Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.0% → 82.6%

Time: 25.1s

Alternatives: 22

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.0%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-+l+ 0.0%

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

      4. distribute-rgt-neg-in 0.0%

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

      5. +-commutative 0.0%

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

      6. fma-def 4.7%

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

      7. sub-neg 4.7%

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

      8. +-commutative 4.7%

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

      9. distribute-neg-in 4.7%

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

      10. unsub-neg 4.7%

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

      11. remove-double-neg 4.7%

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

      12. *-commutative 4.7%

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

   3. Simplified 14.0%

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

   4. Taylor expanded in t around 0 46.7%

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

      1. fma-def 46.7%

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

      2. fma-def 49.0%

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

      3. associate-*r* 49.0%

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

      4. neg-mul-1 49.0%

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

      5. +-commutative 49.0%

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

      6. *-commutative 49.0%

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

      7. *-commutative 49.0%

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

      8. mul-1-neg 49.0%

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

      9. distribute-lft-neg-in 49.0%

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

      10. cancel-sign-sub-inv 49.0%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in z around inf 60.8%

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

4. Final simplification 85.9%

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

Alternative 2: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = i * ((t * b) - (y * j));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * 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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 91.0%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-+l+ 0.0%

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

      4. distribute-rgt-neg-in 0.0%

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

      5. +-commutative 0.0%

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

      6. fma-def 4.7%

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

      7. sub-neg 4.7%

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

      8. +-commutative 4.7%

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

      9. distribute-neg-in 4.7%

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

      10. unsub-neg 4.7%

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

      11. remove-double-neg 4.7%

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

      12. *-commutative 4.7%

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

   3. Simplified 14.0%

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

   4. Taylor expanded in i around inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

   6. Simplified 51.6%

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

4. Final simplification 84.3%

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

Alternative 3: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{+169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.42 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_3 (- (* t (* b i)) (* j (- (* y i) (* a c))))))
   (if (<= j -1.8e+191)
     t_1
     (if (<= j -1.2e+169)
       t_2
       (if (<= j -4.2e+28)
         t_3
         (if (<= j 4.2e-151)
           t_2
           (if (<= j 1.42e-74)
             (* t (- (* b i) (* x a)))
             (if (<= j 3.5e-62)
               (* z (- (* x y) (* b c)))
               (if (<= j 7.5e-13)
                 t_3
                 (if (<= j 8e+19) t_2 (- t_1 (* b (* z c)))))))))))))

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 * ((a * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_3 = (t * (b * i)) - (j * ((y * i) - (a * c)));
	double tmp;
	if (j <= -1.8e+191) {
		tmp = t_1;
	} else if (j <= -1.2e+169) {
		tmp = t_2;
	} else if (j <= -4.2e+28) {
		tmp = t_3;
	} else if (j <= 4.2e-151) {
		tmp = t_2;
	} else if (j <= 1.42e-74) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.5e-62) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 7.5e-13) {
		tmp = t_3;
	} else if (j <= 8e+19) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    t_3 = (t * (b * i)) - (j * ((y * i) - (a * c)))
    if (j <= (-1.8d+191)) then
        tmp = t_1
    else if (j <= (-1.2d+169)) then
        tmp = t_2
    else if (j <= (-4.2d+28)) then
        tmp = t_3
    else if (j <= 4.2d-151) then
        tmp = t_2
    else if (j <= 1.42d-74) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 3.5d-62) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 7.5d-13) then
        tmp = t_3
    else if (j <= 8d+19) then
        tmp = t_2
    else
        tmp = t_1 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_3 = (t * (b * i)) - (j * ((y * i) - (a * c)));
	double tmp;
	if (j <= -1.8e+191) {
		tmp = t_1;
	} else if (j <= -1.2e+169) {
		tmp = t_2;
	} else if (j <= -4.2e+28) {
		tmp = t_3;
	} else if (j <= 4.2e-151) {
		tmp = t_2;
	} else if (j <= 1.42e-74) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.5e-62) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 7.5e-13) {
		tmp = t_3;
	} else if (j <= 8e+19) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	t_3 = (t * (b * i)) - (j * ((y * i) - (a * c)))
	tmp = 0
	if j <= -1.8e+191:
		tmp = t_1
	elif j <= -1.2e+169:
		tmp = t_2
	elif j <= -4.2e+28:
		tmp = t_3
	elif j <= 4.2e-151:
		tmp = t_2
	elif j <= 1.42e-74:
		tmp = t * ((b * i) - (x * a))
	elif j <= 3.5e-62:
		tmp = z * ((x * y) - (b * c))
	elif j <= 7.5e-13:
		tmp = t_3
	elif j <= 8e+19:
		tmp = t_2
	else:
		tmp = t_1 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(Float64(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	tmp = 0.0
	if (j <= -1.8e+191)
		tmp = t_1;
	elseif (j <= -1.2e+169)
		tmp = t_2;
	elseif (j <= -4.2e+28)
		tmp = t_3;
	elseif (j <= 4.2e-151)
		tmp = t_2;
	elseif (j <= 1.42e-74)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 3.5e-62)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 7.5e-13)
		tmp = t_3;
	elseif (j <= 8e+19)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	t_3 = (t * (b * i)) - (j * ((y * i) - (a * c)));
	tmp = 0.0;
	if (j <= -1.8e+191)
		tmp = t_1;
	elseif (j <= -1.2e+169)
		tmp = t_2;
	elseif (j <= -4.2e+28)
		tmp = t_3;
	elseif (j <= 4.2e-151)
		tmp = t_2;
	elseif (j <= 1.42e-74)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 3.5e-62)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 7.5e-13)
		tmp = t_3;
	elseif (j <= 8e+19)
		tmp = t_2;
	else
		tmp = t_1 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+191], t$95$1, If[LessEqual[j, -1.2e+169], t$95$2, If[LessEqual[j, -4.2e+28], t$95$3, If[LessEqual[j, 4.2e-151], t$95$2, If[LessEqual[j, 1.42e-74], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-62], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-13], t$95$3, If[LessEqual[j, 8e+19], t$95$2, N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.8e191

