Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 81.5%

Time: 26.1s

Alternatives: 29

Speedup: 0.5×

• 58.3% 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: 81.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (- (* t c) (* y i))))
   (if (<= (+ (+ (* x (- (* y z) (* t a))) t_1) (* j t_2)) INFINITY)
     (fma j t_2 (+ (* x (fma y z (* t (- a)))) t_1))
     (* y (- (* x z) (* i 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 = b * ((a * i) - (z * c));
	double t_2 = (t * c) - (y * i);
	double tmp;
	if ((((x * ((y * z) - (t * a))) + t_1) + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, ((x * fma(y, z, (t * -a))) + t_1));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	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(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(j * t_2)) <= Inf)
		tmp = fma(j, t_2, Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_1));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return 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[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 90.3%

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

      1. +-commutative 90.3%

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

      2. fma-define 90.3%

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

      3. *-commutative 90.3%

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

      4. *-commutative 90.3%

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

      5. cancel-sign-sub-inv 90.3%

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

      6. cancel-sign-sub 90.3%

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

      7. sub-neg 90.3%

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

      8. sub-neg 90.3%

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

      9. *-commutative 90.3%

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

      10. fma-neg 90.3%

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

      11. *-commutative 90.3%

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

      12. distribute-rgt-neg-out 90.3%

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

      13. remove-double-neg 90.3%

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

      14. *-commutative 90.3%

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

      15. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   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 4.3%

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

      3. *-commutative 4.3%

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

      4. *-commutative 4.3%

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

      5. cancel-sign-sub-inv 4.3%

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

      6. cancel-sign-sub 4.3%

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

      7. sub-neg 4.3%

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

      8. sub-neg 4.3%

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

      9. *-commutative 4.3%

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

      10. fma-neg 6.5%

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

      11. *-commutative 6.5%

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

      12. distribute-rgt-neg-out 6.5%

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

      13. remove-double-neg 6.5%

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

      14. *-commutative 6.5%

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

      15. *-commutative 6.5%

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

   3. Simplified 6.5%

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

   5. Taylor expanded in y around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   7. Simplified 53.6%

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

4. Final simplification 83.7%

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

Alternative 2: 81.5% accurate, 0.5× speedup

Math

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

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 (* y (- (* x z) (* i 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))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	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 = y * ((x * z) - (i * j));
	}
	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 = y * ((x * z) - (i * j))
	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(y * Float64(Float64(x * z) - Float64(i * j)));
	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 = y * ((x * z) - (i * j));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 90.3%

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

   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 4.3%

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

      3. *-commutative 4.3%

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

      4. *-commutative 4.3%

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

      5. cancel-sign-sub-inv 4.3%

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

      6. cancel-sign-sub 4.3%

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

      7. sub-neg 4.3%

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

      8. sub-neg 4.3%

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

      9. *-commutative 4.3%

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

      10. fma-neg 6.5%

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

      11. *-commutative 6.5%

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

      12. distribute-rgt-neg-out 6.5%

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

      13. remove-double-neg 6.5%

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

      14. *-commutative 6.5%

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

      15. *-commutative 6.5%

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

   3. Simplified 6.5%

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

   5. Taylor expanded in y around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   7. Simplified 53.6%

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

4. Final simplification 83.7%

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

Alternative 3: 58.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+54}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-137}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - b \cdot \frac{c}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* c (* z b))))
        (t_2 (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y))))))
   (if (<= z -6e+140)
     (* z (- (* x y) (* b c)))
     (if (<= z -4.1e+54)
       (* (* x y) (- z (* a (/ t y))))
       (if (<= z -1.35e-83)
         t_1
         (if (<= z -2.8e-109)
           (+ (* b (* a i)) (* t (* c j)))
           (if (<= z -3.5e-184)
             t_2
             (if (<= z 2.5e-137)
               (+ (* j (- (* t c) (* y i))) (* a (* b i)))
               (if (<= z 1.02e-15)
                 t_2
                 (if (<= z 4.6e+167)
                   t_1
                   (* (* y z) (- x (* b (/ c y))))))))))))))

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))) - (c * (z * b));
	double t_2 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	double tmp;
	if (z <= -6e+140) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -4.1e+54) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (z <= -1.35e-83) {
		tmp = t_1;
	} else if (z <= -2.8e-109) {
		tmp = (b * (a * i)) + (t * (c * j));
	} else if (z <= -3.5e-184) {
		tmp = t_2;
	} else if (z <= 2.5e-137) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (z <= 1.02e-15) {
		tmp = t_2;
	} else if (z <= 4.6e+167) {
		tmp = t_1;
	} else {
		tmp = (y * z) * (x - (b * (c / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (c * (z * b))
    t_2 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
    if (z <= (-6d+140)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-4.1d+54)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (z <= (-1.35d-83)) then
        tmp = t_1
    else if (z <= (-2.8d-109)) then
        tmp = (b * (a * i)) + (t * (c * j))
    else if (z <= (-3.5d-184)) then
        tmp = t_2
    else if (z <= 2.5d-137) then
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    else if (z <= 1.02d-15) then
        tmp = t_2
    else if (z <= 4.6d+167) then
        tmp = t_1
    else
        tmp = (y * z) * (x - (b * (c / 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 t_1 = (y * ((x * z) - (i * j))) - (c * (z * b));
	double t_2 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	double tmp;
	if (z <= -6e+140) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -4.1e+54) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (z <= -1.35e-83) {
		tmp = t_1;
	} else if (z <= -2.8e-109) {
		tmp = (b * (a * i)) + (t * (c * j));
	} else if (z <= -3.5e-184) {
		tmp = t_2;
	} else if (z <= 2.5e-137) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if (z <= 1.02e-15) {
		tmp = t_2;
	} else if (z <= 4.6e+167) {
		tmp = t_1;
	} else {
		tmp = (y * z) * (x - (b * (c / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (c * (z * b))
	t_2 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	tmp = 0
	if z <= -6e+140:
		tmp = z * ((x * y) - (b * c))
	elif z <= -4.1e+54:
		tmp = (x * y) * (z - (a * (t / y)))
	elif z <= -1.35e-83:
		tmp = t_1
	elif z <= -2.8e-109:
		tmp = (b * (a * i)) + (t * (c * j))
	elif z <= -3.5e-184:
		tmp = t_2
	elif z <= 2.5e-137:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	elif z <= 1.02e-15:
		tmp = t_2
	elif z <= 4.6e+167:
		tmp = t_1
	else:
		tmp = (y * z) * (x - (b * (c / y)))
	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(c * Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))))
	tmp = 0.0
	if (z <= -6e+140)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -4.1e+54)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (z <= -1.35e-83)
		tmp = t_1;
	elseif (z <= -2.8e-109)
		tmp = Float64(Float64(b * Float64(a * i)) + Float64(t * Float64(c * j)));
	elseif (z <= -3.5e-184)
		tmp = t_2;
	elseif (z <= 2.5e-137)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	elseif (z <= 1.02e-15)
		tmp = t_2;
	elseif (z <= 4.6e+167)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * z) * Float64(x - Float64(b * Float64(c / y))));
	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))) - (c * (z * b));
	t_2 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	tmp = 0.0;
	if (z <= -6e+140)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -4.1e+54)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (z <= -1.35e-83)
		tmp = t_1;
	elseif (z <= -2.8e-109)
		tmp = (b * (a * i)) + (t * (c * j));
	elseif (z <= -3.5e-184)
		tmp = t_2;
	elseif (z <= 2.5e-137)
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	elseif (z <= 1.02e-15)
		tmp = t_2;
	elseif (z <= 4.6e+167)
		tmp = t_1;
	else
		tmp = (y * z) * (x - (b * (c / y)));
	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[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+140], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e+54], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-83], t$95$1, If[LessEqual[z, -2.8e-109], N[(N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision] + N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-184], t$95$2, If[LessEqual[z, 2.5e-137], 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, 1.02e-15], t$95$2, If[LessEqual[z, 4.6e+167], t$95$1, N[(N[(y * z), $MachinePrecision] * N[(x - N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -5.99999999999999993e140

   1. Initial program 61.3%

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

      1. +-commutative 61.3%

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

      2. fma-define 61.3%

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

      3. *-commutative 61.3%

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

      4. *-commutative 61.3%

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

      5. cancel-sign-sub-inv 61.3%

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

      6. cancel-sign-sub 61.3%

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

      7. sub-neg 61.3%

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

      8. sub-neg 61.3%

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

      9. *-commutative 61.3%

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

      10. fma-neg 64.9%

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

      11. *-commutative 64.9%

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

      12. distribute-rgt-neg-out 64.9%

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

      13. remove-double-neg 64.9%

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

      14. *-commutative 64.9%

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

      15. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in t around 0 65.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   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* 54.6%

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

      5. distribute-rgt-in 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 78.4%

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

      1. *-commutative 78.4%

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

   10. Simplified 78.4%

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

   if -5.99999999999999993e140 < z < -4.09999999999999967e54

   1. Initial program 74.1%

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

      1. +-commutative 74.1%

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

      2. fma-define 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. cancel-sign-sub-inv 74.1%

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

      6. cancel-sign-sub 74.1%

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

      7. sub-neg 74.1%

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

      8. sub-neg 74.1%

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

      9. *-commutative 74.1%

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

      10. fma-neg 74.1%

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

      11. *-commutative 74.1%

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

      12. distribute-rgt-neg-out 74.1%

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

      13. remove-double-neg 74.1%

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

      14. *-commutative 74.1%

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

      15. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in y around -inf 56.6%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in x around inf 74.9%

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

      1. associate-*r* 74.8%

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

      2. *-commutative 74.8%

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

      3. mul-1-neg 74.8%

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

      4. unsub-neg 74.8%

         \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{\left(z - \frac{a \cdot t}{y}\right)} \]

      5. associate-/l* 78.8%

         \[\leadsto \left(y \cdot x\right) \cdot \left(z - \color{blue}{a \cdot \frac{t}{y}}\right) \]

   10. Simplified 78.8%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \left(z - a \cdot \frac{t}{y}\right)} \]

   if -4.09999999999999967e54 < z < -1.34999999999999996e-83 or 1.02e-15 < z < 4.59999999999999976e167

   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. Step-by-step derivation

      1. +-commutative 75.0%

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

      2. fma-define 76.5%

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

      3. *-commutative 76.5%

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

      4. *-commutative 76.5%

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

      5. cancel-sign-sub-inv 76.5%

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

      6. cancel-sign-sub 76.5%

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

      7. sub-neg 76.5%

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

      8. sub-neg 76.5%

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

      9. *-commutative 76.5%

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

      10. fma-neg 76.5%

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

      11. *-commutative 76.5%

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

      12. distribute-rgt-neg-out 76.5%

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

      13. remove-double-neg 76.5%

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

      14. *-commutative 76.5%

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

      15. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in t around 0 63.4%

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

      1. associate-*r* 63.4%

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

      2. associate-*r* 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*r* 63.4%

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

      5. distribute-rgt-in 66.2%

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

      6. +-commutative 66.2%

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

      7. mul-1-neg 66.2%

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

      8. unsub-neg 66.2%

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

      9. *-commutative 66.2%

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

      10. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in c around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. associate-*l* 66.8%

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

      3. *-commutative 66.8%

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

   10. Simplified 66.8%

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

   if -1.34999999999999996e-83 < z < -2.79999999999999979e-109

   1. Initial program 67.9%

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

   3. Taylor expanded in i around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-*r* 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in c around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

      3. associate-*r* 99.7%

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

   8. Simplified 99.7%

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

   if -2.79999999999999979e-109 < z < -3.49999999999999981e-184 or 2.5e-137 < z < 1.02e-15

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. fma-define 73.8%

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

      3. *-commutative 73.8%

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

      4. *-commutative 73.8%

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

      5. cancel-sign-sub-inv 73.8%

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

      6. cancel-sign-sub 73.8%

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

      7. sub-neg 73.8%

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

      8. sub-neg 73.8%

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

      9. *-commutative 73.8%

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

      10. fma-neg 73.8%

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

      11. *-commutative 73.8%

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

      12. distribute-rgt-neg-out 73.8%

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

      13. remove-double-neg 73.8%

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

      14. *-commutative 73.8%

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

      15. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in y around -inf 71.2%

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

   7. Simplified 73.6%

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

   8. Taylor expanded in x around inf 69.5%

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

      1. associate-*r/ 69.5%

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

      2. associate-*r* 69.5%

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

      3. mul-1-neg 69.5%

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

   10. Simplified 69.5%

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

   if -3.49999999999999981e-184 < z < 2.5e-137

   1. Initial program 82.9%

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

   3. Taylor expanded in i around inf 73.9%

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

   if 4.59999999999999976e167 < z

   1. Initial program 66.6%

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

      1. +-commutative 66.6%

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

      2. fma-define 66.6%

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

      3. *-commutative 66.6%

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

      4. *-commutative 66.6%

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

      5. cancel-sign-sub-inv 66.6%

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

      6. cancel-sign-sub 66.6%

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

      7. sub-neg 66.6%

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

      8. sub-neg 66.6%

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

      9. *-commutative 66.6%

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

      10. fma-neg 66.6%

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

      11. *-commutative 66.6%

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

      12. distribute-rgt-neg-out 66.6%

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

      13. remove-double-neg 66.6%

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

      14. *-commutative 66.6%

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

      15. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in y around -inf 63.7%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in z around inf 74.8%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

      3. associate-/l* 85.6%

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

   10. Simplified 85.6%

       \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot \left(x - b \cdot \frac{c}{y}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+54}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) + t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-137}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - b \cdot \frac{c}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* a (* b i))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= z -8e+141)
     t_2
     (if (<= z -1.66e-17)
       (* (* x y) (- z (* a (/ t y))))
       (if (<= z 7.9e-147)
         t_1
         (if (<= z 1.4e-73)
           t_3
           (if (<= z 5.4e-30)
             t_1
             (if (<= z 2.2e+34)
               (* y (- (* x z) (* i j)))
               (if (<= z 4.2e+55) t_3 (if (<= z 4e+93) 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 = (j * ((t * c) - (y * i))) + (a * (b * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (z <= -8e+141) {
		tmp = t_2;
	} else if (z <= -1.66e-17) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (z <= 7.9e-147) {
		tmp = t_1;
	} else if (z <= 1.4e-73) {
		tmp = t_3;
	} else if (z <= 5.4e-30) {
		tmp = t_1;
	} else if (z <= 2.2e+34) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 4.2e+55) {
		tmp = t_3;
	} else if (z <= 4e+93) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (a * (b * i))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((c * j) - (x * a))
    if (z <= (-8d+141)) then
        tmp = t_2
    else if (z <= (-1.66d-17)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (z <= 7.9d-147) then
        tmp = t_1
    else if (z <= 1.4d-73) then
        tmp = t_3
    else if (z <= 5.4d-30) then
        tmp = t_1
    else if (z <= 2.2d+34) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= 4.2d+55) then
        tmp = t_3
    else if (z <= 4d+93) 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 = (j * ((t * c) - (y * i))) + (a * (b * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (z <= -8e+141) {
		tmp = t_2;
	} else if (z <= -1.66e-17) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (z <= 7.9e-147) {
		tmp = t_1;
	} else if (z <= 1.4e-73) {
		tmp = t_3;
	} else if (z <= 5.4e-30) {
		tmp = t_1;
	} else if (z <= 2.2e+34) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 4.2e+55) {
		tmp = t_3;
	} else if (z <= 4e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (a * (b * i))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if z <= -8e+141:
		tmp = t_2
	elif z <= -1.66e-17:
		tmp = (x * y) * (z - (a * (t / y)))
	elif z <= 7.9e-147:
		tmp = t_1
	elif z <= 1.4e-73:
		tmp = t_3
	elif z <= 5.4e-30:
		tmp = t_1
	elif z <= 2.2e+34:
		tmp = y * ((x * z) - (i * j))
	elif z <= 4.2e+55:
		tmp = t_3
	elif z <= 4e+93:
		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(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (z <= -8e+141)
		tmp = t_2;
	elseif (z <= -1.66e-17)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (z <= 7.9e-147)
		tmp = t_1;
	elseif (z <= 1.4e-73)
		tmp = t_3;
	elseif (z <= 5.4e-30)
		tmp = t_1;
	elseif (z <= 2.2e+34)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= 4.2e+55)
		tmp = t_3;
	elseif (z <= 4e+93)
		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 = (j * ((t * c) - (y * i))) + (a * (b * i));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (z <= -8e+141)
		tmp = t_2;
	elseif (z <= -1.66e-17)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (z <= 7.9e-147)
		tmp = t_1;
	elseif (z <= 1.4e-73)
		tmp = t_3;
	elseif (z <= 5.4e-30)
		tmp = t_1;
	elseif (z <= 2.2e+34)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= 4.2e+55)
		tmp = t_3;
	elseif (z <= 4e+93)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+141], t$95$2, If[LessEqual[z, -1.66e-17], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.9e-147], t$95$1, If[LessEqual[z, 1.4e-73], t$95$3, If[LessEqual[z, 5.4e-30], t$95$1, If[LessEqual[z, 2.2e+34], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+55], t$95$3, If[LessEqual[z, 4e+93], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.00000000000000014e141 or 4.00000000000000017e93 < z

