -1.15e+25)
       (+ t_1 (* a (* b i)))
       (if (<= z -66000000000000.0)
         t_3
         (if (<= z 2e-263)
           (+ t_1 (* b (* a i)))
           (if (<= z 3.4e-161)
             (+ (* c (* t j)) (* a (- (* b i) (* x t))))
             (if (<= z 2e+16)
               (* t (- (* c j) (* x a)))
               (if (<= z 3.9e+147)
                 (* b (- (* a i) (* z c)))
                 (* (* z i) (/ t_2 i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -1.25e+103) {
		tmp = t_3;
	} else if (z <= -1.15e+25) {
		tmp = t_1 + (a * (b * i));
	} else if (z <= -66000000000000.0) {
		tmp = t_3;
	} else if (z <= 2e-263) {
		tmp = t_1 + (b * (a * i));
	} else if (z <= 3.4e-161) {
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	} else if (z <= 2e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.9e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = (x * y) - (b * c)
    t_3 = z * t_2
    if (z <= (-1.25d+103)) then
        tmp = t_3
    else if (z <= (-1.15d+25)) then
        tmp = t_1 + (a * (b * i))
    else if (z <= (-66000000000000.0d0)) then
        tmp = t_3
    else if (z <= 2d-263) then
        tmp = t_1 + (b * (a * i))
    else if (z <= 3.4d-161) then
        tmp = (c * (t * j)) + (a * ((b * i) - (x * t)))
    else if (z <= 2d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.9d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * i) * (t_2 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -1.25e+103) {
		tmp = t_3;
	} else if (z <= -1.15e+25) {
		tmp = t_1 + (a * (b * i));
	} else if (z <= -66000000000000.0) {
		tmp = t_3;
	} else if (z <= 2e-263) {
		tmp = t_1 + (b * (a * i));
	} else if (z <= 3.4e-161) {
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	} else if (z <= 2e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.9e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = (x * y) - (b * c)
	t_3 = z * t_2
	tmp = 0
	if z <= -1.25e+103:
		tmp = t_3
	elif z <= -1.15e+25:
		tmp = t_1 + (a * (b * i))
	elif z <= -66000000000000.0:
		tmp = t_3
	elif z <= 2e-263:
		tmp = t_1 + (b * (a * i))
	elif z <= 3.4e-161:
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)))
	elif z <= 2e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.9e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * i) * (t_2 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(Float64(x * y) - Float64(b * c))
	t_3 = Float64(z * t_2)
	tmp = 0.0
	if (z <= -1.25e+103)
		tmp = t_3;
	elseif (z <= -1.15e+25)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (z <= -66000000000000.0)
		tmp = t_3;
	elseif (z <= 2e-263)
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	elseif (z <= 3.4e-161)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (z <= 2e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.9e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * i) * Float64(t_2 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = (x * y) - (b * c);
	t_3 = z * t_2;
	tmp = 0.0;
	if (z <= -1.25e+103)
		tmp = t_3;
	elseif (z <= -1.15e+25)
		tmp = t_1 + (a * (b * i));
	elseif (z <= -66000000000000.0)
		tmp = t_3;
	elseif (z <= 2e-263)
		tmp = t_1 + (b * (a * i));
	elseif (z <= 3.4e-161)
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	elseif (z <= 2e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.9e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * i) * (t_2 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$2), $MachinePrecision]}, If[LessEqual[z, -1.25e+103], t$95$3, If[LessEqual[z, -1.15e+25], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -66000000000000.0], t$95$3, If[LessEqual[z, 2e-263], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-161], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(t$95$2 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.25e103 or -1.1499999999999999e25 < z < -6.6e13

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 54.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 52.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 52.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 52.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 54.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 54.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 54.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 54.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 54.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 54.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 54.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 76.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 76.2%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -1.25e103 < z < -1.1499999999999999e25

   1. Initial program 58.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 66.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -6.6e13 < z < 2e-263

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 67.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 69.8%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 2e-263 < z < 3.39999999999999982e-161

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 94.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in y around 0 81.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + c \cdot \left(j \cdot t\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 81.9%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} + c \cdot \left(j \cdot t\right) \]

      2. +-commutative 81.9%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) + \left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      3. unsub-neg 81.9%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - a \cdot \left(t \cdot x - b \cdot i\right)} \]

      4. *-commutative 81.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      5. *-commutative 81.9%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      6. *-commutative 81.9%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 81.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 3.39999999999999982e-161 < z < 2e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if 2e16 < z < 3.90000000000000016e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 3.90000000000000016e147 < z

   1. Initial program 40.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 47.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 67.9%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 67.9%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 71.0%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 74.3%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 74.4%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 74.4%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 74.4%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -66000000000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-263}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot y - b \cdot c\\ t_3 := z \cdot t\_2\\ \mathbf{if}\;z \leq -2 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+24}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-262}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_2}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- (* x y) (* b c)))
        (t_3 (* z t_2)))
   (if (<= z -2e+103)
     t_3
     (if (<= z -3.7e+24)
       (+ t_1 (* a (* b i)))
       (if (<= z -3.9e+14)
         t_3
         (if (<= z 1.1e-262)
           (+ t_1 (* b (* a i)))
           (if (<= z 2.85e-161)
             (+ (* c (* t j)) (* a (- (* b i) (* x t))))
             (if (<= z 2.4e+16)
               (- (* t (- (* c j) (* x a))) (* c (* z b)))
               (if (<= z 3.8e+147)
                 (* b (- (* a i) (* z c)))
                 (* (* z i) (/ t_2 i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -2e+103) {
		tmp = t_3;
	} else if (z <= -3.7e+24) {
		tmp = t_1 + (a * (b * i));
	} else if (z <= -3.9e+14) {
		tmp = t_3;
	} else if (z <= 1.1e-262) {
		tmp = t_1 + (b * (a * i));
	} else if (z <= 2.85e-161) {
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	} else if (z <= 2.4e+16) {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	} else if (z <= 3.8e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = (x * y) - (b * c)
    t_3 = z * t_2
    if (z <= (-2d+103)) then
        tmp = t_3
    else if (z <= (-3.7d+24)) then
        tmp = t_1 + (a * (b * i))
    else if (z <= (-3.9d+14)) then
        tmp = t_3
    else if (z <= 1.1d-262) then
        tmp = t_1 + (b * (a * i))
    else if (z <= 2.85d-161) then
        tmp = (c * (t * j)) + (a * ((b * i) - (x * t)))
    else if (z <= 2.4d+16) then
        tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
    else if (z <= 3.8d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * i) * (t_2 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -2e+103) {
		tmp = t_3;
	} else if (z <= -3.7e+24) {
		tmp = t_1 + (a * (b * i));
	} else if (z <= -3.9e+14) {
		tmp = t_3;
	} else if (z <= 1.1e-262) {
		tmp = t_1 + (b * (a * i));
	} else if (z <= 2.85e-161) {
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	} else if (z <= 2.4e+16) {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	} else if (z <= 3.8e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = (x * y) - (b * c)
	t_3 = z * t_2
	tmp = 0
	if z <= -2e+103:
		tmp = t_3
	elif z <= -3.7e+24:
		tmp = t_1 + (a * (b * i))
	elif z <= -3.9e+14:
		tmp = t_3
	elif z <= 1.1e-262:
		tmp = t_1 + (b * (a * i))
	elif z <= 2.85e-161:
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)))
	elif z <= 2.4e+16:
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
	elif z <= 3.8e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * i) * (t_2 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(Float64(x * y) - Float64(b * c))
	t_3 = Float64(z * t_2)
	tmp = 0.0
	if (z <= -2e+103)
		tmp = t_3;
	elseif (z <= -3.7e+24)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (z <= -3.9e+14)
		tmp = t_3;
	elseif (z <= 1.1e-262)
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	elseif (z <= 2.85e-161)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (z <= 2.4e+16)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(c * Float64(z * b)));
	elseif (z <= 3.8e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * i) * Float64(t_2 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = (x * y) - (b * c);
	t_3 = z * t_2;
	tmp = 0.0;
	if (z <= -2e+103)
		tmp = t_3;
	elseif (z <= -3.7e+24)
		tmp = t_1 + (a * (b * i));
	elseif (z <= -3.9e+14)
		tmp = t_3;
	elseif (z <= 1.1e-262)
		tmp = t_1 + (b * (a * i));
	elseif (z <= 2.85e-161)
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	elseif (z <= 2.4e+16)
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	elseif (z <= 3.8e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * i) * (t_2 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$2), $MachinePrecision]}, If[LessEqual[z, -2e+103], t$95$3, If[LessEqual[z, -3.7e+24], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e+14], t$95$3, If[LessEqual[z, 1.1e-262], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e-161], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+16], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(t$95$2 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2e103 or -3.69999999999999999e24 < z < -3.9e14

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 54.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 52.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 52.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 52.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 54.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 54.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 54.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 54.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 54.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 54.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 54.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 76.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 76.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 76.2%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -2e103 < z < -3.69999999999999999e24

   1. Initial program 58.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 66.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -3.9e14 < z < 1.09999999999999994e-262