   1. Initial program 85.6%

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

      1. sub-neg 85.6%

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

      2. +-commutative 85.6%

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

      3. associate-+l+ 85.6%

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

      4. distribute-rgt-neg-in 85.6%

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

      5. +-commutative 85.6%

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

      6. fma-def 85.6%

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

      7. sub-neg 85.6%

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

      8. +-commutative 85.6%

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

      9. distribute-neg-in 85.6%

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

      10. unsub-neg 85.6%

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

      11. remove-double-neg 85.6%

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

      12. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in t around 0 76.5%

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

      1. fma-def 76.5%

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

      2. fma-def 76.5%

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

      3. associate-*r* 76.5%

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

      4. neg-mul-1 76.5%

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

      5. +-commutative 76.5%

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

      6. *-commutative 76.5%

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

      7. *-commutative 76.5%

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

      8. mul-1-neg 76.5%

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

      9. distribute-lft-neg-in 76.5%

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

      10. cancel-sign-sub-inv 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in j around inf 95.2%

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

   if -1.8e191 < j < -1.1999999999999999e169 or -4.19999999999999978e28 < j < 4.19999999999999981e-151 or 7.5000000000000004e-13 < j < 8e19

   1. Initial program 77.3%

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

      1. +-commutative 77.3%

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

      2. fma-def 77.3%

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

      3. *-commutative 77.3%

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

      4. *-commutative 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in j around 0 72.4%

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

   if -1.1999999999999999e169 < j < -4.19999999999999978e28 or 3.5000000000000001e-62 < j < 7.5000000000000004e-13

   1. Initial program 73.0%

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

      1. cancel-sign-sub 73.0%

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

      2. cancel-sign-sub-inv 73.0%

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

      3. *-commutative 73.0%

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

      4. remove-double-neg 73.0%

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

      5. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in i around inf 76.9%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*r* 79.6%

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

   6. Simplified 79.6%

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

   if 4.19999999999999981e-151 < j < 1.4200000000000001e-74

   1. Initial program 48.3%

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

      1. sub-neg 48.3%

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

      2. +-commutative 48.3%

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

      3. associate-+l+ 48.3%

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

      4. distribute-rgt-neg-in 48.3%

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

      5. +-commutative 48.3%

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

      6. fma-def 53.1%

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

      7. sub-neg 53.1%

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

      8. +-commutative 53.1%

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

      9. distribute-neg-in 53.1%

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

      10. unsub-neg 53.1%

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

      11. remove-double-neg 53.1%

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

      12. *-commutative 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in t around inf 71.7%

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

   if 1.4200000000000001e-74 < j < 3.5000000000000001e-62

   1. Initial program 75.0%

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

      1. sub-neg 75.0%

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

      2. +-commutative 75.0%

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

      3. associate-+l+ 75.0%

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

      4. distribute-rgt-neg-in 75.0%

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

      5. +-commutative 75.0%

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

      6. fma-def 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. unsub-neg 100.0%

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

      11. remove-double-neg 100.0%

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

      12. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 50.0%

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

      1. fma-def 50.0%

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

      2. fma-def 50.0%

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

      3. associate-*r* 50.0%

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

      4. neg-mul-1 50.0%

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

      5. +-commutative 50.0%

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

      6. *-commutative 50.0%

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

      7. *-commutative 50.0%

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

      8. mul-1-neg 50.0%

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

      9. distribute-lft-neg-in 50.0%

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

      10. cancel-sign-sub-inv 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in z around inf 100.0%

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

   if 8e19 < j

   1. Initial program 79.9%

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

      1. cancel-sign-sub 79.9%

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

      2. cancel-sign-sub-inv 79.9%

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

      3. *-commutative 79.9%

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

      4. remove-double-neg 79.9%

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

      5. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in c around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*r* 74.1%

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

      4. distribute-rgt-neg-in 74.1%

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

      5. *-commutative 74.1%

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

   6. Simplified 74.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.42 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 4: 65.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := \left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_1\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (- (* c (* a j)) (* a (* x t))) t_1))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -1.02e+105)
     t_3
     (if (<= y 1.2e-62)
       t_2
       (if (<= y 4.6e+92)
         (+ (* x (- (* y z) (* t a))) t_1)
         (if (<= y 2.45e+140) 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 = b * ((t * i) - (z * c));
	double t_2 = ((c * (a * j)) - (a * (x * t))) + t_1;
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.02e+105) {
		tmp = t_3;
	} else if (y <= 1.2e-62) {
		tmp = t_2;
	} else if (y <= 4.6e+92) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (y <= 2.45e+140) {
		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 = b * ((t * i) - (z * c))
    t_2 = ((c * (a * j)) - (a * (x * t))) + t_1
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-1.02d+105)) then
        tmp = t_3
    else if (y <= 1.2d-62) then
        tmp = t_2
    else if (y <= 4.6d+92) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (y <= 2.45d+140) 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 = b * ((t * i) - (z * c));
	double t_2 = ((c * (a * j)) - (a * (x * t))) + t_1;
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.02e+105) {
		tmp = t_3;
	} else if (y <= 1.2e-62) {
		tmp = t_2;
	} else if (y <= 4.6e+92) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (y <= 2.45e+140) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = ((c * (a * j)) - (a * (x * t))) + t_1
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.02e+105:
		tmp = t_3
	elif y <= 1.2e-62:
		tmp = t_2
	elif y <= 4.6e+92:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif y <= 2.45e+140:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(Float64(c * Float64(a * j)) - Float64(a * Float64(x * t))) + t_1)
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.02e+105)
		tmp = t_3;
	elseif (y <= 1.2e-62)
		tmp = t_2;
	elseif (y <= 4.6e+92)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (y <= 2.45e+140)
		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 = b * ((t * i) - (z * c));
	t_2 = ((c * (a * j)) - (a * (x * t))) + t_1;
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.02e+105)
		tmp = t_3;
	elseif (y <= 1.2e-62)
		tmp = t_2;
	elseif (y <= 4.6e+92)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (y <= 2.45e+140)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+105], t$95$3, If[LessEqual[y, 1.2e-62], t$95$2, If[LessEqual[y, 4.6e+92], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 2.45e+140], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e105 or 2.4499999999999998e140 < y