   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 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

      5. cancel-sign-sub-inv 60.4%

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

      6. cancel-sign-sub 60.4%

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

      7. sub-neg 60.4%

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

      8. sub-neg 60.4%

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

      9. *-commutative 60.4%

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

      10. fma-neg 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 t around 0 62.0%

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

      1. associate-*r* 59.2%

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

      2. associate-*r* 59.2%

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

      3. *-commutative 59.2%

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

      4. associate-*r* 56.6%

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

      5. distribute-rgt-in 56.6%

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

      6. +-commutative 56.6%

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

      7. mul-1-neg 56.6%

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

      8. unsub-neg 56.6%

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

      9. *-commutative 56.6%

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

      10. *-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in z around inf 78.7%

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

      1. *-commutative 78.7%

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

   10. Simplified 78.7%

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

   if -8.00000000000000014e141 < z < -1.6600000000000001e-17

   1. Initial program 77.4%

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

      1. +-commutative 77.4%

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

      2. fma-define 77.4%

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

      3. *-commutative 77.4%

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

      4. *-commutative 77.4%

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

      5. cancel-sign-sub-inv 77.4%

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

      6. cancel-sign-sub 77.4%

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

      7. sub-neg 77.4%

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

      8. sub-neg 77.4%

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

      9. *-commutative 77.4%

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

      10. fma-neg 77.4%

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

      11. *-commutative 77.4%

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

      12. distribute-rgt-neg-out 77.4%

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

      13. remove-double-neg 77.4%

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

      14. *-commutative 77.4%

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

      15. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around -inf 69.4%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in x around inf 62.6%

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

      1. associate-*r* 62.5%

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

      2. *-commutative 62.5%

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

      3. mul-1-neg 62.5%

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

      4. unsub-neg 62.5%

         \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{\left(z - \frac{a \cdot t}{y}\right)} \]

      5. associate-/l* 67.3%

         \[\leadsto \left(y \cdot x\right) \cdot \left(z - \color{blue}{a \cdot \frac{t}{y}}\right) \]

   10. Simplified 67.3%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \left(z - a \cdot \frac{t}{y}\right)} \]

   if -1.6600000000000001e-17 < z < 7.8999999999999997e-147 or 1.40000000000000006e-73 < z < 5.39999999999999975e-30 or 4.2000000000000001e55 < z < 4.00000000000000017e93

   1. Initial program 79.9%

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

   3. Taylor expanded in i around inf 65.9%

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

   if 7.8999999999999997e-147 < z < 1.40000000000000006e-73 or 2.2000000000000002e34 < z < 4.2000000000000001e55

   1. Initial program 77.8%

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

      1. +-commutative 77.8%

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

      2. fma-define 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

      5. cancel-sign-sub-inv 77.8%

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

      6. cancel-sign-sub 77.8%

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

      7. sub-neg 77.8%

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

      8. sub-neg 77.8%

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

      9. *-commutative 77.8%

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

      10. fma-neg 77.8%

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

      11. *-commutative 77.8%

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

      12. distribute-rgt-neg-out 77.8%

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

      13. remove-double-neg 77.8%

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

      14. *-commutative 77.8%

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

      15. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in t around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 5.39999999999999975e-30 < z < 2.2000000000000002e34

   1. Initial program 79.8%

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

      1. +-commutative 79.8%

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

      2. fma-define 79.8%

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

      3. *-commutative 79.8%

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

      4. *-commutative 79.8%

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

      5. cancel-sign-sub-inv 79.8%

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

      6. cancel-sign-sub 79.8%

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

      7. sub-neg 79.8%

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

      8. sub-neg 79.8%

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

      9. *-commutative 79.8%

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

      10. fma-neg 79.8%

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

      11. *-commutative 79.8%

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

      12. distribute-rgt-neg-out 79.8%

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

      13. remove-double-neg 79.8%

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

      14. *-commutative 79.8%

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

      15. *-commutative 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in y around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   7. Simplified 61.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-17}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+109}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -3200:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= t -1.3e+163)
     (* t (- (* c j) (* x a)))
     (if (<= t -1.5e+109)
       (+ t_1 (* a (* b i)))
       (if (<= t -3200.0)
         (- t_1 (* x (* t a)))
         (if (<= t -2e-59)
           t_2
           (if (<= t 2.7e-41)
             (- (* y (- (* x z) (* i j))) (* c (* z b)))
             (if (<= t 4.2e-16)
               t_2
               (if (<= t 3.9e+29)
                 (* z (- (* x y) (* b c)))
                 (- t_1 (* a (* x t))))))))))))

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 = a * ((b * i) - (x * t));
	double tmp;
	if (t <= -1.3e+163) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -1.5e+109) {
		tmp = t_1 + (a * (b * i));
	} else if (t <= -3200.0) {
		tmp = t_1 - (x * (t * a));
	} else if (t <= -2e-59) {
		tmp = t_2;
	} else if (t <= 2.7e-41) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (t <= 4.2e-16) {
		tmp = t_2;
	} else if (t <= 3.9e+29) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1 - (a * (x * t));
	}
	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 = j * ((t * c) - (y * i))
    t_2 = a * ((b * i) - (x * t))
    if (t <= (-1.3d+163)) then
        tmp = t * ((c * j) - (x * a))
    else if (t <= (-1.5d+109)) then
        tmp = t_1 + (a * (b * i))
    else if (t <= (-3200.0d0)) then
        tmp = t_1 - (x * (t * a))
    else if (t <= (-2d-59)) then
        tmp = t_2
    else if (t <= 2.7d-41) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else if (t <= 4.2d-16) then
        tmp = t_2
    else if (t <= 3.9d+29) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1 - (a * (x * t))
    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 = a * ((b * i) - (x * t));
	double tmp;
	if (t <= -1.3e+163) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -1.5e+109) {
		tmp = t_1 + (a * (b * i));
	} else if (t <= -3200.0) {
		tmp = t_1 - (x * (t * a));
	} else if (t <= -2e-59) {
		tmp = t_2;
	} else if (t <= 2.7e-41) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (t <= 4.2e-16) {
		tmp = t_2;
	} else if (t <= 3.9e+29) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1 - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if t <= -1.3e+163:
		tmp = t * ((c * j) - (x * a))
	elif t <= -1.5e+109:
		tmp = t_1 + (a * (b * i))
	elif t <= -3200.0:
		tmp = t_1 - (x * (t * a))
	elif t <= -2e-59:
		tmp = t_2
	elif t <= 2.7e-41:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	elif t <= 4.2e-16:
		tmp = t_2
	elif t <= 3.9e+29:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1 - (a * (x * t))
	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(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (t <= -1.3e+163)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (t <= -1.5e+109)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (t <= -3200.0)
		tmp = Float64(t_1 - Float64(x * Float64(t * a)));
	elseif (t <= -2e-59)
		tmp = t_2;
	elseif (t <= 2.7e-41)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	elseif (t <= 4.2e-16)
		tmp = t_2;
	elseif (t <= 3.9e+29)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	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 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (t <= -1.3e+163)
		tmp = t * ((c * j) - (x * a));
	elseif (t <= -1.5e+109)
		tmp = t_1 + (a * (b * i));
	elseif (t <= -3200.0)
		tmp = t_1 - (x * (t * a));
	elseif (t <= -2e-59)
		tmp = t_2;
	elseif (t <= 2.7e-41)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	elseif (t <= 4.2e-16)
		tmp = t_2;
	elseif (t <= 3.9e+29)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1 - (a * (x * t));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+163], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e+109], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3200.0], N[(t$95$1 - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-59], t$95$2, If[LessEqual[t, 2.7e-41], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-16], t$95$2, If[LessEqual[t, 3.9e+29], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.3000000000000001e163

   1. Initial program 70.3%

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

      1. +-commutative 70.3%

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

      2. fma-define 72.8%

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

      3. *-commutative 72.8%

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

      4. *-commutative 72.8%

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

      5. cancel-sign-sub-inv 72.8%

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

      6. cancel-sign-sub 72.8%

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

      7. sub-neg 72.8%

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

      8. sub-neg 72.8%

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

      9. *-commutative 72.8%

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

      10. fma-neg 75.3%

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

      11. *-commutative 75.3%

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

      12. distribute-rgt-neg-out 75.3%

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

      13. remove-double-neg 75.3%

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

      14. *-commutative 75.3%

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

      15. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around inf 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

      4. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -1.3000000000000001e163 < t < -1.50000000000000008e109

   1. Initial program 66.1%

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

   3. Taylor expanded in i around inf 99.5%

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

   if -1.50000000000000008e109 < t < -3200

   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 b around -inf 69.2%

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

      1. associate-*r* 69.2%

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

      2. neg-mul-1 69.2%

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

      3. distribute-lft-out-- 69.2%

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

      4. associate-/l* 62.6%

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

      5. *-commutative 62.6%

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

      6. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in t around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. associate-*r* 64.3%

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

      3. distribute-lft-neg-in 64.3%

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

      4. *-commutative 64.3%

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

      5. distribute-rgt-neg-in 64.3%

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

   8. Simplified 64.3%

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

   if -3200 < t < -2.0000000000000001e-59 or 2.7e-41 < t < 4.2000000000000002e-16

   1. Initial program 95.9%

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

   3. Taylor expanded in a around -inf 81.1%

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

   4. Taylor expanded in a around inf 70.3%

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

   if -2.0000000000000001e-59 < t < 2.7e-41

   1. Initial program 76.9%

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

      1. +-commutative 76.9%

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

      2. fma-define 77.9%

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

      3. *-commutative 77.9%

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

      4. *-commutative 77.9%

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

      5. cancel-sign-sub-inv 77.9%

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

      6. cancel-sign-sub 77.9%

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

      7. sub-neg 77.9%

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

      8. sub-neg 77.9%

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

      9. *-commutative 77.9%

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

      10. fma-neg 77.9%

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

      11. *-commutative 77.9%

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

      12. distribute-rgt-neg-out 77.9%

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

      13. remove-double-neg 77.9%

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

      14. *-commutative 77.9%

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

      15. *-commutative 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in t around 0 74.7%

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

      1. associate-*r* 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* 72.7%

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

      5. distribute-rgt-in 73.7%

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

      6. +-commutative 73.7%

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

      7. mul-1-neg 73.7%

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

      8. unsub-neg 73.7%

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

      9. *-commutative 73.7%

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

      10. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in c around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-*l* 72.0%

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

      3. *-commutative 72.0%

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

   10. Simplified 72.0%

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

   if 4.2000000000000002e-16 < t < 3.89999999999999968e29

   1. Initial program 70.0%

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

      1. +-commutative 70.0%

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

      2. fma-define 70.0%

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

      3. *-commutative 70.0%

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

      4. *-commutative 70.0%

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

      5. cancel-sign-sub-inv 70.0%

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

      6. cancel-sign-sub 70.0%

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

      7. sub-neg 70.0%

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

      8. sub-neg 70.0%

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

      9. *-commutative 70.0%

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

      10. fma-neg 70.0%

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

      11. *-commutative 70.0%

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

      12. distribute-rgt-neg-out 70.0%

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

      13. remove-double-neg 70.0%

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

      14. *-commutative 70.0%

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

      15. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in t around 0 60.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   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* 60.6%

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

      5. distribute-rgt-in 60.6%

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

      6. +-commutative 60.6%

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

      7. mul-1-neg 60.6%

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

      8. unsub-neg 60.6%

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

      9. *-commutative 60.6%

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

      10. *-commutative 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in z around inf 71.1%

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

      1. *-commutative 71.1%

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

   10. Simplified 71.1%

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

   if 3.89999999999999968e29 < t

   1. Initial program 65.8%

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

   3. Taylor expanded in a around -inf 66.5%

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

   4. Taylor expanded in b around 0 61.3%

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

      1. +-commutative 61.3%

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

      2. *-commutative 61.3%

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

      3. *-commutative 61.3%

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

      4. mul-1-neg 61.3%

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

      5. unsub-neg 61.3%

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

      6. *-commutative 61.3%

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

   6. Simplified 61.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+109}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -3200:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(b \cdot \left(\frac{t \cdot j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2.25e+32)
     t_2
     (if (<= y -4.1e-249)
       t_1
       (if (<= y 7.6e-277)
         (* c (- (* t j) (* z b)))
         (if (<= y 1.45e-245)
           t_1
           (if (<= y 2.6e-167)
             (* b (* c (- (* t (/ j b)) z)))
             (if (<= y 2.05e-128)
               (* a (- (* b i) (* x t)))
               (if (<= y 5.6e-27)
                 (* c (* b (- (/ (* t j) b) z)))
                 (if (<= y 5.5e+64) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.25e+32) {
		tmp = t_2;
	} else if (y <= -4.1e-249) {
		tmp = t_1;
	} else if (y <= 7.6e-277) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 1.45e-245) {
		tmp = t_1;
	} else if (y <= 2.6e-167) {
		tmp = b * (c * ((t * (j / b)) - z));
	} else if (y <= 2.05e-128) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 5.6e-27) {
		tmp = c * (b * (((t * j) / b) - z));
	} else if (y <= 5.5e+64) {
		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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2.25d+32)) then
        tmp = t_2
    else if (y <= (-4.1d-249)) then
        tmp = t_1
    else if (y <= 7.6d-277) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 1.45d-245) then
        tmp = t_1
    else if (y <= 2.6d-167) then
        tmp = b * (c * ((t * (j / b)) - z))
    else if (y <= 2.05d-128) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 5.6d-27) then
        tmp = c * (b * (((t * j) / b) - z))
    else if (y <= 5.5d+64) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.25e+32) {
		tmp = t_2;
	} else if (y <= -4.1e-249) {
		tmp = t_1;
	} else if (y <= 7.6e-277) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 1.45e-245) {
		tmp = t_1;
	} else if (y <= 2.6e-167) {
		tmp = b * (c * ((t * (j / b)) - z));
	} else if (y <= 2.05e-128) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 5.6e-27) {
		tmp = c * (b * (((t * j) / b) - z));
	} else if (y <= 5.5e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.25e+32:
		tmp = t_2
	elif y <= -4.1e-249:
		tmp = t_1
	elif y <= 7.6e-277:
		tmp = c * ((t * j) - (z * b))
	elif y <= 1.45e-245:
		tmp = t_1
	elif y <= 2.6e-167:
		tmp = b * (c * ((t * (j / b)) - z))
	elif y <= 2.05e-128:
		tmp = a * ((b * i) - (x * t))
	elif y <= 5.6e-27:
		tmp = c * (b * (((t * j) / b) - z))
	elif y <= 5.5e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.25e+32)
		tmp = t_2;
	elseif (y <= -4.1e-249)
		tmp = t_1;
	elseif (y <= 7.6e-277)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 1.45e-245)
		tmp = t_1;
	elseif (y <= 2.6e-167)
		tmp = Float64(b * Float64(c * Float64(Float64(t * Float64(j / b)) - z)));
	elseif (y <= 2.05e-128)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 5.6e-27)
		tmp = Float64(c * Float64(b * Float64(Float64(Float64(t * j) / b) - z)));
	elseif (y <= 5.5e+64)
		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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.25e+32)
		tmp = t_2;
	elseif (y <= -4.1e-249)
		tmp = t_1;
	elseif (y <= 7.6e-277)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 1.45e-245)
		tmp = t_1;
	elseif (y <= 2.6e-167)
		tmp = b * (c * ((t * (j / b)) - z));
	elseif (y <= 2.05e-128)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 5.6e-27)
		tmp = c * (b * (((t * j) / b) - z));
	elseif (y <= 5.5e+64)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+32], t$95$2, If[LessEqual[y, -4.1e-249], t$95$1, If[LessEqual[y, 7.6e-277], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-245], t$95$1, If[LessEqual[y, 2.6e-167], N[(b * N[(c * N[(N[(t * N[(j / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-128], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-27], N[(c * N[(b * N[(N[(N[(t * j), $MachinePrecision] / b), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+64], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.2500000000000002e32 or 5.4999999999999996e64 < y