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 67.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 69.8%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 69.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 1.09999999999999994e-262 < z < 2.85000000000000011e-161

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 94.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in y around 0 81.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + c \cdot \left(j \cdot t\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 81.9%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} + c \cdot \left(j \cdot t\right) \]

      2. +-commutative 81.9%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) + \left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      3. unsub-neg 81.9%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - a \cdot \left(t \cdot x - b \cdot i\right)} \]

      4. *-commutative 81.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      5. *-commutative 81.9%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      6. *-commutative 81.9%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 81.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 2.85000000000000011e-161 < z < 2.4e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 65.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*l* 65.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 73.2%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.9%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 75.9%

          \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 75.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 76.0%

      \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 76.0%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 76.0%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 76.0%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 76.0%

       \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]

   if 2.4e16 < z < 3.7999999999999997e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 3.7999999999999997e147 < z

   1. Initial program 40.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 47.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 67.9%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 67.9%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 71.0%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 74.3%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 74.4%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 74.4%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 74.4%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-262}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right) - i \cdot \left(y \cdot j\right)\\ t_2 := x \cdot y - b \cdot c\\ t_3 := z \cdot t\_2\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-220}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_2}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a (- (* b i) (* x t))) (* i (* y j))))
        (t_2 (- (* x y) (* b c)))
        (t_3 (* z t_2)))
   (if (<= z -3.15e+103)
     t_3
     (if (<= z -1.2e+28)
       t_1
       (if (<= z -3.5e+14)
         t_3
         (if (<= z 1.25e-220)
           (+ (* j (- (* t c) (* y i))) (* b (* a i)))
           (if (<= z 1.25e-163)
             t_1
             (if (<= z 3.2e+16)
               (- (* t (- (* c j) (* x a))) (* c (* z b)))
               (if (<= z 5.4e+147)
                 (* b (- (* a i) (* z c)))
                 (* (* z i) (/ t_2 i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((b * i) - (x * t))) - (i * (y * j));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -3.15e+103) {
		tmp = t_3;
	} else if (z <= -1.2e+28) {
		tmp = t_1;
	} else if (z <= -3.5e+14) {
		tmp = t_3;
	} else if (z <= 1.25e-220) {
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	} else if (z <= 1.25e-163) {
		tmp = t_1;
	} else if (z <= 3.2e+16) {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	} else if (z <= 5.4e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * ((b * i) - (x * t))) - (i * (y * j))
    t_2 = (x * y) - (b * c)
    t_3 = z * t_2
    if (z <= (-3.15d+103)) then
        tmp = t_3
    else if (z <= (-1.2d+28)) then
        tmp = t_1
    else if (z <= (-3.5d+14)) then
        tmp = t_3
    else if (z <= 1.25d-220) then
        tmp = (j * ((t * c) - (y * i))) + (b * (a * i))
    else if (z <= 1.25d-163) then
        tmp = t_1
    else if (z <= 3.2d+16) then
        tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
    else if (z <= 5.4d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * i) * (t_2 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((b * i) - (x * t))) - (i * (y * j));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -3.15e+103) {
		tmp = t_3;
	} else if (z <= -1.2e+28) {
		tmp = t_1;
	} else if (z <= -3.5e+14) {
		tmp = t_3;
	} else if (z <= 1.25e-220) {
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	} else if (z <= 1.25e-163) {
		tmp = t_1;
	} else if (z <= 3.2e+16) {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	} else if (z <= 5.4e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((b * i) - (x * t))) - (i * (y * j))
	t_2 = (x * y) - (b * c)
	t_3 = z * t_2
	tmp = 0
	if z <= -3.15e+103:
		tmp = t_3
	elif z <= -1.2e+28:
		tmp = t_1
	elif z <= -3.5e+14:
		tmp = t_3
	elif z <= 1.25e-220:
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i))
	elif z <= 1.25e-163:
		tmp = t_1
	elif z <= 3.2e+16:
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
	elif z <= 5.4e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * i) * (t_2 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) - Float64(i * Float64(y * j)))
	t_2 = Float64(Float64(x * y) - Float64(b * c))
	t_3 = Float64(z * t_2)
	tmp = 0.0
	if (z <= -3.15e+103)
		tmp = t_3;
	elseif (z <= -1.2e+28)
		tmp = t_1;
	elseif (z <= -3.5e+14)
		tmp = t_3;
	elseif (z <= 1.25e-220)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(a * i)));
	elseif (z <= 1.25e-163)
		tmp = t_1;
	elseif (z <= 3.2e+16)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(c * Float64(z * b)));
	elseif (z <= 5.4e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * i) * Float64(t_2 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * ((b * i) - (x * t))) - (i * (y * j));
	t_2 = (x * y) - (b * c);
	t_3 = z * t_2;
	tmp = 0.0;
	if (z <= -3.15e+103)
		tmp = t_3;
	elseif (z <= -1.2e+28)
		tmp = t_1;
	elseif (z <= -3.5e+14)
		tmp = t_3;
	elseif (z <= 1.25e-220)
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	elseif (z <= 1.25e-163)
		tmp = t_1;
	elseif (z <= 3.2e+16)
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	elseif (z <= 5.4e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * i) * (t_2 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$2), $MachinePrecision]}, If[LessEqual[z, -3.15e+103], t$95$3, If[LessEqual[z, -1.2e+28], t$95$1, If[LessEqual[z, -3.5e+14], t$95$3, If[LessEqual[z, 1.25e-220], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-163], t$95$1, If[LessEqual[z, 3.2e+16], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(t$95$2 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.14999999999999985e103 or -1.19999999999999991e28 < z < -3.5e14

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 64.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 64.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 64.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 64.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 64.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 64.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 64.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 64.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 64.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 64.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 64.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 64.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 64.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 64.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 53.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 51.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 51.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 51.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 53.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 53.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 53.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 53.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 53.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 53.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 74.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 74.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 74.6%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -3.14999999999999985e103 < z < -1.19999999999999991e28 or 1.25e-220 < z < 1.24999999999999994e-163

   1. Initial program 45.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 85.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in c around 0 80.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 80.2%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) \]

      2. +-commutative 80.2%

         \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      3. unsub-neg 80.2%

         \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - a \cdot \left(t \cdot x - b \cdot i\right)} \]

      4. mul-1-neg 80.2%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      5. distribute-rgt-neg-in 80.2%

         \[\leadsto \color{blue}{i \cdot \left(-j \cdot y\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      6. distribute-rgt-neg-in 80.2%

         \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      7. *-commutative 80.2%

         \[\leadsto i \cdot \left(j \cdot \left(-y\right)\right) - a \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      8. *-commutative 80.2%

         \[\leadsto i \cdot \left(j \cdot \left(-y\right)\right) - a \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right) - a \cdot \left(x \cdot t - i \cdot b\right)} \]

   if -3.5e14 < z < 1.25e-220

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 68.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 68.0%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 70.2%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 1.24999999999999994e-163 < z < 3.2e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 65.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*l* 65.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 73.2%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.9%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 75.9%

          \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 75.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 76.0%

      \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 76.0%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 76.0%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 76.0%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 76.0%

       \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]

   if 3.2e16 < z < 5.39999999999999995e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 5.39999999999999995e147 < z

   1. Initial program 40.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 47.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 67.9%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 67.9%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 71.0%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 74.3%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 74.4%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 74.4%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 74.4%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-220}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.32 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -8.5e+101)
     t_3
     (if (<= c -3.3e-93)
       (* b (- (* a i) (* z c)))
       (if (<= c -1.32e-111)
         t_1
         (if (<= c -3.4e-165)
           t_2
           (if (<= c -8.5e-241)
             t_1
             (if (<= c 7e-263) t_2 (if (<= c 2.65e-6) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.5e+101) {
		tmp = t_3;
	} else if (c <= -3.3e-93) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -1.32e-111) {
		tmp = t_1;
	} else if (c <= -3.4e-165) {
		tmp = t_2;
	} else if (c <= -8.5e-241) {
		tmp = t_1;
	} else if (c <= 7e-263) {
		tmp = t_2;
	} else if (c <= 2.65e-6) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = i * ((a * b) - (y * j))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-8.5d+101)) then
        tmp = t_3
    else if (c <= (-3.3d-93)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= (-1.32d-111)) then
        tmp = t_1
    else if (c <= (-3.4d-165)) then
        tmp = t_2
    else if (c <= (-8.5d-241)) then
        tmp = t_1
    else if (c <= 7d-263) then
        tmp = t_2
    else if (c <= 2.65d-6) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.5e+101) {
		tmp = t_3;
	} else if (c <= -3.3e-93) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -1.32e-111) {
		tmp = t_1;
	} else if (c <= -3.4e-165) {
		tmp = t_2;
	} else if (c <= -8.5e-241) {
		tmp = t_1;
	} else if (c <= 7e-263) {
		tmp = t_2;
	} else if (c <= 2.65e-6) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = i * ((a * b) - (y * j))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -8.5e+101:
		tmp = t_3
	elif c <= -3.3e-93:
		tmp = b * ((a * i) - (z * c))
	elif c <= -1.32e-111:
		tmp = t_1
	elif c <= -3.4e-165:
		tmp = t_2
	elif c <= -8.5e-241:
		tmp = t_1
	elif c <= 7e-263:
		tmp = t_2
	elif c <= 2.65e-6:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -8.5e+101)
		tmp = t_3;
	elseif (c <= -3.3e-93)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= -1.32e-111)
		tmp = t_1;
	elseif (c <= -3.4e-165)
		tmp = t_2;
	elseif (c <= -8.5e-241)
		tmp = t_1;
	elseif (c <= 7e-263)
		tmp = t_2;
	elseif (c <= 2.65e-6)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = i * ((a * b) - (y * j));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -8.5e+101)
		tmp = t_3;
	elseif (c <= -3.3e-93)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= -1.32e-111)
		tmp = t_1;
	elseif (c <= -3.4e-165)
		tmp = t_2;
	elseif (c <= -8.5e-241)
		tmp = t_1;
	elseif (c <= 7e-263)
		tmp = t_2;
	elseif (c <= 2.65e-6)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+101], t$95$3, If[LessEqual[c, -3.3e-93], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.32e-111], t$95$1, If[LessEqual[c, -3.4e-165], t$95$2, If[LessEqual[c, -8.5e-241], t$95$1, If[LessEqual[c, 7e-263], t$95$2, If[LessEqual[c, 2.65e-6], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.5000000000000001e101 or 2.65e-6 < c