   1. Initial program 63.2%

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

      1. sub-neg 63.2%

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

      2. +-commutative 63.2%

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

      3. associate-+l+ 63.2%

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

      4. distribute-rgt-neg-in 63.2%

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

      5. +-commutative 63.2%

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

      6. fma-def 65.9%

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

      7. sub-neg 65.9%

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

      8. +-commutative 65.9%

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

      9. distribute-neg-in 65.9%

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

      10. unsub-neg 65.9%

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

      11. remove-double-neg 65.9%

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

      12. *-commutative 65.9%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in t around 0 71.4%

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

      1. fma-def 72.7%

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

      2. fma-def 72.7%

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

      3. associate-*r* 72.7%

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

      4. neg-mul-1 72.7%

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

      5. +-commutative 72.7%

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

      6. *-commutative 72.7%

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

      7. *-commutative 72.7%

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

      8. mul-1-neg 72.7%

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

      9. distribute-lft-neg-in 72.7%

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

      10. cancel-sign-sub-inv 72.7%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

   9. Simplified 78.5%

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

   if -1.02e105 < y < 1.19999999999999992e-62 or 4.59999999999999997e92 < y < 2.4499999999999998e140

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. fma-def 81.9%

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

      3. *-commutative 81.9%

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

      4. *-commutative 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in y around 0 73.5%

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

   if 1.19999999999999992e-62 < y < 4.59999999999999997e92

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

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

      2. fma-def 75.6%

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

      3. *-commutative 75.6%

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

      4. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in j around 0 67.7%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+140}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 5: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (* b i)) (* j (- (* y i) (* a c)))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -9.5e-22)
     t_2
     (if (<= z -8.5e-239)
       t_1
       (if (<= z -1.95e-306)
         (- (* c (* a j)) (* a (* x t)))
         (if (<= z 9.6e+120) 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 * (b * i)) - (j * ((y * i) - (a * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.5e-22) {
		tmp = t_2;
	} else if (z <= -8.5e-239) {
		tmp = t_1;
	} else if (z <= -1.95e-306) {
		tmp = (c * (a * j)) - (a * (x * t));
	} else if (z <= 9.6e+120) {
		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 * (b * i)) - (j * ((y * i) - (a * c)))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-9.5d-22)) then
        tmp = t_2
    else if (z <= (-8.5d-239)) then
        tmp = t_1
    else if (z <= (-1.95d-306)) then
        tmp = (c * (a * j)) - (a * (x * t))
    else if (z <= 9.6d+120) 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 * (b * i)) - (j * ((y * i) - (a * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -9.5e-22) {
		tmp = t_2;
	} else if (z <= -8.5e-239) {
		tmp = t_1;
	} else if (z <= -1.95e-306) {
		tmp = (c * (a * j)) - (a * (x * t));
	} else if (z <= 9.6e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (b * i)) - (j * ((y * i) - (a * c)))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -9.5e-22:
		tmp = t_2
	elif z <= -8.5e-239:
		tmp = t_1
	elif z <= -1.95e-306:
		tmp = (c * (a * j)) - (a * (x * t))
	elif z <= 9.6e+120:
		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(t * Float64(b * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -9.5e-22)
		tmp = t_2;
	elseif (z <= -8.5e-239)
		tmp = t_1;
	elseif (z <= -1.95e-306)
		tmp = Float64(Float64(c * Float64(a * j)) - Float64(a * Float64(x * t)));
	elseif (z <= 9.6e+120)
		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 * (b * i)) - (j * ((y * i) - (a * c)));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -9.5e-22)
		tmp = t_2;
	elseif (z <= -8.5e-239)
		tmp = t_1;
	elseif (z <= -1.95e-306)
		tmp = (c * (a * j)) - (a * (x * t));
	elseif (z <= 9.6e+120)
		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[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-22], t$95$2, If[LessEqual[z, -8.5e-239], t$95$1, If[LessEqual[z, -1.95e-306], N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+120], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999994e-22 or 9.60000000000000004e120 < z

   1. Initial program 72.8%

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

      1. sub-neg 72.8%

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

      2. +-commutative 72.8%

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

      3. associate-+l+ 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

      5. +-commutative 72.8%

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

      6. fma-def 73.6%

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

      7. sub-neg 73.6%

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

      8. +-commutative 73.6%

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

      9. distribute-neg-in 73.6%

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

      10. unsub-neg 73.6%

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

      11. remove-double-neg 73.6%

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

      12. *-commutative 73.6%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. fma-def 72.8%

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

      2. fma-def 72.8%

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

      3. associate-*r* 72.8%

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

      4. neg-mul-1 72.8%

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

      5. +-commutative 72.8%

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

      6. *-commutative 72.8%

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

      7. *-commutative 72.8%

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

      8. mul-1-neg 72.8%

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

      9. distribute-lft-neg-in 72.8%

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

      10. cancel-sign-sub-inv 72.8%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in z around inf 66.5%

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

   if -9.4999999999999994e-22 < z < -8.49999999999999958e-239 or -1.95e-306 < z < 9.60000000000000004e120

   1. Initial program 81.2%

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

      1. cancel-sign-sub 81.2%

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

      2. cancel-sign-sub-inv 81.2%

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

      3. *-commutative 81.2%

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

      4. remove-double-neg 81.2%

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

      5. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in i around inf 67.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-*r* 63.7%