   1. Initial program 60.2%

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

      1. +-commutative 60.2%

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

      2. fma-define 61.1%

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

      3. *-commutative 61.1%

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

      4. *-commutative 61.1%

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

      5. cancel-sign-sub-inv 61.1%

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

      6. cancel-sign-sub 61.1%

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

      7. sub-neg 61.1%

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

      8. sub-neg 61.1%

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

      9. *-commutative 61.1%

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

      10. fma-neg 62.0%

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

      11. *-commutative 62.0%

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

      12. distribute-rgt-neg-out 62.0%

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

      13. remove-double-neg 62.0%

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

      14. *-commutative 62.0%

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

      15. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   if -2.2500000000000002e32 < y < -4.10000000000000004e-249 or 7.59999999999999972e-277 < y < 1.45e-245 or 5.5999999999999999e-27 < y < 5.4999999999999996e64

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. fma-define 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 inf 63.9%

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

      1. +-commutative 63.9%

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

      2. mul-1-neg 63.9%

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

      3. unsub-neg 63.9%

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

      4. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   if -4.10000000000000004e-249 < y < 7.59999999999999972e-277

   1. Initial program 75.4%

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

      1. +-commutative 75.4%

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

      2. fma-define 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

      5. cancel-sign-sub-inv 75.4%

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

      6. cancel-sign-sub 75.4%

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

      7. sub-neg 75.4%

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

      8. sub-neg 75.4%

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

      9. *-commutative 75.4%

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

      10. fma-neg 75.4%

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

      11. *-commutative 75.4%

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

      12. distribute-rgt-neg-out 75.4%

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

      13. remove-double-neg 75.4%

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

      14. *-commutative 75.4%

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

      15. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in c around inf 59.3%

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

   if 1.45e-245 < y < 2.5999999999999999e-167

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. fma-define 97.7%

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

      3. *-commutative 97.7%

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

      4. *-commutative 97.7%

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

      5. cancel-sign-sub-inv 97.7%

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

      6. cancel-sign-sub 97.7%

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

      7. sub-neg 97.7%

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

      8. sub-neg 97.7%

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

      9. *-commutative 97.7%

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

      10. fma-neg 97.7%

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

      11. *-commutative 97.7%

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

      12. distribute-rgt-neg-out 97.7%

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

      13. remove-double-neg 97.7%

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

      14. *-commutative 97.7%

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

      15. *-commutative 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in c around inf 64.0%

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

   6. Taylor expanded in b around inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. +-commutative 75.9%

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

      3. unsub-neg 75.9%

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

      4. associate-/l* 75.9%

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

      5. associate-/l* 76.0%

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

      6. *-commutative 76.0%

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

   8. Simplified 76.0%

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

   9. Taylor expanded in c around 0 75.9%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{j \cdot t}{b} - z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 75.9%

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

       2. associate-/l* 75.9%

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

   11. Simplified 75.9%

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

   if 2.5999999999999999e-167 < y < 2.05e-128

   1. Initial program 91.9%

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

   3. Taylor expanded in a around -inf 91.4%

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

   4. Taylor expanded in a around inf 60.0%

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

   if 2.05e-128 < y < 5.5999999999999999e-27

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. fma-define 79.3%

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

      3. *-commutative 79.3%

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

      4. *-commutative 79.3%

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

      5. cancel-sign-sub-inv 79.3%

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

      6. cancel-sign-sub 79.3%

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

      7. sub-neg 79.3%

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

      8. sub-neg 79.3%

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

      9. *-commutative 79.3%

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

      10. fma-neg 79.3%

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

      11. *-commutative 79.3%

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

      12. distribute-rgt-neg-out 79.3%

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

      13. remove-double-neg 79.3%

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

      14. *-commutative 79.3%

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

      15. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in c around inf 48.7%

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

   6. Taylor expanded in b around inf 48.8%

      \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(\frac{j \cdot t}{b} - z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(b \cdot \left(\frac{t \cdot j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-281}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-155}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-51}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* b (* c (- (* t (/ j b)) z)))))
   (if (<= y -3.3e+32)
     t_2
     (if (<= y -1.25e-248)
       t_1
       (if (<= y 4.8e-281)
         (* c (- (* t j) (* z b)))
         (if (<= y 1.75e-249)
           t_1
           (if (<= y 1.15e-155)
             t_3
             (if (<= y 1.05e-131)
               (* i (- (* a b) (* y j)))
               (if (<= y 1.32e-51) t_3 (if (<= y 1.15e+69) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * (c * ((t * (j / b)) - z));
	double tmp;
	if (y <= -3.3e+32) {
		tmp = t_2;
	} else if (y <= -1.25e-248) {
		tmp = t_1;
	} else if (y <= 4.8e-281) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 1.75e-249) {
		tmp = t_1;
	} else if (y <= 1.15e-155) {
		tmp = t_3;
	} else if (y <= 1.05e-131) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= 1.32e-51) {
		tmp = t_3;
	} else if (y <= 1.15e+69) {
		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) :: t_3
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = b * (c * ((t * (j / b)) - z))
    if (y <= (-3.3d+32)) then
        tmp = t_2
    else if (y <= (-1.25d-248)) then
        tmp = t_1
    else if (y <= 4.8d-281) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 1.75d-249) then
        tmp = t_1
    else if (y <= 1.15d-155) then
        tmp = t_3
    else if (y <= 1.05d-131) then
        tmp = i * ((a * b) - (y * j))
    else if (y <= 1.32d-51) then
        tmp = t_3
    else if (y <= 1.15d+69) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * (c * ((t * (j / b)) - z));
	double tmp;
	if (y <= -3.3e+32) {
		tmp = t_2;
	} else if (y <= -1.25e-248) {
		tmp = t_1;
	} else if (y <= 4.8e-281) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 1.75e-249) {
		tmp = t_1;
	} else if (y <= 1.15e-155) {
		tmp = t_3;
	} else if (y <= 1.05e-131) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= 1.32e-51) {
		tmp = t_3;
	} else if (y <= 1.15e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	t_3 = b * (c * ((t * (j / b)) - z))
	tmp = 0
	if y <= -3.3e+32:
		tmp = t_2
	elif y <= -1.25e-248:
		tmp = t_1
	elif y <= 4.8e-281:
		tmp = c * ((t * j) - (z * b))
	elif y <= 1.75e-249:
		tmp = t_1
	elif y <= 1.15e-155:
		tmp = t_3
	elif y <= 1.05e-131:
		tmp = i * ((a * b) - (y * j))
	elif y <= 1.32e-51:
		tmp = t_3
	elif y <= 1.15e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(b * Float64(c * Float64(Float64(t * Float64(j / b)) - z)))
	tmp = 0.0
	if (y <= -3.3e+32)
		tmp = t_2;
	elseif (y <= -1.25e-248)
		tmp = t_1;
	elseif (y <= 4.8e-281)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 1.75e-249)
		tmp = t_1;
	elseif (y <= 1.15e-155)
		tmp = t_3;
	elseif (y <= 1.05e-131)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (y <= 1.32e-51)
		tmp = t_3;
	elseif (y <= 1.15e+69)
		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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = b * (c * ((t * (j / b)) - z));
	tmp = 0.0;
	if (y <= -3.3e+32)
		tmp = t_2;
	elseif (y <= -1.25e-248)
		tmp = t_1;
	elseif (y <= 4.8e-281)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 1.75e-249)
		tmp = t_1;
	elseif (y <= 1.15e-155)
		tmp = t_3;
	elseif (y <= 1.05e-131)
		tmp = i * ((a * b) - (y * j));
	elseif (y <= 1.32e-51)
		tmp = t_3;
	elseif (y <= 1.15e+69)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(c * N[(N[(t * N[(j / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+32], t$95$2, If[LessEqual[y, -1.25e-248], t$95$1, If[LessEqual[y, 4.8e-281], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-249], t$95$1, If[LessEqual[y, 1.15e-155], t$95$3, If[LessEqual[y, 1.05e-131], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-51], t$95$3, If[LessEqual[y, 1.15e+69], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3000000000000002e32 or 1.15000000000000008e69 < y

   1. Initial program 60.2%

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

      1. +-commutative 60.2%

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

      2. fma-define 61.1%

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

      3. *-commutative 61.1%

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

      4. *-commutative 61.1%

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

      5. cancel-sign-sub-inv 61.1%

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

      6. cancel-sign-sub 61.1%

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

      7. sub-neg 61.1%

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

      8. sub-neg 61.1%

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

      9. *-commutative 61.1%

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

      10. fma-neg 62.0%

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

      11. *-commutative 62.0%

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

      12. distribute-rgt-neg-out 62.0%

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

      13. remove-double-neg 62.0%

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

      14. *-commutative 62.0%

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

      15. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   if -3.3000000000000002e32 < y < -1.25e-248 or 4.8000000000000001e-281 < y < 1.75000000000000006e-249 or 1.31999999999999998e-51 < y < 1.15000000000000008e69

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. fma-define 86.6%

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

      3. *-commutative 86.6%

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

      4. *-commutative 86.6%

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

      5. cancel-sign-sub-inv 86.6%

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

      6. cancel-sign-sub 86.6%

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

      7. sub-neg 86.6%

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

      8. sub-neg 86.6%

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

      9. *-commutative 86.6%

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

      10. fma-neg 86.6%

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

      11. *-commutative 86.6%

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

      12. distribute-rgt-neg-out 86.6%

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

      13. remove-double-neg 86.6%

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

      14. *-commutative 86.6%

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

      15. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

   7. Simplified 64.0%

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

   if -1.25e-248 < y < 4.8000000000000001e-281

   1. Initial program 75.4%

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

      1. +-commutative 75.4%

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

      2. fma-define 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

      5. cancel-sign-sub-inv 75.4%

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

      6. cancel-sign-sub 75.4%

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

      7. sub-neg 75.4%

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

      8. sub-neg 75.4%

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

      9. *-commutative 75.4%

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

      10. fma-neg 75.4%

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

      11. *-commutative 75.4%

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

      12. distribute-rgt-neg-out 75.4%

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

      13. remove-double-neg 75.4%

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

      14. *-commutative 75.4%

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

      15. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in c around inf 59.3%

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

   if 1.75000000000000006e-249 < y < 1.15000000000000003e-155 or 1.04999999999999999e-131 < y < 1.31999999999999998e-51

   1. Initial program 88.6%

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

      1. +-commutative 88.6%

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

      2. fma-define 88.6%

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

      3. *-commutative 88.6%

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

      4. *-commutative 88.6%

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

      5. cancel-sign-sub-inv 88.6%

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

      6. cancel-sign-sub 88.6%

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

      7. sub-neg 88.6%

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

      8. sub-neg 88.6%

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

      9. *-commutative 88.6%

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

      10. fma-neg 88.6%

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

      11. *-commutative 88.6%

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

      12. distribute-rgt-neg-out 88.6%

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

      13. remove-double-neg 88.6%

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

      14. *-commutative 88.6%

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

      15. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in c around inf 50.3%

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

   6. Taylor expanded in b around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. +-commutative 55.5%

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

      3. unsub-neg 55.5%

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

      4. associate-/l* 55.6%

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

      5. associate-/l* 58.1%

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

      6. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   9. Taylor expanded in c around 0 55.6%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{j \cdot t}{b} - z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 55.6%

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

       2. associate-/l* 58.2%

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

   11. Simplified 58.2%

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

   if 1.15000000000000003e-155 < y < 1.04999999999999999e-131

   1. Initial program 99.8%

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

   3. Taylor expanded in i around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. associate-*r* 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in i around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