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 62.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 66.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -8.5000000000000001e101 < c < -3.3000000000000001e-93

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 72.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 72.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 53.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 53.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 53.9%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 60.1%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 60.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 60.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 60.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 60.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 60.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 60.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 60.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 58.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 58.8%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 58.8%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if -3.3000000000000001e-93 < c < -1.32e-111 or -3.4e-165 < c < -8.49999999999999974e-241 or 6.99999999999999938e-263 < c < 2.65e-6

   1. Initial program 78.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 80.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 80.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 80.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 62.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 62.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 62.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 62.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 62.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.32e-111 < c < -3.4e-165 or -8.49999999999999974e-241 < c < 6.99999999999999938e-263

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 74.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 58.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.7%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 58.7%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 58.7%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 58.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 63.1%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 63.1%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 63.1%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 63.1%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 63.1%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 63.1%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 63.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.32 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-165}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ t_2 := x \cdot y - b \cdot c\\ t_3 := z \cdot t\_2\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_3\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_2}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* b (- (* z c) (* a i)))))
        (t_2 (- (* x y) (* b c)))
        (t_3 (* z t_2)))
   (if (<= z -4.6e+113)
     t_3
     (if (<= z -1.35e-25)
       (+ (* j (- (* t c) (* y i))) t_3)
       (if (<= z -5.5e-290)
         t_1
         (if (<= z 2.2e-89)
           (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))
           (if (<= z 6.6e+152) t_1 (* (* z i) (/ t_2 i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -4.6e+113) {
		tmp = t_3;
	} else if (z <= -1.35e-25) {
		tmp = (j * ((t * c) - (y * i))) + t_3;
	} else if (z <= -5.5e-290) {
		tmp = t_1;
	} else if (z <= 2.2e-89) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else if (z <= 6.6e+152) {
		tmp = t_1;
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
    t_2 = (x * y) - (b * c)
    t_3 = z * t_2
    if (z <= (-4.6d+113)) then
        tmp = t_3
    else if (z <= (-1.35d-25)) then
        tmp = (j * ((t * c) - (y * i))) + t_3
    else if (z <= (-5.5d-290)) then
        tmp = t_1
    else if (z <= 2.2d-89) then
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    else if (z <= 6.6d+152) then
        tmp = t_1
    else
        tmp = (z * i) * (t_2 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -4.6e+113) {
		tmp = t_3;
	} else if (z <= -1.35e-25) {
		tmp = (j * ((t * c) - (y * i))) + t_3;
	} else if (z <= -5.5e-290) {
		tmp = t_1;
	} else if (z <= 2.2e-89) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else if (z <= 6.6e+152) {
		tmp = t_1;
	} else {
		tmp = (z * i) * (t_2 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
	t_2 = (x * y) - (b * c)
	t_3 = z * t_2
	tmp = 0
	if z <= -4.6e+113:
		tmp = t_3
	elif z <= -1.35e-25:
		tmp = (j * ((t * c) - (y * i))) + t_3
	elif z <= -5.5e-290:
		tmp = t_1
	elif z <= 2.2e-89:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	elif z <= 6.6e+152:
		tmp = t_1
	else:
		tmp = (z * i) * (t_2 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))))
	t_2 = Float64(Float64(x * y) - Float64(b * c))
	t_3 = Float64(z * t_2)
	tmp = 0.0
	if (z <= -4.6e+113)
		tmp = t_3;
	elseif (z <= -1.35e-25)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_3);
	elseif (z <= -5.5e-290)
		tmp = t_1;
	elseif (z <= 2.2e-89)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (z <= 6.6e+152)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * i) * Float64(t_2 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	t_2 = (x * y) - (b * c);
	t_3 = z * t_2;
	tmp = 0.0;
	if (z <= -4.6e+113)
		tmp = t_3;
	elseif (z <= -1.35e-25)
		tmp = (j * ((t * c) - (y * i))) + t_3;
	elseif (z <= -5.5e-290)
		tmp = t_1;
	elseif (z <= 2.2e-89)
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	elseif (z <= 6.6e+152)
		tmp = t_1;
	else
		tmp = (z * i) * (t_2 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$2), $MachinePrecision]}, If[LessEqual[z, -4.6e+113], t$95$3, If[LessEqual[z, -1.35e-25], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[z, -5.5e-290], t$95$1, If[LessEqual[z, 2.2e-89], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+152], t$95$1, N[(N[(z * i), $MachinePrecision] * N[(t$95$2 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.59999999999999993e113

   1. Initial program 60.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 52.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 47.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 47.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 47.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 50.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 50.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 50.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 50.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.8%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -4.59999999999999993e113 < z < -1.35000000000000008e-25

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 80.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 80.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -1.35000000000000008e-25 < z < -5.5e-290 or 2.20000000000000012e-89 < z < 6.6000000000000003e152

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 76.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 76.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 76.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 76.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 77.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 77.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 77.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 77.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 77.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 77.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 77.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   if -5.5e-290 < z < 2.20000000000000012e-89

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.8%

         \[\leadsto \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 69.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*l* 69.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 75.2%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 77.1%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 77.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 77.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 77.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 77.1%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 77.1%

          \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 77.1%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   if 6.6000000000000003e152 < z

   1. Initial program 42.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 42.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 49.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 49.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 49.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 49.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 73.5%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 73.5%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 73.5%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 70.2%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 70.2%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 73.5%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 76.9%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 77.0%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 77.0%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 77.0%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 77.0%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot y - b \cdot c\\ t_4 := z \cdot t\_3\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+113}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-24}:\\ \;\;\;\;t\_2 + t\_4\\ \mathbf{elif}\;z \leq 1.01 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7:\\ \;\;\;\;t\_2 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_3}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* b (- (* z c) (* a i)))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- (* x y) (* b c)))
        (t_4 (* z t_3)))
   (if (<= z -6.8e+113)
     t_4
     (if (<= z -1.7e-24)
       (+ t_2 t_4)
       (if (<= z 1.01e-306)
         t_1
         (if (<= z 2.7)
           (+ t_2 (* a (- (* b i) (* x t))))
           (if (<= z 2.05e+152) t_1 (* (* z i) (/ t_3 i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = (x * y) - (b * c);
	double t_4 = z * t_3;
	double tmp;
	if (z <= -6.8e+113) {
		tmp = t_4;
	} else if (z <= -1.7e-24) {
		tmp = t_2 + t_4;
	} else if (z <= 1.01e-306) {
		tmp = t_1;
	} else if (z <= 2.7) {
		tmp = t_2 + (a * ((b * i) - (x * t)));
	} else if (z <= 2.05e+152) {
		tmp = t_1;
	} else {
		tmp = (z * i) * (t_3 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
    t_2 = j * ((t * c) - (y * i))
    t_3 = (x * y) - (b * c)
    t_4 = z * t_3
    if (z <= (-6.8d+113)) then
        tmp = t_4
    else if (z <= (-1.7d-24)) then
        tmp = t_2 + t_4
    else if (z <= 1.01d-306) then
        tmp = t_1
    else if (z <= 2.7d0) then
        tmp = t_2 + (a * ((b * i) - (x * t)))
    else if (z <= 2.05d+152) then
        tmp = t_1
    else
        tmp = (z * i) * (t_3 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = (x * y) - (b * c);
	double t_4 = z * t_3;
	double tmp;
	if (z <= -6.8e+113) {
		tmp = t_4;
	} else if (z <= -1.7e-24) {
		tmp = t_2 + t_4;
	} else if (z <= 1.01e-306) {
		tmp = t_1;
	} else if (z <= 2.7) {
		tmp = t_2 + (a * ((b * i) - (x * t)));
	} else if (z <= 2.05e+152) {
		tmp = t_1;
	} else {
		tmp = (z * i) * (t_3 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
	t_2 = j * ((t * c) - (y * i))
	t_3 = (x * y) - (b * c)
	t_4 = z * t_3
	tmp = 0
	if z <= -6.8e+113:
		tmp = t_4
	elif z <= -1.7e-24:
		tmp = t_2 + t_4
	elif z <= 1.01e-306:
		tmp = t_1
	elif z <= 2.7:
		tmp = t_2 + (a * ((b * i) - (x * t)))
	elif z <= 2.05e+152:
		tmp = t_1
	else:
		tmp = (z * i) * (t_3 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(Float64(x * y) - Float64(b * c))
	t_4 = Float64(z * t_3)
	tmp = 0.0
	if (z <= -6.8e+113)
		tmp = t_4;
	elseif (z <= -1.7e-24)
		tmp = Float64(t_2 + t_4);
	elseif (z <= 1.01e-306)
		tmp = t_1;
	elseif (z <= 2.7)
		tmp = Float64(t_2 + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (z <= 2.05e+152)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * i) * Float64(t_3 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	t_2 = j * ((t * c) - (y * i));
	t_3 = (x * y) - (b * c);
	t_4 = z * t_3;
	tmp = 0.0;
	if (z <= -6.8e+113)
		tmp = t_4;
	elseif (z <= -1.7e-24)
		tmp = t_2 + t_4;
	elseif (z <= 1.01e-306)
		tmp = t_1;
	elseif (z <= 2.7)
		tmp = t_2 + (a * ((b * i) - (x * t)));
	elseif (z <= 2.05e+152)
		tmp = t_1;
	else
		tmp = (z * i) * (t_3 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * t$95$3), $MachinePrecision]}, If[LessEqual[z, -6.8e+113], t$95$4, If[LessEqual[z, -1.7e-24], N[(t$95$2 + t$95$4), $MachinePrecision], If[LessEqual[z, 1.01e-306], t$95$1, If[LessEqual[z, 2.7], N[(t$95$2 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+152], t$95$1, N[(N[(z * i), $MachinePrecision] * N[(t$95$3 / i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.80000000000000038e113