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

   6. Simplified 63.7%

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

   if -8.49999999999999958e-239 < z < -1.95e-306

   1. Initial program 47.6%

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

      1. +-commutative 47.6%

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

      2. fma-def 47.6%

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

      3. *-commutative 47.6%

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

      4. *-commutative 47.6%

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

   3. Simplified 47.6%

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

   4. Taylor expanded in y around 0 84.5%

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

   5. Taylor expanded in b around 0 92.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-306}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(b \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 6: 39.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-116}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= z -1.12e+112)
     (* y (* x z))
     (if (<= z -4.4e-21)
       (* z (* b (- c)))
       (if (<= z -6.5e-84)
         (* y (* i (- j)))
         (if (<= z 3.7e-138)
           t_1
           (if (<= z 4.3e-116)
             (* i (* t b))
             (if (<= z 3.8e+162) t_1 (* c (* b (- z)))))))))))

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 * ((c * j) - (x * t));
	double tmp;
	if (z <= -1.12e+112) {
		tmp = y * (x * z);
	} else if (z <= -4.4e-21) {
		tmp = z * (b * -c);
	} else if (z <= -6.5e-84) {
		tmp = y * (i * -j);
	} else if (z <= 3.7e-138) {
		tmp = t_1;
	} else if (z <= 4.3e-116) {
		tmp = i * (t * b);
	} else if (z <= 3.8e+162) {
		tmp = t_1;
	} else {
		tmp = c * (b * -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) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (z <= (-1.12d+112)) then
        tmp = y * (x * z)
    else if (z <= (-4.4d-21)) then
        tmp = z * (b * -c)
    else if (z <= (-6.5d-84)) then
        tmp = y * (i * -j)
    else if (z <= 3.7d-138) then
        tmp = t_1
    else if (z <= 4.3d-116) then
        tmp = i * (t * b)
    else if (z <= 3.8d+162) then
        tmp = t_1
    else
        tmp = c * (b * -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 t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (z <= -1.12e+112) {
		tmp = y * (x * z);
	} else if (z <= -4.4e-21) {
		tmp = z * (b * -c);
	} else if (z <= -6.5e-84) {
		tmp = y * (i * -j);
	} else if (z <= 3.7e-138) {
		tmp = t_1;
	} else if (z <= 4.3e-116) {
		tmp = i * (t * b);
	} else if (z <= 3.8e+162) {
		tmp = t_1;
	} else {
		tmp = c * (b * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if z <= -1.12e+112:
		tmp = y * (x * z)
	elif z <= -4.4e-21:
		tmp = z * (b * -c)
	elif z <= -6.5e-84:
		tmp = y * (i * -j)
	elif z <= 3.7e-138:
		tmp = t_1
	elif z <= 4.3e-116:
		tmp = i * (t * b)
	elif z <= 3.8e+162:
		tmp = t_1
	else:
		tmp = c * (b * -z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (z <= -1.12e+112)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -4.4e-21)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (z <= -6.5e-84)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (z <= 3.7e-138)
		tmp = t_1;
	elseif (z <= 4.3e-116)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 3.8e+162)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(b * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (z <= -1.12e+112)
		tmp = y * (x * z);
	elseif (z <= -4.4e-21)
		tmp = z * (b * -c);
	elseif (z <= -6.5e-84)
		tmp = y * (i * -j);
	elseif (z <= 3.7e-138)
		tmp = t_1;
	elseif (z <= 4.3e-116)
		tmp = i * (t * b);
	elseif (z <= 3.8e+162)
		tmp = t_1;
	else
		tmp = c * (b * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+112], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-21], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-84], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-138], t$95$1, If[LessEqual[z, 4.3e-116], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+162], t$95$1, N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.12e112

   1. Initial program 71.1%

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

      1. sub-neg 71.1%

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

      2. +-commutative 71.1%

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

      3. associate-+l+ 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. +-commutative 71.1%

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

      6. fma-def 73.7%

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

      7. sub-neg 73.7%

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

      8. +-commutative 73.7%

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

      9. distribute-neg-in 73.7%

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

      10. unsub-neg 73.7%

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

      11. remove-double-neg 73.7%

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

      12. *-commutative 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around 0 66.5%

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

      1. fma-def 66.5%

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

      2. fma-def 66.5%

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

      3. associate-*r* 66.5%

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

      4. neg-mul-1 66.5%

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

      5. +-commutative 66.5%

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

      6. *-commutative 66.5%

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

      7. *-commutative 66.5%

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

      8. mul-1-neg 66.5%

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

      9. distribute-lft-neg-in 66.5%

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

      10. cancel-sign-sub-inv 66.5%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in z around inf 58.9%

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

   8. Taylor expanded in y around inf 51.1%

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

   if -1.12e112 < z < -4.4000000000000001e-21

   1. Initial program 72.6%

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

      1. sub-neg 72.6%

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

      2. +-commutative 72.6%

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

      3. associate-+l+ 72.6%

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

      4. distribute-rgt-neg-in 72.6%

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

      5. +-commutative 72.6%

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

      6. fma-def 72.6%

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

      7. sub-neg 72.6%

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

      8. +-commutative 72.6%

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

      9. distribute-neg-in 72.6%

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

      10. unsub-neg 72.6%

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

      11. remove-double-neg 72.6%

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

      12. *-commutative 72.6%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in t around 0 75.1%

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

      1. fma-def 78.7%

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

      2. fma-def 78.7%

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

      3. associate-*r* 78.7%

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

      4. neg-mul-1 78.7%

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

      5. +-commutative 78.7%

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

      6. *-commutative 78.7%

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

      7. *-commutative 78.7%

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

      8. mul-1-neg 78.7%

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

      9. distribute-lft-neg-in 78.7%

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

      10. cancel-sign-sub-inv 78.7%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in z around inf 68.2%