   8. Simplified 72.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-281}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-165}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(t \cdot \frac{j}{b} - z\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-132}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -6.5e+31)
     t_2
     (if (<= y -1.25e-240)
       t_1
       (if (<= y 1.65e-304)
         (* c (* j (- t (* b (/ z j)))))
         (if (<= y 2e-269)
           (* a (- (* b i) (* x t)))
           (if (<= y 6.5e-165)
             (* (* b c) (- (* t (/ j b)) z))
             (if (<= y 2.2e-132)
               (* (* b i) (- a (* j (/ y b))))
               (if (<= y 3.7e+62) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e+31) {
		tmp = t_2;
	} else if (y <= -1.25e-240) {
		tmp = t_1;
	} else if (y <= 1.65e-304) {
		tmp = c * (j * (t - (b * (z / j))));
	} else if (y <= 2e-269) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 6.5e-165) {
		tmp = (b * c) * ((t * (j / b)) - z);
	} else if (y <= 2.2e-132) {
		tmp = (b * i) * (a - (j * (y / b)));
	} else if (y <= 3.7e+62) {
		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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-6.5d+31)) then
        tmp = t_2
    else if (y <= (-1.25d-240)) then
        tmp = t_1
    else if (y <= 1.65d-304) then
        tmp = c * (j * (t - (b * (z / j))))
    else if (y <= 2d-269) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 6.5d-165) then
        tmp = (b * c) * ((t * (j / b)) - z)
    else if (y <= 2.2d-132) then
        tmp = (b * i) * (a - (j * (y / b)))
    else if (y <= 3.7d+62) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e+31) {
		tmp = t_2;
	} else if (y <= -1.25e-240) {
		tmp = t_1;
	} else if (y <= 1.65e-304) {
		tmp = c * (j * (t - (b * (z / j))));
	} else if (y <= 2e-269) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 6.5e-165) {
		tmp = (b * c) * ((t * (j / b)) - z);
	} else if (y <= 2.2e-132) {
		tmp = (b * i) * (a - (j * (y / b)));
	} else if (y <= 3.7e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6.5e+31:
		tmp = t_2
	elif y <= -1.25e-240:
		tmp = t_1
	elif y <= 1.65e-304:
		tmp = c * (j * (t - (b * (z / j))))
	elif y <= 2e-269:
		tmp = a * ((b * i) - (x * t))
	elif y <= 6.5e-165:
		tmp = (b * c) * ((t * (j / b)) - z)
	elif y <= 2.2e-132:
		tmp = (b * i) * (a - (j * (y / b)))
	elif y <= 3.7e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6.5e+31)
		tmp = t_2;
	elseif (y <= -1.25e-240)
		tmp = t_1;
	elseif (y <= 1.65e-304)
		tmp = Float64(c * Float64(j * Float64(t - Float64(b * Float64(z / j)))));
	elseif (y <= 2e-269)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 6.5e-165)
		tmp = Float64(Float64(b * c) * Float64(Float64(t * Float64(j / b)) - z));
	elseif (y <= 2.2e-132)
		tmp = Float64(Float64(b * i) * Float64(a - Float64(j * Float64(y / b))));
	elseif (y <= 3.7e+62)
		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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6.5e+31)
		tmp = t_2;
	elseif (y <= -1.25e-240)
		tmp = t_1;
	elseif (y <= 1.65e-304)
		tmp = c * (j * (t - (b * (z / j))));
	elseif (y <= 2e-269)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 6.5e-165)
		tmp = (b * c) * ((t * (j / b)) - z);
	elseif (y <= 2.2e-132)
		tmp = (b * i) * (a - (j * (y / b)));
	elseif (y <= 3.7e+62)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+31], t$95$2, If[LessEqual[y, -1.25e-240], t$95$1, If[LessEqual[y, 1.65e-304], N[(c * N[(j * N[(t - N[(b * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-269], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-165], N[(N[(b * c), $MachinePrecision] * N[(N[(t * N[(j / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-132], N[(N[(b * i), $MachinePrecision] * N[(a - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+62], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -6.5000000000000004e31 or 3.70000000000000014e62 < y

   1. Initial program 60.6%

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

      1. +-commutative 60.6%

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

      2. fma-define 61.4%

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

      3. *-commutative 61.4%

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

      4. *-commutative 61.4%

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

      5. cancel-sign-sub-inv 61.4%

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

      6. cancel-sign-sub 61.4%

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

      7. sub-neg 61.4%

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

      8. sub-neg 61.4%

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

      9. *-commutative 61.4%

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

      10. fma-neg 62.3%

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

      11. *-commutative 62.3%

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

      12. distribute-rgt-neg-out 62.3%

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

      13. remove-double-neg 62.3%

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

      14. *-commutative 62.3%

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

      15. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. +-commutative 68.7%

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

      2. mul-1-neg 68.7%

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

      3. unsub-neg 68.7%

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

      4. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if -6.5000000000000004e31 < y < -1.2500000000000001e-240 or 2.19999999999999991e-132 < y < 3.70000000000000014e62

   1. Initial program 84.0%

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

      1. +-commutative 84.0%

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

      2. fma-define 85.2%

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

      3. *-commutative 85.2%

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

      4. *-commutative 85.2%

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

      5. cancel-sign-sub-inv 85.2%

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

      6. cancel-sign-sub 85.2%

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

      7. sub-neg 85.2%

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

      8. sub-neg 85.2%

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

      9. *-commutative 85.2%

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

      10. fma-neg 85.2%

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

      11. *-commutative 85.2%

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

      12. distribute-rgt-neg-out 85.2%

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

      13. remove-double-neg 85.2%

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

      14. *-commutative 85.2%

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

      15. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in t around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

   7. Simplified 56.8%

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

   if -1.2500000000000001e-240 < y < 1.65000000000000006e-304

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. fma-define 77.5%

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

      3. *-commutative 77.5%

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

      4. *-commutative 77.5%

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

      5. cancel-sign-sub-inv 77.5%

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

      6. cancel-sign-sub 77.5%

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

      7. sub-neg 77.5%

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

      8. sub-neg 77.5%

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

      9. *-commutative 77.5%

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

      10. fma-neg 77.5%

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

      11. *-commutative 77.5%

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

      12. distribute-rgt-neg-out 77.5%

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

      13. remove-double-neg 77.5%

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

      14. *-commutative 77.5%

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

      15. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in c around inf 59.9%

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

   6. Taylor expanded in j around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

      3. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

   if 1.65000000000000006e-304 < y < 1.9999999999999999e-269

   1. Initial program 89.4%

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

   3. Taylor expanded in a around -inf 66.8%

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

   4. Taylor expanded in a around inf 66.8%

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

   if 1.9999999999999999e-269 < y < 6.5000000000000004e-165

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. fma-define 89.4%

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

      3. *-commutative 89.4%

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

      4. *-commutative 89.4%

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

      5. cancel-sign-sub-inv 89.4%

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

      6. cancel-sign-sub 89.4%

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

      7. sub-neg 89.4%

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

      8. sub-neg 89.4%

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

      9. *-commutative 89.4%

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

      10. fma-neg 89.4%

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

      11. *-commutative 89.4%

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

      12. distribute-rgt-neg-out 89.4%

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

      13. remove-double-neg 89.4%

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

      14. *-commutative 89.4%

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

      15. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in c around inf 60.9%

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

   6. Taylor expanded in b around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. +-commutative 65.2%

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

      3. unsub-neg 65.2%

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

      4. associate-/l* 65.2%

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

      5. associate-/l* 65.2%

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

      6. *-commutative 65.2%

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

   8. Simplified 65.2%

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

   9. Taylor expanded in b around inf 65.2%

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

       1. neg-mul-1 65.2%

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

       2. +-commutative 65.2%

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

       3. associate-/l* 65.2%

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

       4. associate-*r/ 65.2%

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

       5. distribute-rgt-neg-in 65.2%

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

       6. neg-mul-1 65.2%

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

       7. distribute-lft-in 65.2%

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

       8. associate-*r/ 65.2%

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

       9. neg-mul-1 65.2%

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

       10. sub-neg 65.2%

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

       11. associate-*r* 69.3%

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

       12. *-commutative 69.3%

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

       13. associate-/l* 69.3%

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

   11. Simplified 69.3%

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

   if 6.5000000000000004e-165 < y < 2.19999999999999991e-132

   1. Initial program 99.8%

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

   3. Taylor expanded in i around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-*r* 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in b around inf 64.3%

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

   7. Taylor expanded in i around inf 64.3%

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

      1. associate-*r* 87.6%

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

      2. mul-1-neg 87.6%

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

      3. unsub-neg 87.6%

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

      4. associate-/l* 87.6%

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

   9. Simplified 87.6%

      \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-165}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(t \cdot \frac{j}{b} - z\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-132}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(a - j \cdot \frac{y}{b}\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-156}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(t \cdot \frac{j}{b} - z\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -4.1e+31)
     t_2
     (if (<= y -2e-241)
       t_1
       (if (<= y 1.9e-305)
         (* c (* j (- t (* b (/ z j)))))
         (if (<= y 1.55e-270)
           (* a (- (* b i) (* x t)))
           (if (<= y 2.6e-156)
             (* (* b c) (- (* t (/ j b)) z))
             (if (<= y 9.5e-132)
               (* i (- (* a b) (* y j)))
               (if (<= y 1.3e+63) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.1e+31) {
		tmp = t_2;
	} else if (y <= -2e-241) {
		tmp = t_1;
	} else if (y <= 1.9e-305) {
		tmp = c * (j * (t - (b * (z / j))));
	} else if (y <= 1.55e-270) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 2.6e-156) {
		tmp = (b * c) * ((t * (j / b)) - z);
	} else if (y <= 9.5e-132) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= 1.3e+63) {
		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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-4.1d+31)) then
        tmp = t_2
    else if (y <= (-2d-241)) then
        tmp = t_1
    else if (y <= 1.9d-305) then
        tmp = c * (j * (t - (b * (z / j))))
    else if (y <= 1.55d-270) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 2.6d-156) then
        tmp = (b * c) * ((t * (j / b)) - z)
    else if (y <= 9.5d-132) then
        tmp = i * ((a * b) - (y * j))
    else if (y <= 1.3d+63) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.1e+31) {
		tmp = t_2;
	} else if (y <= -2e-241) {
		tmp = t_1;
	} else if (y <= 1.9e-305) {
		tmp = c * (j * (t - (b * (z / j))));
	} else if (y <= 1.55e-270) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 2.6e-156) {
		tmp = (b * c) * ((t * (j / b)) - z);
	} else if (y <= 9.5e-132) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= 1.3e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.1e+31:
		tmp = t_2
	elif y <= -2e-241:
		tmp = t_1
	elif y <= 1.9e-305:
		tmp = c * (j * (t - (b * (z / j))))
	elif y <= 1.55e-270:
		tmp = a * ((b * i) - (x * t))
	elif y <= 2.6e-156:
		tmp = (b * c) * ((t * (j / b)) - z)
	elif y <= 9.5e-132:
		tmp = i * ((a * b) - (y * j))
	elif y <= 1.3e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.1e+31)
		tmp = t_2;
	elseif (y <= -2e-241)
		tmp = t_1;
	elseif (y <= 1.9e-305)
		tmp = Float64(c * Float64(j * Float64(t - Float64(b * Float64(z / j)))));
	elseif (y <= 1.55e-270)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 2.6e-156)
		tmp = Float64(Float64(b * c) * Float64(Float64(t * Float64(j / b)) - z));
	elseif (y <= 9.5e-132)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (y <= 1.3e+63)
		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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.1e+31)
		tmp = t_2;
	elseif (y <= -2e-241)
		tmp = t_1;
	elseif (y <= 1.9e-305)
		tmp = c * (j * (t - (b * (z / j))));
	elseif (y <= 1.55e-270)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 2.6e-156)
		tmp = (b * c) * ((t * (j / b)) - z);
	elseif (y <= 9.5e-132)
		tmp = i * ((a * b) - (y * j));
	elseif (y <= 1.3e+63)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+31], t$95$2, If[LessEqual[y, -2e-241], t$95$1, If[LessEqual[y, 1.9e-305], N[(c * N[(j * N[(t - N[(b * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-270], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-156], N[(N[(b * c), $MachinePrecision] * N[(N[(t * N[(j / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-132], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+63], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.1000000000000002e31 or 1.3000000000000001e63 < y

   1. Initial program 60.6%

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

      1. +-commutative 60.6%

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

      2. fma-define 61.4%

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

      3. *-commutative 61.4%

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

      4. *-commutative 61.4%

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

      5. cancel-sign-sub-inv 61.4%

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

      6. cancel-sign-sub 61.4%

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

      7. sub-neg 61.4%

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

      8. sub-neg 61.4%

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

      9. *-commutative 61.4%

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

      10. fma-neg 62.3%

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

      11. *-commutative 62.3%

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

      12. distribute-rgt-neg-out 62.3%

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

      13. remove-double-neg 62.3%

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

      14. *-commutative 62.3%

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

      15. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. +-commutative 68.7%

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

      2. mul-1-neg 68.7%

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

      3. unsub-neg 68.7%

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

      4. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if -4.1000000000000002e31 < y < -1.9999999999999999e-241 or 9.49999999999999987e-132 < y < 1.3000000000000001e63

   1. Initial program 84.0%

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

      1. +-commutative 84.0%

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

      2. fma-define 85.2%

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

      3. *-commutative 85.2%

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

      4. *-commutative 85.2%

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

      5. cancel-sign-sub-inv 85.2%

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

      6. cancel-sign-sub 85.2%

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

      7. sub-neg 85.2%

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

      8. sub-neg 85.2%

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

      9. *-commutative 85.2%

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

      10. fma-neg 85.2%

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

      11. *-commutative 85.2%

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

      12. distribute-rgt-neg-out 85.2%

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

      13. remove-double-neg 85.2%

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

      14. *-commutative 85.2%

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

      15. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in t around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

   7. Simplified 56.8%

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

   if -1.9999999999999999e-241 < y < 1.9e-305

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. fma-define 77.5%

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

      3. *-commutative 77.5%

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

      4. *-commutative 77.5%

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

      5. cancel-sign-sub-inv 77.5%

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

      6. cancel-sign-sub 77.5%

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

      7. sub-neg 77.5%

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

      8. sub-neg 77.5%

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

      9. *-commutative 77.5%

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

      10. fma-neg 77.5%

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

      11. *-commutative 77.5%

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

      12. distribute-rgt-neg-out 77.5%

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

      13. remove-double-neg 77.5%

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

      14. *-commutative 77.5%

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

      15. *-commutative 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in c around inf 59.9%

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

   6. Taylor expanded in j around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

      3. associate-/l* 64.3%

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

   8. Simplified 64.3%

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

   if 1.9e-305 < y < 1.55e-270

   1. Initial program 89.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 66.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 66.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   if 1.55e-270 < y < 2.6000000000000001e-156

   1. Initial program 89.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 89.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 89.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 89.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 89.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 89.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 89.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 89.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 89.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 89.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 89.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 89.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 89.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 89.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 89.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 89.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 62.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in b around inf 66.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 66.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

      2. +-commutative 66.7%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

      3. unsub-neg 66.7%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} - c \cdot z\right)} \]

      4. associate-/l* 66.7%

         \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} - c \cdot z\right) \]

      5. associate-/l* 66.7%

         \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} - c \cdot z\right) \]

      6. *-commutative 66.7%

         \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   8. Simplified 66.7%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - z \cdot c\right)} \]

   9. Taylor expanded in b around inf 66.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 66.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

       2. +-commutative 66.7%

          \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

       3. associate-/l* 66.7%

          \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} + \left(-c \cdot z\right)\right) \]

       4. associate-*r/ 66.7%

          \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} + \left(-c \cdot z\right)\right) \]

       5. distribute-rgt-neg-in 66.7%

          \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) + \color{blue}{c \cdot \left(-z\right)}\right) \]

       6. neg-mul-1 66.7%

          \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) + c \cdot \color{blue}{\left(-1 \cdot z\right)}\right) \]

       7. distribute-lft-in 66.7%

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(j \cdot \frac{t}{b} + -1 \cdot z\right)\right)} \]

       8. associate-*r/ 66.7%

          \[\leadsto b \cdot \left(c \cdot \left(\color{blue}{\frac{j \cdot t}{b}} + -1 \cdot z\right)\right) \]

       9. neg-mul-1 66.7%

          \[\leadsto b \cdot \left(c \cdot \left(\frac{j \cdot t}{b} + \color{blue}{\left(-z\right)}\right)\right) \]

       10. sub-neg 66.7%

           \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(\frac{j \cdot t}{b} - z\right)}\right) \]

       11. associate-*r* 70.7%

           \[\leadsto \color{blue}{\left(b \cdot c\right) \cdot \left(\frac{j \cdot t}{b} - z\right)} \]

       12. *-commutative 70.7%

           \[\leadsto \left(b \cdot c\right) \cdot \left(\frac{\color{blue}{t \cdot j}}{b} - z\right) \]

       13. associate-/l* 70.7%

           \[\leadsto \left(b \cdot c\right) \cdot \left(\color{blue}{t \cdot \frac{j}{b}} - z\right) \]