   1. Initial program 60.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 52.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 47.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 47.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 47.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 50.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 50.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 50.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 50.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.8%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -6.80000000000000038e113 < z < -1.69999999999999996e-24

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 80.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 80.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -1.69999999999999996e-24 < z < 1.00999999999999994e-306 or 2.7000000000000002 < z < 2.0499999999999999e152

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 76.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 76.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 76.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 76.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 77.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 77.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 77.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 77.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 77.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 77.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 77.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   if 1.00999999999999994e-306 < z < 2.7000000000000002

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 86.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 2.0499999999999999e152 < z

   1. Initial program 42.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 42.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 49.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 49.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 49.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 49.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 49.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 49.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 73.5%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 73.5%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 73.5%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 73.5%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 70.2%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 70.2%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 73.5%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 76.9%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 77.0%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 77.0%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 77.0%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 77.0%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.01 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;z \leq 2.7:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -1.06 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-165}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-150}:\\ \;\;\;\;t\_1 + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= b -1.06e+96)
     (+ (* t (* c j)) (* b (- (* a i) (* z c))))
     (if (<= b -2.5e-165)
       (+ t_1 (* a (- (* b i) (* x t))))
       (if (<= b 1.95e-150)
         (+ t_1 (- (* x (- (* y z) (* t a))) (* c (* z b))))
         (- (* y (- (* x z) (* i j))) (* b (- (* z c) (* a i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -1.06e+96) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else if (b <= -2.5e-165) {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	} else if (b <= 1.95e-150) {
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (b <= (-1.06d+96)) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else if (b <= (-2.5d-165)) then
        tmp = t_1 + (a * ((b * i) - (x * t)))
    else if (b <= 1.95d-150) then
        tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)))
    else
        tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -1.06e+96) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else if (b <= -2.5e-165) {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	} else if (b <= 1.95e-150) {
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -1.06e+96:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	elif b <= -2.5e-165:
		tmp = t_1 + (a * ((b * i) - (x * t)))
	elif b <= 1.95e-150:
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)))
	else:
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -1.06e+96)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= -2.5e-165)
		tmp = Float64(t_1 + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (b <= 1.95e-150)
		tmp = Float64(t_1 + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -1.06e+96)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	elseif (b <= -2.5e-165)
		tmp = t_1 + (a * ((b * i) - (x * t)));
	elseif (b <= 1.95e-150)
		tmp = t_1 + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	else
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.06e+96], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-165], N[(t$95$1 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e-150], N[(t$95$1 + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.06e96

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 67.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 75.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*l* 75.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 74.9%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 74.9%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 74.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 74.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 74.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 74.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 74.9%

          \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in j around inf 77.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]
   9. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} - b \cdot \left(c \cdot z - i \cdot a\right) \]

      2. *-commutative 76.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]

   10. Simplified 76.9%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} - b \cdot \left(c \cdot z - i \cdot a\right) \]

   if -1.06e96 < b < -2.4999999999999999e-165

   1. Initial program 81.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 77.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -2.4999999999999999e-165 < b < 1.9500000000000001e-150

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 78.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 63.6%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 63.6%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   5. Simplified 86.9%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{c \cdot \left(b \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 1.9500000000000001e-150 < b

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 70.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 70.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 70.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 70.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 70.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 70.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 70.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 70.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 70.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 70.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 70.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 70.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 70.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 69.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 69.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 69.1%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 71.1%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 73.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 73.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 73.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 73.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 73.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 73.1%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 73.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-182}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))))
   (if (<= y -5.5e+156)
     (* y (- (* x z) (* i j)))
     (if (<= y -2.8e-36)
       t_1
       (if (<= y 5e-182)
         (+ (* c (* t j)) (* a (- (* b i) (* x t))))
         (if (<= y 1e-73) (- (* t (- (* c j) (* x a))) (* c (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (y <= -5.5e+156) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -2.8e-36) {
		tmp = t_1;
	} else if (y <= 5e-182) {
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	} else if (y <= 1e-73) {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    if (y <= (-5.5d+156)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-2.8d-36)) then
        tmp = t_1
    else if (y <= 5d-182) then
        tmp = (c * (t * j)) + (a * ((b * i) - (x * t)))
    else if (y <= 1d-73) then
        tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (y <= -5.5e+156) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -2.8e-36) {
		tmp = t_1;
	} else if (y <= 5e-182) {
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	} else if (y <= 1e-73) {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	tmp = 0
	if y <= -5.5e+156:
		tmp = y * ((x * z) - (i * j))
	elif y <= -2.8e-36:
		tmp = t_1
	elif y <= 5e-182:
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)))
	elif y <= 1e-73:
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (y <= -5.5e+156)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -2.8e-36)
		tmp = t_1;
	elseif (y <= 5e-182)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (y <= 1e-73)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(c * Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (y <= -5.5e+156)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -2.8e-36)
		tmp = t_1;
	elseif (y <= 5e-182)
		tmp = (c * (t * j)) + (a * ((b * i) - (x * t)));
	elseif (y <= 1e-73)
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+156], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-36], t$95$1, If[LessEqual[y, 5e-182], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-73], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5000000000000003e156

   1. Initial program 53.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 53.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 53.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 53.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 82.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 82.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 82.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 82.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -5.5000000000000003e156 < y < -2.8000000000000001e-36 or 9.99999999999999997e-74 < y

   1. Initial program 63.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 69.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 69.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -2.8000000000000001e-36 < y < 5.00000000000000024e-182

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 72.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in y around 0 67.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + c \cdot \left(j \cdot t\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 67.6%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} + c \cdot \left(j \cdot t\right) \]

      2. +-commutative 67.6%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) + \left(-a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

      3. unsub-neg 67.6%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - a \cdot \left(t \cdot x - b \cdot i\right)} \]

      4. *-commutative 67.6%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} - a \cdot \left(t \cdot x - b \cdot i\right) \]

      5. *-commutative 67.6%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(\color{blue}{x \cdot t} - b \cdot i\right) \]

      6. *-commutative 67.6%

         \[\leadsto c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - \color{blue}{i \cdot b}\right) \]

   6. Simplified 67.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t - i \cdot b\right)} \]

   if 5.00000000000000024e-182 < y < 9.99999999999999997e-74

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 60.7%

         \[\leadsto \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 68.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*l* 68.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 80.5%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 80.5%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 80.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 80.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 80.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 80.5%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 80.5%

          \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 80.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 80.8%

      \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 80.8%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 80.6%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 80.6%