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

   8. Taylor expanded in c around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. neg-mul-1 47.1%

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

      3. distribute-lft-neg-in 47.1%

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

      4. *-commutative 47.1%

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

      5. associate-*l* 47.2%

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

      6. distribute-rgt-neg-in 47.2%

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

      7. *-commutative 47.2%

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

   10. Simplified 47.2%

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

   if -4.4000000000000001e-21 < z < -6.50000000000000022e-84

   1. Initial program 69.6%

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

      1. sub-neg 69.6%

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

      2. +-commutative 69.6%

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

      3. associate-+l+ 69.6%

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

      4. distribute-rgt-neg-in 69.6%

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

      5. +-commutative 69.6%

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

      6. fma-def 69.6%

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

      7. sub-neg 69.6%

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

      8. +-commutative 69.6%

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

      9. distribute-neg-in 69.6%

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

      10. unsub-neg 69.6%

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

      11. remove-double-neg 69.6%

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

      12. *-commutative 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in t around 0 69.0%

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

      1. fma-def 69.0%

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

      2. fma-def 69.0%

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

      3. associate-*r* 69.0%

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

      4. neg-mul-1 69.0%

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

      5. +-commutative 69.0%

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

      6. *-commutative 69.0%

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

      7. *-commutative 69.0%

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

      8. mul-1-neg 69.0%

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

      9. distribute-lft-neg-in 69.0%

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

      10. cancel-sign-sub-inv 69.0%

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

   6. Simplified 69.0%

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

   7. Taylor expanded in j around inf 38.4%

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

   8. Taylor expanded in c around 0 50.9%

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

      1. associate-*r* 50.9%

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

      2. neg-mul-1 50.9%

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

   10. Simplified 50.9%

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

   if -6.50000000000000022e-84 < z < 3.69999999999999991e-138 or 4.2999999999999997e-116 < z < 3.80000000000000024e162

   1. Initial program 78.7%

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

      1. sub-neg 78.7%

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

      2. +-commutative 78.7%

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

      3. associate-+l+ 78.7%

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

      4. distribute-rgt-neg-in 78.7%

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

      5. +-commutative 78.7%

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

      6. fma-def 79.4%

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

      7. sub-neg 79.4%

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

      8. +-commutative 79.4%

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

      9. distribute-neg-in 79.4%

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

      10. unsub-neg 79.4%

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

      11. remove-double-neg 79.4%

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

      12. *-commutative 79.4%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 83.3%

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

      1. fma-def 83.3%

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

      2. fma-def 84.1%

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

      3. associate-*r* 84.1%

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

      4. neg-mul-1 84.1%

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

      5. +-commutative 84.1%

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

      6. *-commutative 84.1%

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

      7. *-commutative 84.1%

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

      8. mul-1-neg 84.1%

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

      9. distribute-lft-neg-in 84.1%

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

      10. cancel-sign-sub-inv 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in a around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

   9. Simplified 52.3%

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

   if 3.69999999999999991e-138 < z < 4.2999999999999997e-116

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. +-commutative 80.0%

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

      3. associate-+l+ 80.0%

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

      4. distribute-rgt-neg-in 80.0%

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

      5. +-commutative 80.0%

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

      6. fma-def 80.0%

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

      7. sub-neg 80.0%

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

      8. +-commutative 80.0%

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

      9. distribute-neg-in 80.0%

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

      10. unsub-neg 80.0%

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

      11. remove-double-neg 80.0%

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

      12. *-commutative 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in t around inf 62.6%

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

   5. Taylor expanded in i around inf 100.0%

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

   if 3.80000000000000024e162 < z

   1. Initial program 73.7%

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

      1. sub-neg 73.7%

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

      2. +-commutative 73.7%

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

      3. associate-+l+ 73.7%

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

      4. distribute-rgt-neg-in 73.7%

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

      5. +-commutative 73.7%

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

      6. fma-def 73.7%

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

      7. sub-neg 73.7%

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

      8. +-commutative 73.7%

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

      9. distribute-neg-in 73.7%

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

      10. unsub-neg 73.7%

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

      11. remove-double-neg 73.7%

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

      12. *-commutative 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in c around inf 59.8%