   11. Simplified 70.7%

       \[\leadsto \color{blue}{\left(b \cdot c\right) \cdot \left(t \cdot \frac{j}{b} - z\right)} \]

   if 2.6000000000000001e-156 < y < 9.49999999999999987e-132

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 72.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 72.2%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in i around inf 72.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]
   7. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 72.2%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 72.2%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      4. *-commutative 72.2%

         \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   8. Simplified 72.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-156}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(t \cdot \frac{j}{b} - z\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-148}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - b \cdot \frac{c}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- t_1 (* x (- (* t a) (* y z))))))
   (if (<= z -1.75e+131)
     (* z (- (* x y) (* b c)))
     (if (<= z -1.12e-157)
       t_2
       (if (<= z 2.05e-148)
         (+ t_1 (* a (* b i)))
         (if (<= z 2.6e+58)
           t_2
           (if (<= z 1.7e+169)
             (- (* y (- (* x z) (* i j))) (* c (* z b)))
             (* (* y z) (- x (* b (/ c y)))))))))))

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 - (x * ((t * a) - (y * z)));
	double tmp;
	if (z <= -1.75e+131) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.12e-157) {
		tmp = t_2;
	} else if (z <= 2.05e-148) {
		tmp = t_1 + (a * (b * i));
	} else if (z <= 2.6e+58) {
		tmp = t_2;
	} else if (z <= 1.7e+169) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = (y * z) * (x - (b * (c / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 - (x * ((t * a) - (y * z)))
    if (z <= (-1.75d+131)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-1.12d-157)) then
        tmp = t_2
    else if (z <= 2.05d-148) then
        tmp = t_1 + (a * (b * i))
    else if (z <= 2.6d+58) then
        tmp = t_2
    else if (z <= 1.7d+169) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else
        tmp = (y * z) * (x - (b * (c / 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 t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (z <= -1.75e+131) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.12e-157) {
		tmp = t_2;
	} else if (z <= 2.05e-148) {
		tmp = t_1 + (a * (b * i));
	} else if (z <= 2.6e+58) {
		tmp = t_2;
	} else if (z <= 1.7e+169) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = (y * z) * (x - (b * (c / y)));
	}
	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 - (x * ((t * a) - (y * z)))
	tmp = 0
	if z <= -1.75e+131:
		tmp = z * ((x * y) - (b * c))
	elif z <= -1.12e-157:
		tmp = t_2
	elif z <= 2.05e-148:
		tmp = t_1 + (a * (b * i))
	elif z <= 2.6e+58:
		tmp = t_2
	elif z <= 1.7e+169:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	else:
		tmp = (y * z) * (x - (b * (c / y)))
	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(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (z <= -1.75e+131)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -1.12e-157)
		tmp = t_2;
	elseif (z <= 2.05e-148)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (z <= 2.6e+58)
		tmp = t_2;
	elseif (z <= 1.7e+169)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	else
		tmp = Float64(Float64(y * z) * Float64(x - Float64(b * Float64(c / y))));
	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 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (z <= -1.75e+131)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -1.12e-157)
		tmp = t_2;
	elseif (z <= 2.05e-148)
		tmp = t_1 + (a * (b * i));
	elseif (z <= 2.6e+58)
		tmp = t_2;
	elseif (z <= 1.7e+169)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	else
		tmp = (y * z) * (x - (b * (c / y)));
	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[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+131], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e-157], t$95$2, If[LessEqual[z, 2.05e-148], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+58], t$95$2, If[LessEqual[z, 1.7e+169], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(x - N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7499999999999999e131

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 58.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 58.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 58.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 58.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 58.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 58.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 58.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 58.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 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 t around 0 65.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 61.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 61.9%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 55.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 55.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 55.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 55.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 55.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 55.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 55.8%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 55.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   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 -1.7499999999999999e131 < z < -1.12000000000000001e-157 or 2.0500000000000001e-148 < z < 2.59999999999999988e58

   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. Add Preprocessing

   3. Taylor expanded in b around -inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - -1 \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-*r* 75.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(-1 \cdot \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - -1 \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. neg-mul-1 75.2%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(-1 \cdot \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - -1 \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. distribute-lft-out-- 75.2%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(-1 \cdot \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - \left(c \cdot z - a \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. associate-/l* 74.2%

         \[\leadsto \left(-b\right) \cdot \left(-1 \cdot \left(\color{blue}{x \cdot \frac{y \cdot z - a \cdot t}{b}} - \left(c \cdot z - a \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 74.2%

         \[\leadsto \left(-b\right) \cdot \left(-1 \cdot \left(x \cdot \frac{y \cdot z - \color{blue}{t \cdot a}}{b} - \left(c \cdot z - a \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.2%

         \[\leadsto \left(-b\right) \cdot \left(-1 \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b} - \left(c \cdot z - \color{blue}{i \cdot a}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-1 \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b} - \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around 0 64.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -1.12000000000000001e-157 < z < 2.0500000000000001e-148

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 73.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 2.59999999999999988e58 < z < 1.70000000000000014e169

   1. Initial program 54.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 54.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 54.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 54.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 54.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 54.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 54.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 54.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 54.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 54.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 54.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 54.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 54.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 54.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 54.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 54.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 60.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 60.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 60.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 64.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 68.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 68.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 68.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 68.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 68.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 68.3%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 68.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 70.5%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 70.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 73.9%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 73.9%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 73.9%

       \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]

   if 1.70000000000000014e169 < z

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 66.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 66.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 66.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 66.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 66.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 66.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 66.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 66.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 66.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 66.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 66.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 66.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 63.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{y} + i \cdot j\right)\right)\right)} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(i \cdot j - \frac{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{y}\right) - z \cdot x\right)\right)} \]

   8. Taylor expanded in z around inf 74.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(x - \frac{b \cdot c}{y}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 78.2%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(x - \frac{b \cdot c}{y}\right)} \]

      2. *-commutative 78.2%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot \left(x - \frac{b \cdot c}{y}\right) \]

      3. associate-/l* 85.6%

         \[\leadsto \left(z \cdot y\right) \cdot \left(x - \color{blue}{b \cdot \frac{c}{y}}\right) \]

   10. Simplified 85.6%

       \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot \left(x - b \cdot \frac{c}{y}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-157}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - b \cdot \frac{c}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -0.32:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* x t)))))
   (if (<= t -3.3e+156)
     (* t (- (* c j) (* x a)))
     (if (<= t -3.8e+108)
       (+ t_1 (* a (* b i)))
       (if (<= t -0.32)
         t_2
         (if (<= t -2e-59)
           (* a (- (* b i) (* x t)))
           (if (<= t 1.75e-40)
             (- (* y (- (* x z) (* i j))) (* c (* z b)))
             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 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (a * (x * t));
	double tmp;
	if (t <= -3.3e+156) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -3.8e+108) {
		tmp = t_1 + (a * (b * i));
	} else if (t <= -0.32) {
		tmp = t_2;
	} else if (t <= -2e-59) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= 1.75e-40) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} 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 = j * ((t * c) - (y * i))
    t_2 = t_1 - (a * (x * t))
    if (t <= (-3.3d+156)) then
        tmp = t * ((c * j) - (x * a))
    else if (t <= (-3.8d+108)) then
        tmp = t_1 + (a * (b * i))
    else if (t <= (-0.32d0)) then
        tmp = t_2
    else if (t <= (-2d-59)) then
        tmp = a * ((b * i) - (x * t))
    else if (t <= 1.75d-40) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    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 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (a * (x * t));
	double tmp;
	if (t <= -3.3e+156) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -3.8e+108) {
		tmp = t_1 + (a * (b * i));
	} else if (t <= -0.32) {
		tmp = t_2;
	} else if (t <= -2e-59) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= 1.75e-40) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else {
		tmp = t_2;
	}
	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 * (x * t))
	tmp = 0
	if t <= -3.3e+156:
		tmp = t * ((c * j) - (x * a))
	elif t <= -3.8e+108:
		tmp = t_1 + (a * (b * i))
	elif t <= -0.32:
		tmp = t_2
	elif t <= -2e-59:
		tmp = a * ((b * i) - (x * t))
	elif t <= 1.75e-40:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	else:
		tmp = t_2
	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(x * t)))
	tmp = 0.0
	if (t <= -3.3e+156)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (t <= -3.8e+108)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (t <= -0.32)
		tmp = t_2;
	elseif (t <= -2e-59)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (t <= 1.75e-40)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	else
		tmp = t_2;
	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 * (x * t));
	tmp = 0.0;
	if (t <= -3.3e+156)
		tmp = t * ((c * j) - (x * a));
	elseif (t <= -3.8e+108)
		tmp = t_1 + (a * (b * i));
	elseif (t <= -0.32)
		tmp = t_2;
	elseif (t <= -2e-59)
		tmp = a * ((b * i) - (x * t));
	elseif (t <= 1.75e-40)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+156], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e+108], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.32], t$95$2, If[LessEqual[t, -2e-59], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-40], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2999999999999999e156

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 76.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 76.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 76.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 76.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if -3.2999999999999999e156 < t < -3.80000000000000008e108

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 99.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -3.80000000000000008e108 < t < -0.320000000000000007 or 1.7500000000000001e-40 < t

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 65.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around 0 58.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. *-commutative 58.5%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) \]

      3. *-commutative 58.5%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) \]

      4. mul-1-neg 58.5%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      5. unsub-neg 58.5%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(t \cdot x\right)} \]

      6. *-commutative 58.5%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)} \]

   if -0.320000000000000007 < t < -2.0000000000000001e-59

   1. Initial program 93.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 74.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   if -2.0000000000000001e-59 < t < 1.7500000000000001e-40

   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. Step-by-step derivation

      1. +-commutative 77.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 78.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 78.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 78.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 78.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 78.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 78.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   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* 73.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 73.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 73.8%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 73.0%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 74.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 74.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 74.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 74.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 74.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 74.0%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 74.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 69.7%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 71.3%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 71.3%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 71.3%

       \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -0.32:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + a \cdot \left(b \cdot i\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+141}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* a (* b i))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -1.35e+141)
     t_3
     (if (<= z -2.5e-22)
       (* (* x y) (- z (* a (/ t y))))
       (if (<= z 9.4e-151)
         t_2
         (if (<= z 1.7e+39)
           (- t_1 (* a (* x t)))
           (if (<= z 2.1e+93) 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 = t_1 + (a * (b * i));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.35e+141) {
		tmp = t_3;
	} else if (z <= -2.5e-22) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (z <= 9.4e-151) {
		tmp = t_2;
	} else if (z <= 1.7e+39) {
		tmp = t_1 - (a * (x * t));
	} else if (z <= 2.1e+93) {
		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 = t_1 + (a * (b * i))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-1.35d+141)) then
        tmp = t_3
    else if (z <= (-2.5d-22)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (z <= 9.4d-151) then
        tmp = t_2
    else if (z <= 1.7d+39) then
        tmp = t_1 - (a * (x * t))
    else if (z <= 2.1d+93) 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 = t_1 + (a * (b * i));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.35e+141) {
		tmp = t_3;
	} else if (z <= -2.5e-22) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (z <= 9.4e-151) {
		tmp = t_2;
	} else if (z <= 1.7e+39) {
		tmp = t_1 - (a * (x * t));
	} else if (z <= 2.1e+93) {
		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 = t_1 + (a * (b * i))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.35e+141:
		tmp = t_3
	elif z <= -2.5e-22:
		tmp = (x * y) * (z - (a * (t / y)))
	elif z <= 9.4e-151:
		tmp = t_2
	elif z <= 1.7e+39:
		tmp = t_1 - (a * (x * t))
	elif z <= 2.1e+93:
		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(t_1 + Float64(a * Float64(b * i)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.35e+141)
		tmp = t_3;
	elseif (z <= -2.5e-22)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (z <= 9.4e-151)
		tmp = t_2;
	elseif (z <= 1.7e+39)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (z <= 2.1e+93)
		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 = t_1 + (a * (b * i));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.35e+141)
		tmp = t_3;
	elseif (z <= -2.5e-22)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (z <= 9.4e-151)
		tmp = t_2;
	elseif (z <= 1.7e+39)
		tmp = t_1 - (a * (x * t));
	elseif (z <= 2.1e+93)
		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[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+141], t$95$3, If[LessEqual[z, -2.5e-22], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e-151], t$95$2, If[LessEqual[z, 1.7e+39], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+93], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e141 or 2.0999999999999998e93 < z

   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 60.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 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 t around 0 62.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 59.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 59.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 56.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 56.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 56.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 56.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 56.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 56.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 56.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 56.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in z around inf 78.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   9. Step-by-step derivation

      1. *-commutative 78.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   10. Simplified 78.7%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -1.35e141 < z < -2.49999999999999977e-22

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 69.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{y} + i \cdot j\right)\right)\right)} \]

   7. Simplified 72.1%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(i \cdot j - \frac{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{y}\right) - z \cdot x\right)\right)} \]

   8. Taylor expanded in x around inf 62.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)} \]

      2. *-commutative 62.5%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right) \]

      3. mul-1-neg 62.5%

         \[\leadsto \left(y \cdot x\right) \cdot \left(z + \color{blue}{\left(-\frac{a \cdot t}{y}\right)}\right) \]

      4. unsub-neg 62.5%

         \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{\left(z - \frac{a \cdot t}{y}\right)} \]

      5. associate-/l* 67.3%

         \[\leadsto \left(y \cdot x\right) \cdot \left(z - \color{blue}{a \cdot \frac{t}{y}}\right) \]

   10. Simplified 67.3%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \left(z - a \cdot \frac{t}{y}\right)} \]

   if -2.49999999999999977e-22 < z < 9.40000000000000057e-151 or 1.6999999999999999e39 < z < 2.0999999999999998e93

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 65.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 9.40000000000000057e-151 < z < 1.6999999999999999e39

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 58.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in b around 0 55.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. *-commutative 55.8%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) \]

      3. *-commutative 55.8%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) \]

      4. mul-1-neg 55.8%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      5. unsub-neg 55.8%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(t \cdot x\right)} \]

      6. *-commutative 55.8%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \color{blue}{\left(x \cdot t\right)} \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2e+32)
     t_2
     (if (<= y -8.8e-241)
       t_1
       (if (<= y 8.8e-305)
         (* c (* j (- t (* b (/ z j)))))
         (if (<= y 7.5e-271)
           (* a (- (* b i) (* x t)))
           (if (<= y 3.2e-54)
             (* b (* c (- (* t (/ j b)) z)))
             (if (<= y 3.6e+64) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2e+32) {
		tmp = t_2;
	} else if (y <= -8.8e-241) {
		tmp = t_1;
	} else if (y <= 8.8e-305) {
		tmp = c * (j * (t - (b * (z / j))));
	} else if (y <= 7.5e-271) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 3.2e-54) {
		tmp = b * (c * ((t * (j / b)) - z));
	} else if (y <= 3.6e+64) {
		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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2d+32)) then
        tmp = t_2
    else if (y <= (-8.8d-241)) then
        tmp = t_1
    else if (y <= 8.8d-305) then
        tmp = c * (j * (t - (b * (z / j))))
    else if (y <= 7.5d-271) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 3.2d-54) then
        tmp = b * (c * ((t * (j / b)) - z))
    else if (y <= 3.6d+64) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2e+32) {
		tmp = t_2;
	} else if (y <= -8.8e-241) {
		tmp = t_1;
	} else if (y <= 8.8e-305) {
		tmp = c * (j * (t - (b * (z / j))));
	} else if (y <= 7.5e-271) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 3.2e-54) {
		tmp = b * (c * ((t * (j / b)) - z));
	} else if (y <= 3.6e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2e+32:
		tmp = t_2
	elif y <= -8.8e-241:
		tmp = t_1
	elif y <= 8.8e-305:
		tmp = c * (j * (t - (b * (z / j))))
	elif y <= 7.5e-271:
		tmp = a * ((b * i) - (x * t))
	elif y <= 3.2e-54:
		tmp = b * (c * ((t * (j / b)) - z))
	elif y <= 3.6e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2e+32)
		tmp = t_2;
	elseif (y <= -8.8e-241)
		tmp = t_1;
	elseif (y <= 8.8e-305)
		tmp = Float64(c * Float64(j * Float64(t - Float64(b * Float64(z / j)))));
	elseif (y <= 7.5e-271)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 3.2e-54)
		tmp = Float64(b * Float64(c * Float64(Float64(t * Float64(j / b)) - z)));
	elseif (y <= 3.6e+64)
		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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2e+32)
		tmp = t_2;
	elseif (y <= -8.8e-241)
		tmp = t_1;
	elseif (y <= 8.8e-305)
		tmp = c * (j * (t - (b * (z / j))));
	elseif (y <= 7.5e-271)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 3.2e-54)
		tmp = b * (c * ((t * (j / b)) - z));
	elseif (y <= 3.6e+64)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+32], t$95$2, If[LessEqual[y, -8.8e-241], t$95$1, If[LessEqual[y, 8.8e-305], N[(c * N[(j * N[(t - N[(b * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-271], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-54], N[(b * N[(c * N[(N[(t * N[(j / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+64], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.00000000000000011e32 or 3.60000000000000014e64 < y