         \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 80.6%

       \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-182}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-34} \lor \neg \left(y \leq 7.5 \cdot 10^{-67}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.42e+154)
   (* y (- (* x z) (* i j)))
   (if (or (<= y -8.5e-34) (not (<= y 7.5e-67)))
     (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))
     (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.42e+154) {
		tmp = y * ((x * z) - (i * j));
	} else if ((y <= -8.5e-34) || !(y <= 7.5e-67)) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.42d+154)) then
        tmp = y * ((x * z) - (i * j))
    else if ((y <= (-8.5d-34)) .or. (.not. (y <= 7.5d-67))) then
        tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.42e+154) {
		tmp = y * ((x * z) - (i * j));
	} else if ((y <= -8.5e-34) || !(y <= 7.5e-67)) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.42e+154:
		tmp = y * ((x * z) - (i * j))
	elif (y <= -8.5e-34) or not (y <= 7.5e-67):
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	else:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.42e+154)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif ((y <= -8.5e-34) || !(y <= 7.5e-67))
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.42e+154)
		tmp = y * ((x * z) - (i * j));
	elseif ((y <= -8.5e-34) || ~((y <= 7.5e-67)))
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	else
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.42e+154], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.5e-34], N[Not[LessEqual[y, 7.5e-67]], $MachinePrecision]], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.42e154

   1. Initial program 53.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 53.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 53.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 53.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 53.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 53.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 82.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 82.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 82.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 82.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 82.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.42e154 < y < -8.5000000000000001e-34 or 7.5000000000000005e-67 < y

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 69.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 69.6%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 69.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -8.5000000000000001e-34 < y < 7.5000000000000005e-67

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto \left(-1 \cdot \left(a \cdot \color{blue}{\left(x \cdot t\right)}\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 71.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(a \cdot x\right) \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*l* 71.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 74.0%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 74.9%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 74.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 74.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 74.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 74.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 74.9%

          \[\leadsto t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 74.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-34} \lor \neg \left(y \leq 7.5 \cdot 10^{-67}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 55.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - b \cdot c\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;z \cdot t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-170}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{t\_1}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x y) (* b c))))
   (if (<= z -1.05e+101)
     (* z t_1)
     (if (<= z 4e-170)
       (+ (* j (- (* t c) (* y i))) (* a (* b i)))
       (if (<= z 3.3e+16)
         (* t (- (* c j) (* x a)))
         (if (<= z 3.8e+147)
           (* b (- (* a i) (* z c)))
           (* (* z i) (/ t_1 i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * y) - (b * c);
	double tmp;
	if (z <= -1.05e+101) {
		tmp = z * t_1;
	} else if (z <= 4e-170) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (z <= 3.3e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_1 / i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (b * c)
    if (z <= (-1.05d+101)) then
        tmp = z * t_1
    else if (z <= 4d-170) then
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    else if (z <= 3.3d+16) then
        tmp = t * ((c * j) - (x * a))
    else if (z <= 3.8d+147) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * i) * (t_1 / i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * y) - (b * c);
	double tmp;
	if (z <= -1.05e+101) {
		tmp = z * t_1;
	} else if (z <= 4e-170) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (z <= 3.3e+16) {
		tmp = t * ((c * j) - (x * a));
	} else if (z <= 3.8e+147) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * i) * (t_1 / i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * y) - (b * c)
	tmp = 0
	if z <= -1.05e+101:
		tmp = z * t_1
	elif z <= 4e-170:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	elif z <= 3.3e+16:
		tmp = t * ((c * j) - (x * a))
	elif z <= 3.8e+147:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * i) * (t_1 / i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * y) - Float64(b * c))
	tmp = 0.0
	if (z <= -1.05e+101)
		tmp = Float64(z * t_1);
	elseif (z <= 4e-170)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	elseif (z <= 3.3e+16)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (z <= 3.8e+147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * i) * Float64(t_1 / i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * y) - (b * c);
	tmp = 0.0;
	if (z <= -1.05e+101)
		tmp = z * t_1;
	elseif (z <= 4e-170)
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	elseif (z <= 3.3e+16)
		tmp = t * ((c * j) - (x * a));
	elseif (z <= 3.8e+147)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * i) * (t_1 / i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+101], N[(z * t$95$1), $MachinePrecision], If[LessEqual[z, 4e-170], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+16], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * i), $MachinePrecision] * N[(t$95$1 / i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.05e101

   1. Initial program 59.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 59.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 62.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 62.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 62.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 52.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 47.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 47.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 47.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 50.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 50.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 50.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 50.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 50.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 50.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 50.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 73.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 73.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 73.9%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -1.05e101 < z < 3.99999999999999993e-170

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 66.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 3.99999999999999993e-170 < z < 3.3e16

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 68.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if 3.3e16 < z < 3.7999999999999997e147

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 81.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 81.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 84.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 84.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 84.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 84.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 84.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 71.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 71.1%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 71.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 3.7999999999999997e147 < z

   1. Initial program 40.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 40.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 47.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 47.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 47.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 47.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 47.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - a \cdot b\right)\right)} \]

   7. Simplified 53.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot t - b \cdot z, x \cdot \left(y \cdot z - t \cdot a\right)\right)}{i}\right) - b \cdot a\right) \cdot \left(-i\right)} \]

   8. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right)} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \left(-1 \cdot \frac{b \cdot c}{i} + \frac{x \cdot y}{i}\right) \]

      3. +-commutative 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} + -1 \cdot \frac{b \cdot c}{i}\right)} \]

      4. mul-1-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\frac{x \cdot y}{i} + \color{blue}{\left(-\frac{b \cdot c}{i}\right)}\right) \]

      5. unsub-neg 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \color{blue}{\left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)} \]

      6. associate-/l* 71.1%

         \[\leadsto \left(z \cdot i\right) \cdot \left(\color{blue}{x \cdot \frac{y}{i}} - \frac{b \cdot c}{i}\right) \]

      7. associate-/l* 67.9%

         \[\leadsto \left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - \color{blue}{b \cdot \frac{c}{i}}\right) \]

   10. Simplified 67.9%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \left(x \cdot \frac{y}{i} - b \cdot \frac{c}{i}\right)} \]

   11. Taylor expanded in z around 0 71.0%

       \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(\frac{x \cdot y}{i} - \frac{b \cdot c}{i}\right)\right)} \]
   12. Step-by-step derivation

       1. div-sub 74.3%

          \[\leadsto i \cdot \left(z \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{i}}\right) \]

       2. associate-*r* 74.4%

          \[\leadsto \color{blue}{\left(i \cdot z\right) \cdot \frac{x \cdot y - b \cdot c}{i}} \]

       3. *-commutative 74.4%

          \[\leadsto \color{blue}{\left(z \cdot i\right)} \cdot \frac{x \cdot y - b \cdot c}{i} \]

       4. *-commutative 74.4%

          \[\leadsto \left(z \cdot i\right) \cdot \frac{\color{blue}{y \cdot x} - b \cdot c}{i} \]

   13. Simplified 74.4%

       \[\leadsto \color{blue}{\left(z \cdot i\right) \cdot \frac{y \cdot x - b \cdot c}{i}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-170}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i\right) \cdot \frac{x \cdot y - b \cdot c}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+235}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.25e+46)
   (* t (* c j))
   (if (<= j -1.85e-196)
     (* a (* b i))
     (if (<= j -8.5e-267)
       (* x (* y z))
       (if (<= j 3.6e-26)
         (* y (* x z))
         (if (<= j 2.3e+235) (* j (* y (- i))) (* j (* t c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.25e+46) {
		tmp = t * (c * j);
	} else if (j <= -1.85e-196) {
		tmp = a * (b * i);
	} else if (j <= -8.5e-267) {
		tmp = x * (y * z);
	} else if (j <= 3.6e-26) {
		tmp = y * (x * z);
	} else if (j <= 2.3e+235) {
		tmp = j * (y * -i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.25d+46)) then
        tmp = t * (c * j)
    else if (j <= (-1.85d-196)) then
        tmp = a * (b * i)
    else if (j <= (-8.5d-267)) then
        tmp = x * (y * z)
    else if (j <= 3.6d-26) then
        tmp = y * (x * z)
    else if (j <= 2.3d+235) then
        tmp = j * (y * -i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.25e+46) {
		tmp = t * (c * j);
	} else if (j <= -1.85e-196) {
		tmp = a * (b * i);
	} else if (j <= -8.5e-267) {
		tmp = x * (y * z);
	} else if (j <= 3.6e-26) {
		tmp = y * (x * z);
	} else if (j <= 2.3e+235) {
		tmp = j * (y * -i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.25e+46:
		tmp = t * (c * j)
	elif j <= -1.85e-196:
		tmp = a * (b * i)
	elif j <= -8.5e-267:
		tmp = x * (y * z)
	elif j <= 3.6e-26:
		tmp = y * (x * z)
	elif j <= 2.3e+235:
		tmp = j * (y * -i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.25e+46)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= -1.85e-196)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= -8.5e-267)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 3.6e-26)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 2.3e+235)
		tmp = Float64(j * Float64(y * Float64(-i)));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.25e+46)
		tmp = t * (c * j);
	elseif (j <= -1.85e-196)
		tmp = a * (b * i);
	elseif (j <= -8.5e-267)
		tmp = x * (y * z);
	elseif (j <= 3.6e-26)
		tmp = y * (x * z);
	elseif (j <= 2.3e+235)
		tmp = j * (y * -i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.25e+46], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.85e-196], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-267], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e-26], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+235], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.2500000000000001e46

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 68.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 49.0%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 49.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if -1.2500000000000001e46 < j < -1.85000000000000005e-196