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

      1. distribute-rgt-in 59.8%

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

      2. *-commutative 59.8%

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

      3. mul-1-neg 59.8%

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

      4. cancel-sign-sub-inv 59.8%

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

      5. *-commutative 59.8%

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

      6. distribute-rgt-out-- 59.8%

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

   6. Simplified 59.8%

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

   7. Taylor expanded in a around 0 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

      5. neg-mul-1 60.4%

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

   9. Simplified 60.4%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-116}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 7: 52.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* c (- (* a j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -4.5e-14)
     t_3
     (if (<= y -2.4e-101)
       t_1
       (if (<= y 5.6e-236)
         (* a (- (* c j) (* x t)))
         (if (<= y 2.85e-64)
           t_2
           (if (<= y 1100.0) t_1 (if (<= y 5.5e+53) 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 = b * ((t * i) - (z * c));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.5e-14) {
		tmp = t_3;
	} else if (y <= -2.4e-101) {
		tmp = t_1;
	} else if (y <= 5.6e-236) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 2.85e-64) {
		tmp = t_2;
	} else if (y <= 1100.0) {
		tmp = t_1;
	} else if (y <= 5.5e+53) {
		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 = b * ((t * i) - (z * c))
    t_2 = c * ((a * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-4.5d-14)) then
        tmp = t_3
    else if (y <= (-2.4d-101)) then
        tmp = t_1
    else if (y <= 5.6d-236) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 2.85d-64) then
        tmp = t_2
    else if (y <= 1100.0d0) then
        tmp = t_1
    else if (y <= 5.5d+53) 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 = b * ((t * i) - (z * c));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.5e-14) {
		tmp = t_3;
	} else if (y <= -2.4e-101) {
		tmp = t_1;
	} else if (y <= 5.6e-236) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 2.85e-64) {
		tmp = t_2;
	} else if (y <= 1100.0) {
		tmp = t_1;
	} else if (y <= 5.5e+53) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = c * ((a * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.5e-14:
		tmp = t_3
	elif y <= -2.4e-101:
		tmp = t_1
	elif y <= 5.6e-236:
		tmp = a * ((c * j) - (x * t))
	elif y <= 2.85e-64:
		tmp = t_2
	elif y <= 1100.0:
		tmp = t_1
	elif y <= 5.5e+53:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.5e-14)
		tmp = t_3;
	elseif (y <= -2.4e-101)
		tmp = t_1;
	elseif (y <= 5.6e-236)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 2.85e-64)
		tmp = t_2;
	elseif (y <= 1100.0)
		tmp = t_1;
	elseif (y <= 5.5e+53)
		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 = b * ((t * i) - (z * c));
	t_2 = c * ((a * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.5e-14)
		tmp = t_3;
	elseif (y <= -2.4e-101)
		tmp = t_1;
	elseif (y <= 5.6e-236)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 2.85e-64)
		tmp = t_2;
	elseif (y <= 1100.0)
		tmp = t_1;
	elseif (y <= 5.5e+53)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-14], t$95$3, If[LessEqual[y, -2.4e-101], t$95$1, If[LessEqual[y, 5.6e-236], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e-64], t$95$2, If[LessEqual[y, 1100.0], t$95$1, If[LessEqual[y, 5.5e+53], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999998e-14 or 5.49999999999999975e53 < y

   1. Initial program 69.6%

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

      1. sub-neg 69.6%

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

      2. +-commutative 69.6%

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

      3. associate-+l+ 69.6%

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

      4. distribute-rgt-neg-in 69.6%

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

      5. +-commutative 69.6%

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

      6. fma-def 71.4%

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

      7. sub-neg 71.4%

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

      8. +-commutative 71.4%

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

      9. distribute-neg-in 71.4%

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

      10. unsub-neg 71.4%

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

      11. remove-double-neg 71.4%

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

      12. *-commutative 71.4%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in t around 0 74.1%

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

      1. fma-def 75.0%

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

      2. fma-def 75.0%

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

      3. associate-*r* 75.0%

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

      4. neg-mul-1 75.0%

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

      5. +-commutative 75.0%

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

      6. *-commutative 75.0%

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

      7. *-commutative 75.0%

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

      8. mul-1-neg 75.0%

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

      9. distribute-lft-neg-in 75.0%

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

      10. cancel-sign-sub-inv 75.0%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

   9. Simplified 69.9%

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

   if -4.4999999999999998e-14 < y < -2.4e-101 or 2.8500000000000001e-64 < y < 1100

   1. Initial program 79.3%

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

      1. sub-neg 79.3%

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

      2. +-commutative 79.3%

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

      3. associate-+l+ 79.3%

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

      4. distribute-rgt-neg-in 79.3%

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

      5. +-commutative 79.3%

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

      6. fma-def 79.3%

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

      7. sub-neg 79.3%

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

      8. +-commutative 79.3%

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

      9. distribute-neg-in 79.3%

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

      10. unsub-neg 79.3%

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

      11. remove-double-neg 79.3%

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

      12. *-commutative 79.3%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around 0 80.3%

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

      1. fma-def 80.3%

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

      2. fma-def 80.3%

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

      3. associate-*r* 80.3%

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

      4. neg-mul-1 80.3%

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

      5. +-commutative 80.3%

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

      6. *-commutative 80.3%

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

      7. *-commutative 80.3%

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

      8. mul-1-neg 80.3%

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

      9. distribute-lft-neg-in 80.3%

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

      10. cancel-sign-sub-inv 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in b around inf 62.7%

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

   if -2.4e-101 < y < 5.59999999999999973e-236

   1. Initial program 83.7%

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

      1. sub-neg 83.7%

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

      2. +-commutative 83.7%

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

      3. associate-+l+ 83.7%

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

      4. distribute-rgt-neg-in 83.7%

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

      5. +-commutative 83.7%

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

      6. fma-def 83.7%

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

      7. sub-neg 83.7%

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

      8. +-commutative 83.7%

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

      9. distribute-neg-in 83.7%

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

      10. unsub-neg 83.7%

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

      11. remove-double-neg 83.7%

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

      12. *-commutative 83.7%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around 0 78.8%

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

      1. fma-def 78.8%

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

      2. fma-def 78.8%

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

      3. associate-*r* 78.8%

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

      4. neg-mul-1 78.8%

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

      5. +-commutative 78.8%

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

      6. *-commutative 78.8%

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

      7. *-commutative 78.8%

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

      8. mul-1-neg 78.8%

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

      9. distribute-lft-neg-in 78.8%

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

      10. cancel-sign-sub-inv 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in a around inf 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

      4. *-commutative 59.8%

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

   9. Simplified 59.8%

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

   if 5.59999999999999973e-236 < y < 2.8500000000000001e-64 or 1100 < y < 5.49999999999999975e53