   1. Initial program 60.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 69.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 69.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 69.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2.00000000000000011e32 < y < -8.7999999999999997e-241 or 3.19999999999999998e-54 < y < 3.60000000000000014e64

   1. Initial program 84.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 85.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 85.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 85.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 85.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 85.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 85.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 85.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 85.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 63.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 63.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 63.8%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 63.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 63.8%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 63.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if -8.7999999999999997e-241 < y < 8.79999999999999987e-305

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 59.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 59.8%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot \left(t + -1 \cdot \frac{b \cdot z}{j}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto c \cdot \left(j \cdot \left(t + \color{blue}{\left(-\frac{b \cdot z}{j}\right)}\right)\right) \]

      2. unsub-neg 59.8%

         \[\leadsto c \cdot \left(j \cdot \color{blue}{\left(t - \frac{b \cdot z}{j}\right)}\right) \]

      3. associate-/l* 64.3%

         \[\leadsto c \cdot \left(j \cdot \left(t - \color{blue}{b \cdot \frac{z}{j}}\right)\right) \]

   8. Simplified 64.3%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)} \]

   if 8.79999999999999987e-305 < y < 7.50000000000000031e-271

   1. Initial program 89.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 66.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 66.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   if 7.50000000000000031e-271 < y < 3.19999999999999998e-54

   1. Initial program 89.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 89.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 89.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 89.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 89.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 89.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 89.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 89.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 89.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 89.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 89.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 89.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 89.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in b around inf 47.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.4%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

      2. +-commutative 47.4%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

      3. unsub-neg 47.4%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} - c \cdot z\right)} \]

      4. associate-/l* 47.5%

         \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} - c \cdot z\right) \]

      5. associate-/l* 49.4%

         \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} - c \cdot z\right) \]

      6. *-commutative 49.4%

         \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - z \cdot c\right)} \]

   9. Taylor expanded in c around 0 47.5%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{j \cdot t}{b} - z\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 47.5%

          \[\leadsto b \cdot \left(c \cdot \left(\frac{\color{blue}{t \cdot j}}{b} - z\right)\right) \]

       2. associate-/l* 49.5%

          \[\leadsto b \cdot \left(c \cdot \left(\color{blue}{t \cdot \frac{j}{b}} - z\right)\right) \]

   11. Simplified 49.5%

       \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-305}:\\ \;\;\;\;c \cdot \left(j \cdot \left(t - b \cdot \frac{z}{j}\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(c \cdot \left(t \cdot \frac{j}{b} - z\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -2.45e+32)
     t_3
     (if (<= y -7.8e-249)
       t_2
       (if (<= y 1.12e-167)
         t_1
         (if (<= y 1.4e-129)
           (* a (- (* b i) (* x t)))
           (if (<= y 6.5e-25) t_1 (if (<= y 1.1e+66) 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 = c * ((t * j) - (z * b));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.45e+32) {
		tmp = t_3;
	} else if (y <= -7.8e-249) {
		tmp = t_2;
	} else if (y <= 1.12e-167) {
		tmp = t_1;
	} else if (y <= 1.4e-129) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 6.5e-25) {
		tmp = t_1;
	} else if (y <= 1.1e+66) {
		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 = c * ((t * j) - (z * b))
    t_2 = t * ((c * j) - (x * a))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-2.45d+32)) then
        tmp = t_3
    else if (y <= (-7.8d-249)) then
        tmp = t_2
    else if (y <= 1.12d-167) then
        tmp = t_1
    else if (y <= 1.4d-129) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 6.5d-25) then
        tmp = t_1
    else if (y <= 1.1d+66) 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 = c * ((t * j) - (z * b));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.45e+32) {
		tmp = t_3;
	} else if (y <= -7.8e-249) {
		tmp = t_2;
	} else if (y <= 1.12e-167) {
		tmp = t_1;
	} else if (y <= 1.4e-129) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 6.5e-25) {
		tmp = t_1;
	} else if (y <= 1.1e+66) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = t * ((c * j) - (x * a))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.45e+32:
		tmp = t_3
	elif y <= -7.8e-249:
		tmp = t_2
	elif y <= 1.12e-167:
		tmp = t_1
	elif y <= 1.4e-129:
		tmp = a * ((b * i) - (x * t))
	elif y <= 6.5e-25:
		tmp = t_1
	elif y <= 1.1e+66:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.45e+32)
		tmp = t_3;
	elseif (y <= -7.8e-249)
		tmp = t_2;
	elseif (y <= 1.12e-167)
		tmp = t_1;
	elseif (y <= 1.4e-129)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 6.5e-25)
		tmp = t_1;
	elseif (y <= 1.1e+66)
		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 = c * ((t * j) - (z * b));
	t_2 = t * ((c * j) - (x * a));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.45e+32)
		tmp = t_3;
	elseif (y <= -7.8e-249)
		tmp = t_2;
	elseif (y <= 1.12e-167)
		tmp = t_1;
	elseif (y <= 1.4e-129)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 6.5e-25)
		tmp = t_1;
	elseif (y <= 1.1e+66)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e+32], t$95$3, If[LessEqual[y, -7.8e-249], t$95$2, If[LessEqual[y, 1.12e-167], t$95$1, If[LessEqual[y, 1.4e-129], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-25], t$95$1, If[LessEqual[y, 1.1e+66], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4500000000000001e32 or 1.0999999999999999e66 < y

   1. Initial program 60.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 69.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 69.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 69.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2.4500000000000001e32 < y < -7.7999999999999998e-249 or 6.5e-25 < y < 1.0999999999999999e66

   1. Initial program 85.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 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 inf 62.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 62.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 62.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 62.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 62.3%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 62.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if -7.7999999999999998e-249 < y < 1.1200000000000001e-167 or 1.4e-129 < y < 6.5e-25

   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. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 83.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 83.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 83.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 83.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 83.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 83.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 83.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 55.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if 1.1200000000000001e-167 < y < 1.4e-129

   1. Initial program 91.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 91.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 0.0068:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.5e+119)
     t_2
     (if (<= a -1.3e+35)
       (- (* y (- (* x z) (* i j))) (* c (* z b)))
       (if (<= a -4.8e+26)
         t_2
         (if (<= a 0.0068) (+ t_1 (* z (- (* x y) (* b c)))) (+ 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 = j * ((t * c) - (y * i));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.5e+119) {
		tmp = t_2;
	} else if (a <= -1.3e+35) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (a <= -4.8e+26) {
		tmp = t_2;
	} else if (a <= 0.0068) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1 + 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 = j * ((t * c) - (y * i))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1.5d+119)) then
        tmp = t_2
    else if (a <= (-1.3d+35)) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else if (a <= (-4.8d+26)) then
        tmp = t_2
    else if (a <= 0.0068d0) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    else
        tmp = t_1 + 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 = j * ((t * c) - (y * i));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.5e+119) {
		tmp = t_2;
	} else if (a <= -1.3e+35) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (a <= -4.8e+26) {
		tmp = t_2;
	} else if (a <= 0.0068) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.5e+119:
		tmp = t_2
	elif a <= -1.3e+35:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	elif a <= -4.8e+26:
		tmp = t_2
	elif a <= 0.0068:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1 + t_2
	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(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+119)
		tmp = t_2;
	elseif (a <= -1.3e+35)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	elseif (a <= -4.8e+26)
		tmp = t_2;
	elseif (a <= 0.0068)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = Float64(t_1 + t_2);
	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 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+119)
		tmp = t_2;
	elseif (a <= -1.3e+35)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	elseif (a <= -4.8e+26)
		tmp = t_2;
	elseif (a <= 0.0068)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	else
		tmp = t_1 + t_2;
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+119], t$95$2, If[LessEqual[a, -1.3e+35], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e+26], t$95$2, If[LessEqual[a, 0.0068], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.50000000000000001e119 or -1.30000000000000003e35 < a < -4.80000000000000009e26

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 64.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 74.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   if -1.50000000000000001e119 < a < -1.30000000000000003e35

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 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 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* 69.1%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 76.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 76.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 76.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 76.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 76.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 76.8%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 76.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 84.5%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 84.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 84.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 84.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 84.5%

       \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]

   if -4.80000000000000009e26 < a < 0.00679999999999999962

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 75.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 75.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 75.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 0.00679999999999999962 < a

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 62.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 0.0068:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+32}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -6.6e+119)
     t_1
     (if (<= a -1.55e+35)
       (- (* y (- (* x z) (* i j))) (* c (* z b)))
       (if (<= a -1.8e+24)
         t_1
         (if (<= a 2.65e+32)
           (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))
           (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y))))))))))

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 tmp;
	if (a <= -6.6e+119) {
		tmp = t_1;
	} else if (a <= -1.55e+35) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (a <= -1.8e+24) {
		tmp = t_1;
	} else if (a <= 2.65e+32) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / 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) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-6.6d+119)) then
        tmp = t_1
    else if (a <= (-1.55d+35)) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else if (a <= (-1.8d+24)) then
        tmp = t_1
    else if (a <= 2.65d+32) then
        tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else
        tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / 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 t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.6e+119) {
		tmp = t_1;
	} else if (a <= -1.55e+35) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (a <= -1.8e+24) {
		tmp = t_1;
	} else if (a <= 2.65e+32) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -6.6e+119:
		tmp = t_1
	elif a <= -1.55e+35:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	elif a <= -1.8e+24:
		tmp = t_1
	elif a <= 2.65e+32:
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	else:
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	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)))
	tmp = 0.0
	if (a <= -6.6e+119)
		tmp = t_1;
	elseif (a <= -1.55e+35)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	elseif (a <= -1.8e+24)
		tmp = t_1;
	elseif (a <= 2.65e+32)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))));
	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));
	tmp = 0.0;
	if (a <= -6.6e+119)
		tmp = t_1;
	elseif (a <= -1.55e+35)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	elseif (a <= -1.8e+24)
		tmp = t_1;
	elseif (a <= 2.65e+32)
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	else
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	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]}, If[LessEqual[a, -6.6e+119], t$95$1, If[LessEqual[a, -1.55e+35], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e+24], t$95$1, If[LessEqual[a, 2.65e+32], 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[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.6000000000000004e119 or -1.54999999999999993e35 < a < -1.79999999999999992e24

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 64.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in a around inf 74.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   if -6.6000000000000004e119 < a < -1.54999999999999993e35

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 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 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* 69.1%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 76.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 76.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 76.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 76.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 76.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 76.8%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 76.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in c around inf 84.5%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 84.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(c \cdot z\right) \cdot b} \]

      2. associate-*l* 84.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(z \cdot b\right)} \]

      3. *-commutative 84.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \color{blue}{\left(b \cdot z\right)} \]

   10. Simplified 84.5%

       \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{c \cdot \left(b \cdot z\right)} \]

   if -1.79999999999999992e24 < a < 2.65e32

   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 z around inf 74.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 74.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 74.4%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 74.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if 2.65e32 < a

   1. Initial program 64.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 64.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 66.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 66.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 66.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 66.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 66.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 66.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 66.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 66.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 66.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 66.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 66.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 66.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{y} + i \cdot j\right)\right)\right)} \]

   7. Simplified 57.5%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(i \cdot j - \frac{t \cdot \left(j \cdot c - a \cdot x\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{y}\right) - z \cdot x\right)\right)} \]

   8. Taylor expanded in x around inf 59.9%

      \[\leadsto y \cdot \left(-\left(\left(i \cdot j - \color{blue}{-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{y}}\right) - z \cdot x\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 59.9%

         \[\leadsto y \cdot \left(-\left(\left(i \cdot j - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)}{y}}\right) - z \cdot x\right)\right) \]

      2. associate-*r* 59.9%

         \[\leadsto y \cdot \left(-\left(\left(i \cdot j - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)}}{y}\right) - z \cdot x\right)\right) \]

      3. mul-1-neg 59.9%

         \[\leadsto y \cdot \left(-\left(\left(i \cdot j - \frac{\color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right)}{y}\right) - z \cdot x\right)\right) \]

   10. Simplified 59.9%

       \[\leadsto y \cdot \left(-\left(\left(i \cdot j - \color{blue}{\frac{\left(-a\right) \cdot \left(t \cdot x\right)}{y}}\right) - z \cdot x\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+32}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.34 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-256}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.34e+166)
     t_1
     (if (<= t -3.7e-256)
       (* (* y j) (- i))
       (if (<= t 1.8e-292)
         (* z (* c (- b)))
         (if (<= t 1.15e-16)
           (* y (* x z))
           (if (<= t 6.2e+97) (* 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 = c * (t * j);
	double tmp;
	if (t <= -1.34e+166) {
		tmp = t_1;
	} else if (t <= -3.7e-256) {
		tmp = (y * j) * -i;
	} else if (t <= 1.8e-292) {
		tmp = z * (c * -b);
	} else if (t <= 1.15e-16) {
		tmp = y * (x * z);
	} else if (t <= 6.2e+97) {
		tmp = 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 = c * (t * j)
    if (t <= (-1.34d+166)) then
        tmp = t_1
    else if (t <= (-3.7d-256)) then
        tmp = (y * j) * -i
    else if (t <= 1.8d-292) then
        tmp = z * (c * -b)
    else if (t <= 1.15d-16) then
        tmp = y * (x * z)
    else if (t <= 6.2d+97) then
        tmp = 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 = c * (t * j);
	double tmp;
	if (t <= -1.34e+166) {
		tmp = t_1;
	} else if (t <= -3.7e-256) {
		tmp = (y * j) * -i;
	} else if (t <= 1.8e-292) {
		tmp = z * (c * -b);
	} else if (t <= 1.15e-16) {
		tmp = y * (x * z);
	} else if (t <= 6.2e+97) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.34e+166:
		tmp = t_1
	elif t <= -3.7e-256:
		tmp = (y * j) * -i
	elif t <= 1.8e-292:
		tmp = z * (c * -b)
	elif t <= 1.15e-16:
		tmp = y * (x * z)
	elif t <= 6.2e+97:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -1.34e+166)
		tmp = t_1;
	elseif (t <= -3.7e-256)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (t <= 1.8e-292)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (t <= 1.15e-16)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 6.2e+97)
		tmp = Float64(c * Float64(z * Float64(-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 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.34e+166)
		tmp = t_1;
	elseif (t <= -3.7e-256)
		tmp = (y * j) * -i;
	elseif (t <= 1.8e-292)
		tmp = z * (c * -b);
	elseif (t <= 1.15e-16)
		tmp = y * (x * z);
	elseif (t <= 6.2e+97)
		tmp = 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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.34e+166], t$95$1, If[LessEqual[t, -3.7e-256], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[t, 1.8e-292], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-16], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+97], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.34000000000000007e166 or 6.19999999999999962e97 < t