   1. Initial program 57.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 47.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 36.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 36.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.85000000000000005e-196 < j < -8.49999999999999987e-267

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 68.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 68.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 68.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 68.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 68.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 68.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 68.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 68.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 68.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 68.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 68.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 68.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around 0 38.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -8.49999999999999987e-267 < j < 3.6000000000000001e-26

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 69.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 69.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 69.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 69.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 69.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 69.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 69.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 61.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 61.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 61.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 61.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 61.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 61.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 61.5%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 61.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 56.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 56.2%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 37.5%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 37.5%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 37.5%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

       3. associate-*r* 40.3%

          \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   13. Simplified 40.3%

       \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 3.6000000000000001e-26 < j < 2.3e235

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 56.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around 0 47.2%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. distribute-lft-neg-out 47.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-i\right) \cdot y\right)} \]

      3. *-commutative 47.2%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   7. Simplified 47.2%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 2.3e235 < j

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 48.5%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 48.5%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.85 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+235}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+234}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1e+49)
   (* t (* c j))
   (if (<= j -1.15e-173)
     (* a (* b i))
     (if (<= j -1.22e-275)
       (* x (* t (- a)))
       (if (<= j 3.6e-26)
         (* y (* x z))
         (if (<= j 6.5e+234) (* j (* y (- i))) (* j (* t c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1e+49) {
		tmp = t * (c * j);
	} else if (j <= -1.15e-173) {
		tmp = a * (b * i);
	} else if (j <= -1.22e-275) {
		tmp = x * (t * -a);
	} else if (j <= 3.6e-26) {
		tmp = y * (x * z);
	} else if (j <= 6.5e+234) {
		tmp = j * (y * -i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1d+49)) then
        tmp = t * (c * j)
    else if (j <= (-1.15d-173)) then
        tmp = a * (b * i)
    else if (j <= (-1.22d-275)) then
        tmp = x * (t * -a)
    else if (j <= 3.6d-26) then
        tmp = y * (x * z)
    else if (j <= 6.5d+234) then
        tmp = j * (y * -i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1e+49) {
		tmp = t * (c * j);
	} else if (j <= -1.15e-173) {
		tmp = a * (b * i);
	} else if (j <= -1.22e-275) {
		tmp = x * (t * -a);
	} else if (j <= 3.6e-26) {
		tmp = y * (x * z);
	} else if (j <= 6.5e+234) {
		tmp = j * (y * -i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1e+49:
		tmp = t * (c * j)
	elif j <= -1.15e-173:
		tmp = a * (b * i)
	elif j <= -1.22e-275:
		tmp = x * (t * -a)
	elif j <= 3.6e-26:
		tmp = y * (x * z)
	elif j <= 6.5e+234:
		tmp = j * (y * -i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1e+49)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= -1.15e-173)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= -1.22e-275)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 3.6e-26)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 6.5e+234)
		tmp = Float64(j * Float64(y * Float64(-i)));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1e+49)
		tmp = t * (c * j);
	elseif (j <= -1.15e-173)
		tmp = a * (b * i);
	elseif (j <= -1.22e-275)
		tmp = x * (t * -a);
	elseif (j <= 3.6e-26)
		tmp = y * (x * z);
	elseif (j <= 6.5e+234)
		tmp = j * (y * -i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1e+49], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.15e-173], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.22e-275], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e-26], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e+234], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -9.99999999999999946e48

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 68.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 49.0%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 49.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if -9.99999999999999946e48 < j < -1.14999999999999994e-173

   1. Initial program 56.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 45.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 36.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.14999999999999994e-173 < j < -1.21999999999999995e-275

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 48.7%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around inf 33.5%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 33.5%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. distribute-rgt-neg-in 33.5%

         \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]

   8. Simplified 33.5%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]

   if -1.21999999999999995e-275 < j < 3.6000000000000001e-26

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 61.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 61.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 61.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 61.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 61.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 61.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 61.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 61.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 55.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 55.7%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 39.2%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 39.1%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 39.1%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

       3. associate-*r* 42.1%

          \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   13. Simplified 42.1%

       \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 3.6000000000000001e-26 < j < 6.4999999999999995e234

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 56.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around 0 47.2%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. distribute-lft-neg-out 47.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-i\right) \cdot y\right)} \]

      3. *-commutative 47.2%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   7. Simplified 47.2%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 6.4999999999999995e234 < j

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 48.5%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 48.5%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -1.22 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+234}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+238}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.4e+45)
   (* t (* c j))
   (if (<= j -8.5e-193)
     (* a (* b i))
     (if (<= j -6.2e-279)
       (* b (* z (- c)))
       (if (<= j 3.5e-26)
         (* y (* x z))
         (if (<= j 2e+238) (* j (* y (- i))) (* j (* t c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.4e+45) {
		tmp = t * (c * j);
	} else if (j <= -8.5e-193) {
		tmp = a * (b * i);
	} else if (j <= -6.2e-279) {
		tmp = b * (z * -c);
	} else if (j <= 3.5e-26) {
		tmp = y * (x * z);
	} else if (j <= 2e+238) {
		tmp = j * (y * -i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.4d+45)) then
        tmp = t * (c * j)
    else if (j <= (-8.5d-193)) then
        tmp = a * (b * i)
    else if (j <= (-6.2d-279)) then
        tmp = b * (z * -c)
    else if (j <= 3.5d-26) then
        tmp = y * (x * z)
    else if (j <= 2d+238) then
        tmp = j * (y * -i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.4e+45) {
		tmp = t * (c * j);
	} else if (j <= -8.5e-193) {
		tmp = a * (b * i);
	} else if (j <= -6.2e-279) {
		tmp = b * (z * -c);
	} else if (j <= 3.5e-26) {
		tmp = y * (x * z);
	} else if (j <= 2e+238) {
		tmp = j * (y * -i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.4e+45:
		tmp = t * (c * j)
	elif j <= -8.5e-193:
		tmp = a * (b * i)
	elif j <= -6.2e-279:
		tmp = b * (z * -c)
	elif j <= 3.5e-26:
		tmp = y * (x * z)
	elif j <= 2e+238:
		tmp = j * (y * -i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.4e+45)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= -8.5e-193)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= -6.2e-279)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (j <= 3.5e-26)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 2e+238)
		tmp = Float64(j * Float64(y * Float64(-i)));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.4e+45)
		tmp = t * (c * j);
	elseif (j <= -8.5e-193)
		tmp = a * (b * i);
	elseif (j <= -6.2e-279)
		tmp = b * (z * -c);
	elseif (j <= 3.5e-26)
		tmp = y * (x * z);
	elseif (j <= 2e+238)
		tmp = j * (y * -i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.4e+45], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-193], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.2e-279], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-26], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e+238], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.39999999999999989e45

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 68.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 46.8%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 49.0%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 49.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if -2.39999999999999989e45 < j < -8.50000000000000004e-193

   1. Initial program 57.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 47.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 36.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 36.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -8.50000000000000004e-193 < j < -6.1999999999999998e-279

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 73.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 73.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 73.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 73.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 73.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 73.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 73.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 73.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 73.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 73.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 73.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 73.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 73.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 73.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 73.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 73.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 73.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 73.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 73.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 73.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 73.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 33.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 33.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 33.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 33.9%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   10. Simplified 33.9%

       \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]

   if -6.1999999999999998e-279 < j < 3.49999999999999985e-26

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 67.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 61.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 61.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 61.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 61.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 61.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 61.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 61.2%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 61.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 55.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 55.7%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 39.2%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 39.1%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 39.1%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

       3. associate-*r* 42.1%

          \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   13. Simplified 42.1%

       \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 3.49999999999999985e-26 < j < 2.0000000000000001e238

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 56.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around 0 47.2%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. distribute-lft-neg-out 47.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-i\right) \cdot y\right)} \]

      3. *-commutative 47.2%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   7. Simplified 47.2%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 2.0000000000000001e238 < j

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 48.5%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 48.5%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+238}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 42.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -5.1e-99)
     t_1
     (if (<= b -5.1e-241)
       (* t (* c j))
       (if (<= b 1.02e-297)
         (* x (* y z))
         (if (<= b 9e-144) (* x (* t (- a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.1e-99) {
		tmp = t_1;
	} else if (b <= -5.1e-241) {
		tmp = t * (c * j);
	} else if (b <= 1.02e-297) {
		tmp = x * (y * z);
	} else if (b <= 9e-144) {
		tmp = x * (t * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-5.1d-99)) then
        tmp = t_1
    else if (b <= (-5.1d-241)) then
        tmp = t * (c * j)
    else if (b <= 1.02d-297) then
        tmp = x * (y * z)
    else if (b <= 9d-144) then
        tmp = x * (t * -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.1e-99) {
		tmp = t_1;
	} else if (b <= -5.1e-241) {
		tmp = t * (c * j);
	} else if (b <= 1.02e-297) {
		tmp = x * (y * z);
	} else if (b <= 9e-144) {
		tmp = x * (t * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.1e-99:
		tmp = t_1
	elif b <= -5.1e-241:
		tmp = t * (c * j)
	elif b <= 1.02e-297:
		tmp = x * (y * z)
	elif b <= 9e-144:
		tmp = x * (t * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.1e-99)
		tmp = t_1;
	elseif (b <= -5.1e-241)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 1.02e-297)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 9e-144)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.1e-99)
		tmp = t_1;
	elseif (b <= -5.1e-241)
		tmp = t * (c * j);
	elseif (b <= 1.02e-297)
		tmp = x * (y * z);
	elseif (b <= 9e-144)
		tmp = x * (t * -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.1e-99], t$95$1, If[LessEqual[b, -5.1e-241], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-297], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-144], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.0999999999999999e-99 or 8.9999999999999996e-144 < b