   1. Initial program 76.7%

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

      1. sub-neg 76.7%

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

      2. +-commutative 76.7%

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

      3. associate-+l+ 76.7%

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

      4. distribute-rgt-neg-in 76.7%

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

      5. +-commutative 76.7%

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

      6. fma-def 76.7%

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

      7. sub-neg 76.7%

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

      8. +-commutative 76.7%

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

      9. distribute-neg-in 76.7%

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

      10. unsub-neg 76.7%

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

      11. remove-double-neg 76.7%

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

      12. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in c around inf 65.5%

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

      1. distribute-rgt-in 65.5%

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

      2. *-commutative 65.5%

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

      3. mul-1-neg 65.5%

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

      4. cancel-sign-sub-inv 65.5%

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

      5. *-commutative 65.5%

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

      6. distribute-rgt-out-- 65.5%

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

   6. Simplified 65.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1100:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 8: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -4.3e-21)
     t_2
     (if (<= z -7.5e-84)
       t_1
       (if (<= z 1.4e-307)
         (- (* c (* a j)) (* a (* x t)))
         (if (<= z 1.15e-115)
           t_1
           (if (<= z 4.8e+46)
             (* y (- (* x z) (* i j)))
             (if (<= z 2.5e+126) (* j (- (* a c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.3e-21) {
		tmp = t_2;
	} else if (z <= -7.5e-84) {
		tmp = t_1;
	} else if (z <= 1.4e-307) {
		tmp = (c * (a * j)) - (a * (x * t));
	} else if (z <= 1.15e-115) {
		tmp = t_1;
	} else if (z <= 4.8e+46) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 2.5e+126) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-4.3d-21)) then
        tmp = t_2
    else if (z <= (-7.5d-84)) then
        tmp = t_1
    else if (z <= 1.4d-307) then
        tmp = (c * (a * j)) - (a * (x * t))
    else if (z <= 1.15d-115) then
        tmp = t_1
    else if (z <= 4.8d+46) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= 2.5d+126) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.3e-21) {
		tmp = t_2;
	} else if (z <= -7.5e-84) {
		tmp = t_1;
	} else if (z <= 1.4e-307) {
		tmp = (c * (a * j)) - (a * (x * t));
	} else if (z <= 1.15e-115) {
		tmp = t_1;
	} else if (z <= 4.8e+46) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 2.5e+126) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -4.3e-21:
		tmp = t_2
	elif z <= -7.5e-84:
		tmp = t_1
	elif z <= 1.4e-307:
		tmp = (c * (a * j)) - (a * (x * t))
	elif z <= 1.15e-115:
		tmp = t_1
	elif z <= 4.8e+46:
		tmp = y * ((x * z) - (i * j))
	elif z <= 2.5e+126:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -4.3e-21)
		tmp = t_2;
	elseif (z <= -7.5e-84)
		tmp = t_1;
	elseif (z <= 1.4e-307)
		tmp = Float64(Float64(c * Float64(a * j)) - Float64(a * Float64(x * t)));
	elseif (z <= 1.15e-115)
		tmp = t_1;
	elseif (z <= 4.8e+46)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= 2.5e+126)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -4.3e-21)
		tmp = t_2;
	elseif (z <= -7.5e-84)
		tmp = t_1;
	elseif (z <= 1.4e-307)
		tmp = (c * (a * j)) - (a * (x * t));
	elseif (z <= 1.15e-115)
		tmp = t_1;
	elseif (z <= 4.8e+46)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= 2.5e+126)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e-21], t$95$2, If[LessEqual[z, -7.5e-84], t$95$1, If[LessEqual[z, 1.4e-307], N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-115], t$95$1, If[LessEqual[z, 4.8e+46], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+126], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2999999999999998e-21 or 2.49999999999999989e126 < z

   1. Initial program 73.8%

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

      1. sub-neg 73.8%

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

      2. +-commutative 73.8%

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

      3. associate-+l+ 73.8%

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

      4. distribute-rgt-neg-in 73.8%

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

      5. +-commutative 73.8%

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

      6. fma-def 74.7%

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

      7. sub-neg 74.7%

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

      8. +-commutative 74.7%

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

      9. distribute-neg-in 74.7%

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

      10. unsub-neg 74.7%

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

      11. remove-double-neg 74.7%

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

      12. *-commutative 74.7%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in t around 0 73.0%

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

      1. fma-def 73.9%

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

      2. fma-def 73.9%

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

      3. associate-*r* 73.9%

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

      4. neg-mul-1 73.9%

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

      5. +-commutative 73.9%

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

      6. *-commutative 73.9%

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

      7. *-commutative 73.9%

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

      8. mul-1-neg 73.9%

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

      9. distribute-lft-neg-in 73.9%

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

      10. cancel-sign-sub-inv 73.9%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in z around inf 67.4%

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

   if -4.2999999999999998e-21 < z < -7.50000000000000026e-84 or 1.4e-307 < z < 1.14999999999999992e-115

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. associate-+l+ 75.5%

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

      4. distribute-rgt-neg-in 75.5%

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

      5. +-commutative 75.5%

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

      6. fma-def 75.5%

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

      7. sub-neg 75.5%

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

      8. +-commutative 75.5%

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

      9. distribute-neg-in 75.5%

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

      10. unsub-neg 75.5%

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

      11. remove-double-neg 75.5%

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

      12. *-commutative 75.5%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in i around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

   6. Simplified 69.6%

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

   if -7.50000000000000026e-84 < z < 1.4e-307

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. fma-def 75.9%

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

      3. *-commutative 75.9%

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

      4. *-commutative 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in y around 0 77.5%

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

   5. Taylor expanded in b around 0 64.4%

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

   if 1.14999999999999992e-115 < z < 4.80000000000000017e46

   1. Initial program 80.4%

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

      1. sub-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. associate-+l+ 80.4%

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

      4. distribute-rgt-neg-in 80.4%

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

      5. +-commutative 80.4%

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

      6. fma-def 83.5%

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

      7. sub-neg 83.5%

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

      8. +-commutative 83.5%

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

      9. distribute-neg-in 83.5%

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

      10. unsub-neg 83.5%

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

      11. remove-double-neg 83.5%

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

      12. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in t around 0 93.5%

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

      1. fma-def 93.6%

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

      2. fma-def 96.7%

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

      3. associate-*r* 96.7%

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

      4. neg-mul-1 96.7%

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

      5. +-commutative 96.7%

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

      6. *-commutative 96.7%

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

      7. *-commutative 96.7%

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

      8. mul-1-neg 96.7%

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

      9. distribute-lft-neg-in 96.7%

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

      10. cancel-sign-sub-inv 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in y around inf 53.4%