   1. Initial program 65.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 67.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 67.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 67.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 40.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.8%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 40.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.34000000000000007e166 < t < -3.70000000000000029e-256

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 45.6%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 47.0%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 32.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.6%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 32.6%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 32.6%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 32.6%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -3.70000000000000029e-256 < t < 1.8000000000000001e-292

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 79.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 79.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 79.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 79.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 79.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 79.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 51.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.4%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

      2. +-commutative 51.4%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

      3. unsub-neg 51.4%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} - c \cdot z\right)} \]

      4. associate-/l* 51.4%

         \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} - c \cdot z\right) \]

      5. associate-/l* 51.4%

         \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} - c \cdot z\right) \]

      6. *-commutative 51.4%

         \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   8. Simplified 51.4%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - z \cdot c\right)} \]

   9. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 51.4%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. associate-*r* 58.1%

          \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

   11. Simplified 58.1%

       \[\leadsto \color{blue}{-\left(b \cdot c\right) \cdot z} \]

   if 1.8000000000000001e-292 < t < 1.15e-16

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 79.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 79.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 79.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 79.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 53.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 53.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 53.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 53.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 53.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 53.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 37.8%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.8%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 37.8%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 1.15e-16 < t < 6.19999999999999962e97

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 73.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 73.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 73.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 73.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 73.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 73.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 43.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around 0 36.4%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 36.4%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-lft-neg-in 36.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)} \]

      3. *-commutative 36.4%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   8. Simplified 36.4%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.34 \cdot 10^{+166}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-256}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;i \leq -9.8 \cdot 10^{+214}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq 2.75 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= i -9.8e+214)
     (* a (* b i))
     (if (<= i -4.6e-7)
       (* b (* c (- z)))
       (if (<= i 2.75e-263)
         t_1
         (if (<= i 1.1e-175)
           (* c (* z (- b)))
           (if (<= i 2.85e-77) t_1 (* y (* i (- 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 = y * (x * z);
	double tmp;
	if (i <= -9.8e+214) {
		tmp = a * (b * i);
	} else if (i <= -4.6e-7) {
		tmp = b * (c * -z);
	} else if (i <= 2.75e-263) {
		tmp = t_1;
	} else if (i <= 1.1e-175) {
		tmp = c * (z * -b);
	} else if (i <= 2.85e-77) {
		tmp = t_1;
	} else {
		tmp = y * (i * -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) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (i <= (-9.8d+214)) then
        tmp = a * (b * i)
    else if (i <= (-4.6d-7)) then
        tmp = b * (c * -z)
    else if (i <= 2.75d-263) then
        tmp = t_1
    else if (i <= 1.1d-175) then
        tmp = c * (z * -b)
    else if (i <= 2.85d-77) then
        tmp = t_1
    else
        tmp = y * (i * -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 t_1 = y * (x * z);
	double tmp;
	if (i <= -9.8e+214) {
		tmp = a * (b * i);
	} else if (i <= -4.6e-7) {
		tmp = b * (c * -z);
	} else if (i <= 2.75e-263) {
		tmp = t_1;
	} else if (i <= 1.1e-175) {
		tmp = c * (z * -b);
	} else if (i <= 2.85e-77) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if i <= -9.8e+214:
		tmp = a * (b * i)
	elif i <= -4.6e-7:
		tmp = b * (c * -z)
	elif i <= 2.75e-263:
		tmp = t_1
	elif i <= 1.1e-175:
		tmp = c * (z * -b)
	elif i <= 2.85e-77:
		tmp = t_1
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (i <= -9.8e+214)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -4.6e-7)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (i <= 2.75e-263)
		tmp = t_1;
	elseif (i <= 1.1e-175)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 2.85e-77)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (i <= -9.8e+214)
		tmp = a * (b * i);
	elseif (i <= -4.6e-7)
		tmp = b * (c * -z);
	elseif (i <= 2.75e-263)
		tmp = t_1;
	elseif (i <= 1.1e-175)
		tmp = c * (z * -b);
	elseif (i <= 2.85e-77)
		tmp = t_1;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.8e+214], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.6e-7], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.75e-263], t$95$1, If[LessEqual[i, 1.1e-175], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.85e-77], t$95$1, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -9.80000000000000065e214

   1. Initial program 52.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 64.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 64.6%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 64.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf 60.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

   7. Taylor expanded in b around inf 49.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -9.80000000000000065e214 < i < -4.5999999999999999e-7

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 74.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 74.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 74.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 74.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 74.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 74.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 74.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 52.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in b around inf 52.5%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.5%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

      2. +-commutative 52.5%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

      3. unsub-neg 52.5%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} - c \cdot z\right)} \]

      4. associate-/l* 55.3%

         \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} - c \cdot z\right) \]

      5. associate-/l* 55.1%

         \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} - c \cdot z\right) \]

      6. *-commutative 55.1%

         \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   8. Simplified 55.1%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - z \cdot c\right)} \]

   9. Taylor expanded in j around 0 39.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 39.0%

          \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

       2. distribute-lft-neg-in 39.0%

          \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

   11. Simplified 39.0%

       \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

   if -4.5999999999999999e-7 < i < 2.74999999999999986e-263 or 1.1e-175 < i < 2.84999999999999991e-77

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 81.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 81.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 81.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 81.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 81.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 81.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 81.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 81.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 39.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 39.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 39.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 39.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 39.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 39.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 36.1%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 36.1%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 2.74999999999999986e-263 < i < 1.1e-175

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 79.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 79.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 79.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 79.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 79.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 79.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 79.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 63.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around 0 48.1%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 48.1%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-lft-neg-in 48.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)} \]

      3. *-commutative 48.1%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   8. Simplified 48.1%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if 2.84999999999999991e-77 < i

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 73.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 73.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 73.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 73.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 73.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 73.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 44.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 44.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 44.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 44.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 44.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 44.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around 0 33.0%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 33.0%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-lft-neg-out 33.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(-i\right) \cdot j\right)} \]

      3. *-commutative 33.0%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   10. Simplified 33.0%

       \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.8 \cdot 10^{+214}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;i \leq 2.75 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 0.00033:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= y -1.65e-27)
     t_1
     (if (<= y -7.8e-247)
       (* c (* t j))
       (if (<= y 3.3e-292)
         (* a (* b i))
         (if (<= y 0.00033)
           (* z (* c (- b)))
           (if (<= y 4.3e+133) (* j (* y (- i))) 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 = y * (x * z);
	double tmp;
	if (y <= -1.65e-27) {
		tmp = t_1;
	} else if (y <= -7.8e-247) {
		tmp = c * (t * j);
	} else if (y <= 3.3e-292) {
		tmp = a * (b * i);
	} else if (y <= 0.00033) {
		tmp = z * (c * -b);
	} else if (y <= 4.3e+133) {
		tmp = j * (y * -i);
	} 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 = y * (x * z)
    if (y <= (-1.65d-27)) then
        tmp = t_1
    else if (y <= (-7.8d-247)) then
        tmp = c * (t * j)
    else if (y <= 3.3d-292) then
        tmp = a * (b * i)
    else if (y <= 0.00033d0) then
        tmp = z * (c * -b)
    else if (y <= 4.3d+133) then
        tmp = j * (y * -i)
    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 = y * (x * z);
	double tmp;
	if (y <= -1.65e-27) {
		tmp = t_1;
	} else if (y <= -7.8e-247) {
		tmp = c * (t * j);
	} else if (y <= 3.3e-292) {
		tmp = a * (b * i);
	} else if (y <= 0.00033) {
		tmp = z * (c * -b);
	} else if (y <= 4.3e+133) {
		tmp = j * (y * -i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if y <= -1.65e-27:
		tmp = t_1
	elif y <= -7.8e-247:
		tmp = c * (t * j)
	elif y <= 3.3e-292:
		tmp = a * (b * i)
	elif y <= 0.00033:
		tmp = z * (c * -b)
	elif y <= 4.3e+133:
		tmp = j * (y * -i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (y <= -1.65e-27)
		tmp = t_1;
	elseif (y <= -7.8e-247)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 3.3e-292)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= 0.00033)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (y <= 4.3e+133)
		tmp = Float64(j * Float64(y * Float64(-i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (y <= -1.65e-27)
		tmp = t_1;
	elseif (y <= -7.8e-247)
		tmp = c * (t * j);
	elseif (y <= 3.3e-292)
		tmp = a * (b * i);
	elseif (y <= 0.00033)
		tmp = z * (c * -b);
	elseif (y <= 4.3e+133)
		tmp = j * (y * -i);
	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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e-27], t$95$1, If[LessEqual[y, -7.8e-247], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-292], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00033], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+133], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.64999999999999999e-27 or 4.29999999999999994e133 < y

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 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 63.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 63.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 63.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 63.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 63.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 63.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 65.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 65.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 65.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 65.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 65.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 40.7%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 40.7%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -1.64999999999999999e-27 < y < -7.8000000000000006e-247

   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. Step-by-step derivation

      1. +-commutative 88.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 88.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 30.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 30.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -7.8000000000000006e-247 < y < 3.29999999999999995e-292

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 58.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 50.2%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

   7. Taylor expanded in b around inf 44.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 3.29999999999999995e-292 < y < 3.3e-4

   1. Initial program 88.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 88.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 88.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 88.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 88.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 88.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 88.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 88.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 88.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 88.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 88.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 88.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in b around inf 47.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.7%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

      2. +-commutative 47.7%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

      3. unsub-neg 47.7%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} - c \cdot z\right)} \]

      4. associate-/l* 47.7%

         \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} - c \cdot z\right) \]

      5. associate-/l* 49.2%

         \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} - c \cdot z\right) \]

      6. *-commutative 49.2%

         \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - z \cdot c\right)} \]

   9. Taylor expanded in b around inf 33.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 33.8%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. associate-*r* 35.3%

          \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

   11. Simplified 35.3%

       \[\leadsto \color{blue}{-\left(b \cdot c\right) \cdot z} \]

   if 3.3e-4 < y < 4.29999999999999994e133

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 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* 61.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 64.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 64.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 64.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 64.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 64.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 64.7%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot a}\right) \]

   7. Simplified 64.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)} \]

   8. Taylor expanded in j around inf 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. associate-*r* 41.6%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. *-commutative 41.6%

         \[\leadsto -\color{blue}{\left(j \cdot i\right)} \cdot y \]

      4. associate-*r* 47.7%

         \[\leadsto -\color{blue}{j \cdot \left(i \cdot y\right)} \]

      5. distribute-rgt-neg-out 47.7%

         \[\leadsto \color{blue}{j \cdot \left(-i \cdot y\right)} \]

      6. distribute-rgt-neg-in 47.7%

         \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(-y\right)\right)} \]

   10. Simplified 47.7%

       \[\leadsto \color{blue}{j \cdot \left(i \cdot \left(-y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 0.00033:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3 \cdot 10^{-72}:\\ \;\;\;\;t\_2 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+18}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - t\_1\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -3e-72)
     (+ t_2 (* z (- (* x y) (* b c))))
     (if (<= j 9.5e+18) (- (- (* c (* t j)) t_1) (* b (* z c))) (- t_2 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 = x * ((t * a) - (y * z));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3e-72) {
		tmp = t_2 + (z * ((x * y) - (b * c)));
	} else if (j <= 9.5e+18) {
		tmp = ((c * (t * j)) - t_1) - (b * (z * c));
	} else {
		tmp = t_2 - 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((t * a) - (y * z))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-3d-72)) then
        tmp = t_2 + (z * ((x * y) - (b * c)))
    else if (j <= 9.5d+18) then
        tmp = ((c * (t * j)) - t_1) - (b * (z * c))
    else
        tmp = t_2 - 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 = x * ((t * a) - (y * z));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3e-72) {
		tmp = t_2 + (z * ((x * y) - (b * c)));
	} else if (j <= 9.5e+18) {
		tmp = ((c * (t * j)) - t_1) - (b * (z * c));
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3e-72:
		tmp = t_2 + (z * ((x * y) - (b * c)))
	elif j <= 9.5e+18:
		tmp = ((c * (t * j)) - t_1) - (b * (z * c))
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3e-72)
		tmp = Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (j <= 9.5e+18)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) - t_1) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3e-72)
		tmp = t_2 + (z * ((x * y) - (b * c)));
	elseif (j <= 9.5e+18)
		tmp = ((c * (t * j)) - t_1) - (b * (z * c));
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3e-72], N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+18], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3e-72

   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. Add Preprocessing

   3. Taylor expanded in z around inf 74.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. *-commutative 74.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 74.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if -3e-72 < j < 9.5e18

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 72.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 72.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 72.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around 0 72.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   if 9.5e18 < j

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around -inf 71.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - -1 \cdot \left(c \cdot z - a \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-*r* 71.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(-1 \cdot \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - -1 \cdot \left(c \cdot z - a \cdot i\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. neg-mul-1 71.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(-1 \cdot \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - -1 \cdot \left(c \cdot z - a \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. distribute-lft-out-- 71.9%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(-1 \cdot \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b} - \left(c \cdot z - a \cdot i\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. associate-/l* 75.2%

         \[\leadsto \left(-b\right) \cdot \left(-1 \cdot \left(\color{blue}{x \cdot \frac{y \cdot z - a \cdot t}{b}} - \left(c \cdot z - a \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 75.2%

         \[\leadsto \left(-b\right) \cdot \left(-1 \cdot \left(x \cdot \frac{y \cdot z - \color{blue}{t \cdot a}}{b} - \left(c \cdot z - a \cdot i\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.2%

         \[\leadsto \left(-b\right) \cdot \left(-1 \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b} - \left(c \cdot z - \color{blue}{i \cdot a}\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 75.2%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(-1 \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b} - \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around 0 70.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+18}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-203}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -9e+31)
     t_2
     (if (<= y -1.75e-248)
       t_1
       (if (<= y 1.85e-203)
         (* c (- (* t j) (* z b)))
         (if (<= y 3.3e+65) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9e+31) {
		tmp = t_2;
	} else if (y <= -1.75e-248) {
		tmp = t_1;
	} else if (y <= 1.85e-203) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3.3e+65) {
		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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-9d+31)) then
        tmp = t_2
    else if (y <= (-1.75d-248)) then
        tmp = t_1
    else if (y <= 1.85d-203) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 3.3d+65) 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9e+31) {
		tmp = t_2;
	} else if (y <= -1.75e-248) {
		tmp = t_1;
	} else if (y <= 1.85e-203) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3.3e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -9e+31:
		tmp = t_2
	elif y <= -1.75e-248:
		tmp = t_1
	elif y <= 1.85e-203:
		tmp = c * ((t * j) - (z * b))
	elif y <= 3.3e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -9e+31)
		tmp = t_2;
	elseif (y <= -1.75e-248)
		tmp = t_1;
	elseif (y <= 1.85e-203)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 3.3e+65)
		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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -9e+31)
		tmp = t_2;
	elseif (y <= -1.75e-248)
		tmp = t_1;
	elseif (y <= 1.85e-203)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 3.3e+65)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+31], t$95$2, If[LessEqual[y, -1.75e-248], t$95$1, If[LessEqual[y, 1.85e-203], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999992e31 or 3.30000000000000023e65 < y