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 73.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 73.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 73.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 73.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 73.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 73.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 73.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 73.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 73.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 73.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 67.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 67.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 67.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 68.9%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 70.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 70.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 70.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 70.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 70.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 70.0%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 70.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 52.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 52.4%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 52.4%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 52.4%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if -5.0999999999999999e-99 < b < -5.0999999999999998e-241

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 59.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 42.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.5%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 42.5%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 45.9%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 45.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if -5.0999999999999998e-241 < b < 1.0200000000000001e-297

   1. Initial program 51.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 51.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 57.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 57.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 57.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 57.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 57.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 57.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 57.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 57.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 57.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 57.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 57.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 57.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 57.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 57.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 69.2%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around 0 63.1%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if 1.0200000000000001e-297 < b < 8.9999999999999996e-144

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 63.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 63.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.6%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around inf 37.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.8%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. distribute-rgt-neg-in 37.8%

         \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]

   8. Simplified 37.8%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 45.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.65e+103)
     t_2
     (if (<= c 1.4e-256)
       t_1
       (if (<= c 7.8e-184) (* z (* x y)) (if (<= c 5.8e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.65e+103) {
		tmp = t_2;
	} else if (c <= 1.4e-256) {
		tmp = t_1;
	} else if (c <= 7.8e-184) {
		tmp = z * (x * y);
	} else if (c <= 5.8e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.65d+103)) then
        tmp = t_2
    else if (c <= 1.4d-256) then
        tmp = t_1
    else if (c <= 7.8d-184) then
        tmp = z * (x * y)
    else if (c <= 5.8d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.65e+103) {
		tmp = t_2;
	} else if (c <= 1.4e-256) {
		tmp = t_1;
	} else if (c <= 7.8e-184) {
		tmp = z * (x * y);
	} else if (c <= 5.8e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.65e+103:
		tmp = t_2
	elif c <= 1.4e-256:
		tmp = t_1
	elif c <= 7.8e-184:
		tmp = z * (x * y)
	elif c <= 5.8e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.65e+103)
		tmp = t_2;
	elseif (c <= 1.4e-256)
		tmp = t_1;
	elseif (c <= 7.8e-184)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 5.8e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.65e+103)
		tmp = t_2;
	elseif (c <= 1.4e-256)
		tmp = t_1;
	elseif (c <= 7.8e-184)
		tmp = z * (x * y);
	elseif (c <= 5.8e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+103], t$95$2, If[LessEqual[c, 1.4e-256], t$95$1, If[LessEqual[c, 7.8e-184], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.65000000000000004e103 or 5.7999999999999994e45 < c

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 60.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 60.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 60.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 60.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 60.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 60.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 60.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 67.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -1.65000000000000004e103 < c < 1.40000000000000012e-256 or 7.79999999999999988e-184 < c < 5.7999999999999994e45

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 67.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 67.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 67.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 67.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 69.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 69.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 69.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 69.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 69.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 69.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 69.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

      2. *-commutative 43.8%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{z \cdot c}\right) \]

   10. Simplified 43.8%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a - z \cdot c\right)} \]

   if 1.40000000000000012e-256 < c < 7.79999999999999988e-184

   1. Initial program 88.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 88.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 88.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 88.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 88.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 88.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 88.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 88.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 88.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 88.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 88.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 88.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 71.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 71.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 71.1%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 71.0%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 71.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 71.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 71.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 71.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 71.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 71.0%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 71.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 54.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 54.2%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 54.1%

       \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2.5e-84)
     t_2
     (if (<= c -7.5e-177)
       t_1
       (if (<= c -2.6e-212) (* y (* x z)) (if (<= c 9.5e-6) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.5e-84) {
		tmp = t_2;
	} else if (c <= -7.5e-177) {
		tmp = t_1;
	} else if (c <= -2.6e-212) {
		tmp = y * (x * z);
	} else if (c <= 9.5e-6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2.5d-84)) then
        tmp = t_2
    else if (c <= (-7.5d-177)) then
        tmp = t_1
    else if (c <= (-2.6d-212)) then
        tmp = y * (x * z)
    else if (c <= 9.5d-6) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.5e-84) {
		tmp = t_2;
	} else if (c <= -7.5e-177) {
		tmp = t_1;
	} else if (c <= -2.6e-212) {
		tmp = y * (x * z);
	} else if (c <= 9.5e-6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.5e-84:
		tmp = t_2
	elif c <= -7.5e-177:
		tmp = t_1
	elif c <= -2.6e-212:
		tmp = y * (x * z)
	elif c <= 9.5e-6:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.5e-84)
		tmp = t_2;
	elseif (c <= -7.5e-177)
		tmp = t_1;
	elseif (c <= -2.6e-212)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 9.5e-6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.5e-84)
		tmp = t_2;
	elseif (c <= -7.5e-177)
		tmp = t_1;
	elseif (c <= -2.6e-212)
		tmp = y * (x * z);
	elseif (c <= 9.5e-6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e-84], t$95$2, If[LessEqual[c, -7.5e-177], t$95$1, If[LessEqual[c, -2.6e-212], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-6], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.5000000000000001e-84 or 9.5000000000000005e-6 < c

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 66.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 66.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 66.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 66.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 66.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 66.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 62.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -2.5000000000000001e-84 < c < -7.5e-177 or -2.6e-212 < c < 9.5000000000000005e-6

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 65.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around 0 48.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.3%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. *-commutative 48.3%

         \[\leadsto \left(-\color{blue}{\left(j \cdot y\right) \cdot i}\right) + a \cdot \left(b \cdot i\right) \]

      3. distribute-lft-neg-in 48.3%

         \[\leadsto \color{blue}{\left(-j \cdot y\right) \cdot i} + a \cdot \left(b \cdot i\right) \]

      4. mul-1-neg 48.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \cdot i + a \cdot \left(b \cdot i\right) \]

      5. associate-*r* 51.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      6. distribute-rgt-in 52.7%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 52.7%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 52.7%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 52.7%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      10. *-commutative 52.7%

          \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   6. Simplified 52.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if -7.5e-177 < c < -2.6e-212

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 69.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 69.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 69.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 69.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 69.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 69.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 69.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 69.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 69.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 69.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 40.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 40.4%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 47.2%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 40.1%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 40.1%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

       3. associate-*r* 54.5%

          \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   13. Simplified 54.5%

       \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.95e+30)
   (* x (* y z))
   (if (<= y 9.2e-178)
     (* i (* a b))
     (if (<= y 4.8e-66) (* (* x t) (- a)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.95e+30) {
		tmp = x * (y * z);
	} else if (y <= 9.2e-178) {
		tmp = i * (a * b);
	} else if (y <= 4.8e-66) {
		tmp = (x * t) * -a;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.95d+30)) then
        tmp = x * (y * z)
    else if (y <= 9.2d-178) then
        tmp = i * (a * b)
    else if (y <= 4.8d-66) then
        tmp = (x * t) * -a
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.95e+30) {
		tmp = x * (y * z);
	} else if (y <= 9.2e-178) {
		tmp = i * (a * b);
	} else if (y <= 4.8e-66) {
		tmp = (x * t) * -a;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.95e+30:
		tmp = x * (y * z)
	elif y <= 9.2e-178:
		tmp = i * (a * b)
	elif y <= 4.8e-66:
		tmp = (x * t) * -a
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.95e+30)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 9.2e-178)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 4.8e-66)
		tmp = Float64(Float64(x * t) * Float64(-a));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.95e+30)
		tmp = x * (y * z);
	elseif (y <= 9.2e-178)
		tmp = i * (a * b);
	elseif (y <= 4.8e-66)
		tmp = (x * t) * -a;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.95e+30], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-178], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-66], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.95000000000000005e30

   1. Initial program 53.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 53.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 53.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 53.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 53.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 53.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 53.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 53.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 53.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 53.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 53.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 53.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 53.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 53.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 53.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 53.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.2%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around 0 37.5%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -1.95000000000000005e30 < y < 9.19999999999999978e-178

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 83.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 83.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 83.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 83.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 83.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 83.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 83.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 83.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 61.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 59.4%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 59.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 59.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 59.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 59.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 59.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 59.4%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 59.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in a around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 38.4%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

   10. Simplified 38.4%

       \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]

   if 9.19999999999999978e-178 < y < 4.80000000000000052e-66

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 81.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 81.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 81.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 81.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 81.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 81.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 81.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 81.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 57.5%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + \frac{x \cdot \left(y \cdot z\right)}{a}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 53.0%

         \[\leadsto a \cdot \color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{a} + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.0%

         \[\leadsto a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.0%

         \[\leadsto a \cdot \color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{a} - t \cdot x\right)} \]

      4. associate-/l* 53.0%

         \[\leadsto a \cdot \left(\color{blue}{x \cdot \frac{y \cdot z}{a}} - t \cdot x\right) \]

      5. associate-/l* 48.7%

         \[\leadsto a \cdot \left(x \cdot \color{blue}{\left(y \cdot \frac{z}{a}\right)} - t \cdot x\right) \]

      6. *-commutative 48.7%

         \[\leadsto a \cdot \left(x \cdot \left(y \cdot \frac{z}{a}\right) - \color{blue}{x \cdot t}\right) \]

   8. Simplified 48.7%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot \frac{z}{a}\right) - x \cdot t\right)} \]

   9. Taylor expanded in y around 0 49.0%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 49.0%

          \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

       2. distribute-rgt-neg-in 49.0%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   11. Simplified 49.0%

       \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   if 4.80000000000000052e-66 < y

   1. Initial program 63.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 63.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 66.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 66.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 66.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 58.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 58.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 58.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 63.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 63.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 63.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 63.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 63.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 63.0%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 63.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 59.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 59.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 59.1%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 40.0%

       \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 28.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.5e+131)
   (* j (* t c))
   (if (<= c 1.8e-255)
     (* a (* b i))
     (if (<= c 4.4e-7) (* x (* y z)) (* c (* t j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.5e+131) {
		tmp = j * (t * c);
	} else if (c <= 1.8e-255) {
		tmp = a * (b * i);
	} else if (c <= 4.4e-7) {
		tmp = x * (y * z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-2.5d+131)) then
        tmp = j * (t * c)
    else if (c <= 1.8d-255) then
        tmp = a * (b * i)
    else if (c <= 4.4d-7) then
        tmp = x * (y * z)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.5e+131) {
		tmp = j * (t * c);
	} else if (c <= 1.8e-255) {
		tmp = a * (b * i);
	} else if (c <= 4.4e-7) {
		tmp = x * (y * z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.5e+131:
		tmp = j * (t * c)
	elif c <= 1.8e-255:
		tmp = a * (b * i)
	elif c <= 4.4e-7:
		tmp = x * (y * z)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.5e+131)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= 1.8e-255)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 4.4e-7)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.5e+131)
		tmp = j * (t * c);
	elseif (c <= 1.8e-255)
		tmp = a * (b * i);
	elseif (c <= 4.4e-7)
		tmp = x * (y * z);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.5e+131], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e-255], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.4e-7], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.49999999999999998e131

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 61.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 55.0%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 55.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -2.49999999999999998e131 < c < 1.8000000000000001e-255

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 63.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 35.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 1.8000000000000001e-255 < c < 4.4000000000000002e-7

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.4%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]

   6. Taylor expanded in a around 0 39.0%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if 4.4000000000000002e-7 < c

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 35.5%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.5%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 35.5%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 28.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.8 \cdot 10^{+130}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -8.8e+130)
   (* j (* t c))
   (if (<= c 2.9e-257)
     (* a (* b i))
     (if (<= c 1.15e-7) (* y (* x z)) (* c (* t j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.8e+130) {
		tmp = j * (t * c);
	} else if (c <= 2.9e-257) {
		tmp = a * (b * i);
	} else if (c <= 1.15e-7) {
		tmp = y * (x * z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-8.8d+130)) then
        tmp = j * (t * c)
    else if (c <= 2.9d-257) then
        tmp = a * (b * i)
    else if (c <= 1.15d-7) then
        tmp = y * (x * z)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.8e+130) {
		tmp = j * (t * c);
	} else if (c <= 2.9e-257) {
		tmp = a * (b * i);
	} else if (c <= 1.15e-7) {
		tmp = y * (x * z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -8.8e+130:
		tmp = j * (t * c)
	elif c <= 2.9e-257:
		tmp = a * (b * i)
	elif c <= 1.15e-7:
		tmp = y * (x * z)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -8.8e+130)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= 2.9e-257)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 1.15e-7)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -8.8e+130)
		tmp = j * (t * c);
	elseif (c <= 2.9e-257)
		tmp = a * (b * i);
	elseif (c <= 1.15e-7)
		tmp = y * (x * z);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -8.8e+130], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-257], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-7], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.79999999999999974e130

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 61.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 55.0%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 55.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -8.79999999999999974e130 < c < 2.9000000000000002e-257

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 63.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 35.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 2.9000000000000002e-257 < c < 1.14999999999999997e-7

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 70.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 72.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 72.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 72.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 72.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 72.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 72.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 72.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 72.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 72.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 72.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 54.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 54.4%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 39.0%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 39.8%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 39.8%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

       3. associate-*r* 39.0%

          \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   13. Simplified 39.0%

       \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 1.14999999999999997e-7 < c

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 35.5%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.5%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 35.5%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.8 \cdot 10^{+130}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 28.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.18 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.15e+131)
   (* j (* t c))
   (if (<= c 6.8e-256)
     (* a (* b i))
     (if (<= c 1.18e-8) (* z (* x y)) (* c (* t j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.15e+131) {
		tmp = j * (t * c);
	} else if (c <= 6.8e-256) {
		tmp = a * (b * i);
	} else if (c <= 1.18e-8) {
		tmp = z * (x * y);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.15d+131)) then
        tmp = j * (t * c)
    else if (c <= 6.8d-256) then
        tmp = a * (b * i)
    else if (c <= 1.18d-8) then
        tmp = z * (x * y)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.15e+131) {
		tmp = j * (t * c);
	} else if (c <= 6.8e-256) {
		tmp = a * (b * i);
	} else if (c <= 1.18e-8) {
		tmp = z * (x * y);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.15e+131:
		tmp = j * (t * c)
	elif c <= 6.8e-256:
		tmp = a * (b * i)
	elif c <= 1.18e-8:
		tmp = z * (x * y)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.15e+131)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= 6.8e-256)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 1.18e-8)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.15e+131)
		tmp = j * (t * c);
	elseif (c <= 6.8e-256)
		tmp = a * (b * i);
	elseif (c <= 1.18e-8)
		tmp = z * (x * y);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.15e+131], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-256], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.18e-8], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.14999999999999996e131

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 61.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 55.0%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 55.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -1.14999999999999996e131 < c < 6.8000000000000001e-256

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 63.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 35.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 6.8000000000000001e-256 < c < 1.18e-8

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 70.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 72.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 72.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 72.3%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 72.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 72.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 72.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 72.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 72.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 72.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 72.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 54.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 54.4%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   11. Taylor expanded in y around inf 39.8%

       \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if 1.18e-8 < c

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 62.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 62.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 35.5%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.5%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 35.5%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.18 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+133} \lor \neg \left(c \leq 1.3 \cdot 10^{+97}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.1e+133) (not (<= c 1.3e+97))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.1e+133) || !(c <= 1.3e+97)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.1d+133)) .or. (.not. (c <= 1.3d+97))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.1e+133) || !(c <= 1.3e+97)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.1e+133) or not (c <= 1.3e+97):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.1e+133) || !(c <= 1.3e+97))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.1e+133) || ~((c <= 1.3e+97)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.1e+133], N[Not[LessEqual[c, 1.3e+97]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.1e133 or 1.3e97 < c

   1. Initial program 53.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 54.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 54.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 54.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 54.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 54.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 54.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 54.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 54.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 54.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 54.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 54.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 54.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 54.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 54.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 54.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 70.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 46.2%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 46.2%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   if -3.1e133 < c < 1.3e97

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 61.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+133} \lor \neg \left(c \leq 1.3 \cdot 10^{+97}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.75 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.75e+136)
   (* j (* t c))
   (if (<= c 1.6e+90) (* a (* b i)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.75e+136) {
		tmp = j * (t * c);
	} else if (c <= 1.6e+90) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.75d+136)) then
        tmp = j * (t * c)
    else if (c <= 1.6d+90) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.75e+136) {
		tmp = j * (t * c);
	} else if (c <= 1.6e+90) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.75e+136:
		tmp = j * (t * c)
	elif c <= 1.6e+90:
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.75e+136)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= 1.6e+90)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.75e+136)
		tmp = j * (t * c);
	elseif (c <= 1.6e+90)
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.75e+136], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e+90], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.75000000000000001e136

   1. Initial program 57.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around 0 61.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   5. Taylor expanded in c around inf 55.0%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   7. Simplified 55.0%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if -1.75000000000000001e136 < c < 1.59999999999999999e90

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 61.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. *-commutative 31.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   6. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 1.59999999999999999e90 < c

   1. Initial program 50.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 52.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 52.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 52.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 52.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 52.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 52.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 52.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 52.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 52.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 52.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 52.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 52.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 52.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 52.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 69.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 45.1%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 45.1%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.75 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in a around -inf 59.8%

   \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

4. Taylor expanded in b around inf 25.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
5. Step-by-step derivation

   1. *-commutative 25.7%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

6. Simplified 25.7%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

7. Final simplification 25.7%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))