   1. Initial program 60.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 61.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 62.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 69.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 69.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 69.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -8.9999999999999992e31 < y < -1.74999999999999991e-248 or 1.85000000000000001e-203 < y < 3.30000000000000023e65

   1. Initial program 85.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 86.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 86.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 54.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 54.8%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 54.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 54.8%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 54.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]

   if -1.74999999999999991e-248 < y < 1.85000000000000001e-203

   1. Initial program 83.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 83.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 83.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 83.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 83.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 83.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 83.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 83.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 83.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 83.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 83.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 83.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 83.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 83.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 83.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 83.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 58.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-203}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.9 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.9e+174)
     t_2
     (if (<= i -1.45e-74)
       t_1
       (if (<= i 7.6e-249)
         (* t (- (* c j) (* x a)))
         (if (<= i 9.5e-134) 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 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.9e+174) {
		tmp = t_2;
	} else if (i <= -1.45e-74) {
		tmp = t_1;
	} else if (i <= 7.6e-249) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 9.5e-134) {
		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 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.9d+174)) then
        tmp = t_2
    else if (i <= (-1.45d-74)) then
        tmp = t_1
    else if (i <= 7.6d-249) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 9.5d-134) 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 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.9e+174) {
		tmp = t_2;
	} else if (i <= -1.45e-74) {
		tmp = t_1;
	} else if (i <= 7.6e-249) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 9.5e-134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.9e+174:
		tmp = t_2
	elif i <= -1.45e-74:
		tmp = t_1
	elif i <= 7.6e-249:
		tmp = t * ((c * j) - (x * a))
	elif i <= 9.5e-134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.9e+174)
		tmp = t_2;
	elseif (i <= -1.45e-74)
		tmp = t_1;
	elseif (i <= 7.6e-249)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 9.5e-134)
		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 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.9e+174)
		tmp = t_2;
	elseif (i <= -1.45e-74)
		tmp = t_1;
	elseif (i <= 7.6e-249)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 9.5e-134)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.9e+174], t$95$2, If[LessEqual[i, -1.45e-74], t$95$1, If[LessEqual[i, 7.6e-249], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e-134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.9000000000000001e174 or 9.5000000000000008e-134 < i

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 54.1%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in i around inf 52.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.6%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 52.6%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 52.6%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      4. *-commutative 52.6%

         \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   8. Simplified 52.6%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if -1.9000000000000001e174 < i < -1.45e-74 or 7.6000000000000002e-249 < i < 9.5000000000000008e-134

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 51.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -1.45e-74 < i < 7.6000000000000002e-249

   1. Initial program 80.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 80.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 58.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 58.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 58.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 58.1%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   7. Simplified 58.1%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+174}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 42.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{-137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -8.5e-137)
     t_2
     (if (<= c 8.5e-298)
       t_1
       (if (<= c 9.2e-225) (* a (* b i)) (if (<= c 5.2e-109) 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);
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.5e-137) {
		tmp = t_2;
	} else if (c <= 8.5e-298) {
		tmp = t_1;
	} else if (c <= 9.2e-225) {
		tmp = a * (b * i);
	} else if (c <= 5.2e-109) {
		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_2 = c * ((t * j) - (z * b))
    if (c <= (-8.5d-137)) then
        tmp = t_2
    else if (c <= 8.5d-298) then
        tmp = t_1
    else if (c <= 9.2d-225) then
        tmp = a * (b * i)
    else if (c <= 5.2d-109) 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);
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.5e-137) {
		tmp = t_2;
	} else if (c <= 8.5e-298) {
		tmp = t_1;
	} else if (c <= 9.2e-225) {
		tmp = a * (b * i);
	} else if (c <= 5.2e-109) {
		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_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -8.5e-137:
		tmp = t_2
	elif c <= 8.5e-298:
		tmp = t_1
	elif c <= 9.2e-225:
		tmp = a * (b * i)
	elif c <= 5.2e-109:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -8.5e-137)
		tmp = t_2;
	elseif (c <= 8.5e-298)
		tmp = t_1;
	elseif (c <= 9.2e-225)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 5.2e-109)
		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_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -8.5e-137)
		tmp = t_2;
	elseif (c <= 8.5e-298)
		tmp = t_1;
	elseif (c <= 9.2e-225)
		tmp = a * (b * i);
	elseif (c <= 5.2e-109)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e-137], t$95$2, If[LessEqual[c, 8.5e-298], t$95$1, If[LessEqual[c, 9.2e-225], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e-109], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.5000000000000001e-137 or 5.1999999999999997e-109 < c

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      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 c around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -8.5000000000000001e-137 < c < 8.49999999999999957e-298 or 9.1999999999999995e-225 < c < 5.1999999999999997e-109

   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. Step-by-step derivation

      1. +-commutative 77.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 78.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 78.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 78.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 78.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 78.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 78.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 78.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 78.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 78.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 59.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 59.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 59.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 38.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   10. Simplified 38.9%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 8.49999999999999957e-298 < c < 9.1999999999999995e-225

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 68.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 64.1%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 64.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf 49.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

   7. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-225}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= y -2.75e-30)
     t_1
     (if (<= y -1.9e-246)
       (* c (* t j))
       (if (<= y 2.65e-292)
         (* a (* b i))
         (if (<= y 2.4e-14) (* z (* c (- 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 = y * (x * z);
	double tmp;
	if (y <= -2.75e-30) {
		tmp = t_1;
	} else if (y <= -1.9e-246) {
		tmp = c * (t * j);
	} else if (y <= 2.65e-292) {
		tmp = a * (b * i);
	} else if (y <= 2.4e-14) {
		tmp = z * (c * -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 = y * (x * z)
    if (y <= (-2.75d-30)) then
        tmp = t_1
    else if (y <= (-1.9d-246)) then
        tmp = c * (t * j)
    else if (y <= 2.65d-292) then
        tmp = a * (b * i)
    else if (y <= 2.4d-14) then
        tmp = z * (c * -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 = y * (x * z);
	double tmp;
	if (y <= -2.75e-30) {
		tmp = t_1;
	} else if (y <= -1.9e-246) {
		tmp = c * (t * j);
	} else if (y <= 2.65e-292) {
		tmp = a * (b * i);
	} else if (y <= 2.4e-14) {
		tmp = z * (c * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if y <= -2.75e-30:
		tmp = t_1
	elif y <= -1.9e-246:
		tmp = c * (t * j)
	elif y <= 2.65e-292:
		tmp = a * (b * i)
	elif y <= 2.4e-14:
		tmp = z * (c * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (y <= -2.75e-30)
		tmp = t_1;
	elseif (y <= -1.9e-246)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 2.65e-292)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= 2.4e-14)
		tmp = Float64(z * Float64(c * Float64(-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 = y * (x * z);
	tmp = 0.0;
	if (y <= -2.75e-30)
		tmp = t_1;
	elseif (y <= -1.9e-246)
		tmp = c * (t * j);
	elseif (y <= 2.65e-292)
		tmp = a * (b * i);
	elseif (y <= 2.4e-14)
		tmp = z * (c * -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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e-30], t$95$1, If[LessEqual[y, -1.9e-246], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-292], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-14], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.74999999999999988e-30 or 2.4e-14 < y

   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. Step-by-step derivation

      1. +-commutative 64.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 66.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 66.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 66.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 66.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 66.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 66.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 66.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 66.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 63.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 63.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 63.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 63.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 63.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 36.6%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 36.6%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -2.74999999999999988e-30 < y < -1.89999999999999988e-246

   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. Step-by-step derivation

      1. +-commutative 88.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 88.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 88.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 88.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 30.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.3%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 30.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.89999999999999988e-246 < y < 2.6499999999999998e-292

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 58.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 50.2%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

   7. Taylor expanded in b around inf 44.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 2.6499999999999998e-292 < y < 2.4e-14

   1. Initial program 87.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 87.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 87.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 87.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 87.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in b around inf 48.3%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z\right) + \frac{c \cdot \left(j \cdot t\right)}{b}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 48.3%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + \frac{c \cdot \left(j \cdot t\right)}{b}\right) \]

      2. +-commutative 48.3%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} + \left(-c \cdot z\right)\right)} \]

      3. unsub-neg 48.3%

         \[\leadsto b \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{b} - c \cdot z\right)} \]

      4. associate-/l* 48.3%

         \[\leadsto b \cdot \left(\color{blue}{c \cdot \frac{j \cdot t}{b}} - c \cdot z\right) \]

      5. associate-/l* 49.9%

         \[\leadsto b \cdot \left(c \cdot \color{blue}{\left(j \cdot \frac{t}{b}\right)} - c \cdot z\right) \]

      6. *-commutative 49.9%

         \[\leadsto b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   8. Simplified 49.9%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(j \cdot \frac{t}{b}\right) - z \cdot c\right)} \]

   9. Taylor expanded in b around inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 35.5%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. associate-*r* 37.0%

          \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

   11. Simplified 37.0%

       \[\leadsto \color{blue}{-\left(b \cdot c\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-246}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-292}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -6.3 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= x -6.3e+50)
     t_1
     (if (<= x -2.05e-109)
       (* a (* b i))
       (if (<= x 6.4e-35) (* c (* t j)) 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 = x * (y * z);
	double tmp;
	if (x <= -6.3e+50) {
		tmp = t_1;
	} else if (x <= -2.05e-109) {
		tmp = a * (b * i);
	} else if (x <= 6.4e-35) {
		tmp = c * (t * j);
	} 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 = x * (y * z)
    if (x <= (-6.3d+50)) then
        tmp = t_1
    else if (x <= (-2.05d-109)) then
        tmp = a * (b * i)
    else if (x <= 6.4d-35) then
        tmp = c * (t * j)
    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 = x * (y * z);
	double tmp;
	if (x <= -6.3e+50) {
		tmp = t_1;
	} else if (x <= -2.05e-109) {
		tmp = a * (b * i);
	} else if (x <= 6.4e-35) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if x <= -6.3e+50:
		tmp = t_1
	elif x <= -2.05e-109:
		tmp = a * (b * i)
	elif x <= 6.4e-35:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (x <= -6.3e+50)
		tmp = t_1;
	elseif (x <= -2.05e-109)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 6.4e-35)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (x <= -6.3e+50)
		tmp = t_1;
	elseif (x <= -2.05e-109)
		tmp = a * (b * i);
	elseif (x <= 6.4e-35)
		tmp = c * (t * j);
	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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.3e+50], t$95$1, If[LessEqual[x, -2.05e-109], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e-35], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.29999999999999986e50 or 6.3999999999999996e-35 < x

   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. Step-by-step derivation

      1. +-commutative 76.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 50.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 50.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 50.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 37.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.6%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   10. Simplified 37.6%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if -6.29999999999999986e50 < x < -2.0500000000000001e-109

   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. Add Preprocessing

   3. Taylor expanded in i around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 42.4%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 42.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf 40.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

   7. Taylor expanded in b around inf 33.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -2.0500000000000001e-109 < x < 6.3999999999999996e-35

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 27.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 49.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{+174} \lor \neg \left(i \leq 2.7 \cdot 10^{-134}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.85e+174) (not (<= i 2.7e-134)))
   (* i (- (* a b) (* y 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 tmp;
	if ((i <= -1.85e+174) || !(i <= 2.7e-134)) {
		tmp = i * ((a * b) - (y * 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) :: tmp
    if ((i <= (-1.85d+174)) .or. (.not. (i <= 2.7d-134))) then
        tmp = i * ((a * b) - (y * 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 tmp;
	if ((i <= -1.85e+174) || !(i <= 2.7e-134)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.85e+174) or not (i <= 2.7e-134):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.85e+174) || !(i <= 2.7e-134))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * 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)
	tmp = 0.0;
	if ((i <= -1.85e+174) || ~((i <= 2.7e-134)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.85e+174], N[Not[LessEqual[i, 2.7e-134]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.8500000000000001e174 or 2.6999999999999998e-134 < i

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 54.1%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in i around inf 52.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.6%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 52.6%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 52.6%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      4. *-commutative 52.6%

         \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   8. Simplified 52.6%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]

   if -1.8500000000000001e174 < i < 2.6999999999999998e-134

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 77.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 77.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 77.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 77.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 77.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 77.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 77.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 77.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 77.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 77.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 77.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 77.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{+174} \lor \neg \left(i \leq 2.7 \cdot 10^{-134}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-11} \lor \neg \left(t \leq 1.6 \cdot 10^{+62}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.05e-11) (not (<= t 1.6e+62))) (* c (* t j)) (* y (* x z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.05e-11) || !(t <= 1.6e+62)) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	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 ((t <= (-1.05d-11)) .or. (.not. (t <= 1.6d+62))) then
        tmp = c * (t * j)
    else
        tmp = y * (x * z)
    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 ((t <= -1.05e-11) || !(t <= 1.6e+62)) {
		tmp = c * (t * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.05e-11) or not (t <= 1.6e+62):
		tmp = c * (t * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.05e-11) || !(t <= 1.6e+62))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.05e-11) || ~((t <= 1.6e+62)))
		tmp = c * (t * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.05e-11], N[Not[LessEqual[t, 1.6e+62]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e-11 or 1.59999999999999992e62 < t

   1. Initial program 67.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 67.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 67.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 67.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 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 c around inf 44.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 34.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.0499999999999999e-11 < t < 1.59999999999999992e62

   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. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 80.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 80.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 80.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 80.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 80.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 80.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 80.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 80.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 80.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 80.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 80.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 49.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 49.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 49.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   7. Simplified 49.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 31.3%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 31.3%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-11} \lor \neg \left(t \leq 1.6 \cdot 10^{+62}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+26} \lor \neg \left(b \leq 5.2 \cdot 10^{-73}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -9e+26) (not (<= b 5.2e-73))) (* 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 ((b <= -9e+26) || !(b <= 5.2e-73)) {
		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 ((b <= (-9d+26)) .or. (.not. (b <= 5.2d-73))) 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 ((b <= -9e+26) || !(b <= 5.2e-73)) {
		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 (b <= -9e+26) or not (b <= 5.2e-73):
		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 ((b <= -9e+26) || !(b <= 5.2e-73))
		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 ((b <= -9e+26) || ~((b <= 5.2e-73)))
		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[Or[LessEqual[b, -9e+26], N[Not[LessEqual[b, 5.2e-73]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.99999999999999957e26 or 5.2000000000000002e-73 < b

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 44.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-*r* 43.3%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in b around inf 44.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

   7. Taylor expanded in b around inf 30.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -8.99999999999999957e26 < b < 5.2000000000000002e-73

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 74.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 74.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fma-neg 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      15. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 34.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   6. Taylor expanded in j around inf 26.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.9%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   8. Simplified 26.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+26} \lor \neg \left(b \leq 5.2 \cdot 10^{-73}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.7% 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 74.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in i around inf 43.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]
4. Step-by-step derivation

   1. *-commutative 43.7%

      \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. associate-*r* 42.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

5. Simplified 42.9%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

6. Taylor expanded in b around inf 40.5%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{b}\right)} \]

7. Taylor expanded in b around inf 18.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
8. Add Preprocessing

Developer target: 68.0% 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 2024091 
(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)))))