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

      1. *-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

   9. Simplified 53.4%

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

   if 4.80000000000000017e46 < z < 2.49999999999999989e126

   1. Initial program 78.9%

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

      1. sub-neg 78.9%

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

      2. +-commutative 78.9%

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

      3. associate-+l+ 78.9%

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

      4. distribute-rgt-neg-in 78.9%

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

      5. +-commutative 78.9%

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

      6. fma-def 78.9%

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

      7. sub-neg 78.9%

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

      8. +-commutative 78.9%

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

      9. distribute-neg-in 78.9%

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

      10. unsub-neg 78.9%

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

      11. remove-double-neg 78.9%

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

      12. *-commutative 78.9%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in t around 0 73.4%

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

      1. fma-def 73.4%

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

      2. fma-def 73.4%

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

      3. associate-*r* 73.4%

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

      4. neg-mul-1 73.4%

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

      5. +-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

      8. mul-1-neg 73.4%

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

      9. distribute-lft-neg-in 73.4%

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

      10. cancel-sign-sub-inv 73.4%

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

   6. Simplified 73.4%

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

   7. Taylor expanded in j around inf 69.2%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-84}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-115}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 9: 59.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+104}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -5.8e+115)
     t_1
     (if (<= x 6.1e+31)
       (- (* j (- (* a c) (* y i))) (* b (* z c)))
       (if (<= x 1.08e+104)
         (* z (- (* x y) (* b c)))
         (if (<= x 2.6e+138) (- (* c (* a j)) (* a (* x t))) 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) - (t * a));
	double tmp;
	if (x <= -5.8e+115) {
		tmp = t_1;
	} else if (x <= 6.1e+31) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (x <= 1.08e+104) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= 2.6e+138) {
		tmp = (c * (a * j)) - (a * (x * t));
	} 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) - (t * a))
    if (x <= (-5.8d+115)) then
        tmp = t_1
    else if (x <= 6.1d+31) then
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    else if (x <= 1.08d+104) then
        tmp = z * ((x * y) - (b * c))
    else if (x <= 2.6d+138) then
        tmp = (c * (a * j)) - (a * (x * t))
    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) - (t * a));
	double tmp;
	if (x <= -5.8e+115) {
		tmp = t_1;
	} else if (x <= 6.1e+31) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (x <= 1.08e+104) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= 2.6e+138) {
		tmp = (c * (a * j)) - (a * (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.8e+115:
		tmp = t_1
	elif x <= 6.1e+31:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	elif x <= 1.08e+104:
		tmp = z * ((x * y) - (b * c))
	elif x <= 2.6e+138:
		tmp = (c * (a * j)) - (a * (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.8e+115)
		tmp = t_1;
	elseif (x <= 6.1e+31)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 1.08e+104)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (x <= 2.6e+138)
		tmp = Float64(Float64(c * Float64(a * j)) - Float64(a * Float64(x * t)));
	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) - (t * a));
	tmp = 0.0;
	if (x <= -5.8e+115)
		tmp = t_1;
	elseif (x <= 6.1e+31)
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	elseif (x <= 1.08e+104)
		tmp = z * ((x * y) - (b * c));
	elseif (x <= 2.6e+138)
		tmp = (c * (a * j)) - (a * (x * t));
	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[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+115], t$95$1, If[LessEqual[x, 6.1e+31], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e+104], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+138], N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.80000000000000009e115 or 2.6000000000000001e138 < x

   1. Initial program 75.3%

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

      1. sub-neg 75.3%

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

      2. +-commutative 75.3%

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

      3. associate-+l+ 75.3%

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

      4. distribute-rgt-neg-in 75.3%

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

      5. +-commutative 75.3%

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

      6. fma-def 76.9%

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

      7. sub-neg 76.9%

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

      8. +-commutative 76.9%

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

      9. distribute-neg-in 76.9%

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

      10. unsub-neg 76.9%

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

      11. remove-double-neg 76.9%

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

      12. *-commutative 76.9%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around 0 60.2%

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

      1. fma-def 60.2%

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

      2. fma-def 61.8%

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

      3. associate-*r* 61.8%

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

      4. neg-mul-1 61.8%

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

      5. +-commutative 61.8%

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

      6. *-commutative 61.8%

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

      7. *-commutative 61.8%

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

      8. mul-1-neg 61.8%

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

      9. distribute-lft-neg-in 61.8%

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

      10. cancel-sign-sub-inv 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in z around inf 69.7%

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

   8. Taylor expanded in b around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. associate-*r* 63.3%

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

      3. associate-*r* 63.3%

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

      4. associate-*r* 65.3%

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

      5. associate-*r* 65.3%

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

      6. distribute-rgt-in 71.4%

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

      7. mul-1-neg 71.4%

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

      8. *-commutative 71.4%

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

      9. unsub-neg 71.4%

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

   10. Simplified 71.4%

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

   if -5.80000000000000009e115 < x < 6.10000000000000009e31

   1. Initial program 76.3%

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

      1. cancel-sign-sub 76.3%

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

      2. cancel-sign-sub-inv 76.3%

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

      3. *-commutative 76.3%

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

      4. remove-double-neg 76.3%

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

      5. *-commutative 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in c around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 66.4%

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

      4. distribute-rgt-neg-in 66.4%

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

      5. *-commutative 66.4%

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

   6. Simplified 66.4%

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

   if 6.10000000000000009e31 < x < 1.07999999999999997e104

   1. Initial program 71.9%

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

      1. sub-neg 71.9%

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

      2. +-commutative 71.9%

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

      3. associate-+l+ 71.9%

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

      4. distribute-rgt-neg-in 71.9%

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

      5. +-commutative 71.9%

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

      6. fma-def 79.0%

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

      7. sub-neg 79.0%

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

      8. +-commutative 79.0%

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

      9. distribute-neg-in 79.0%

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

      10. unsub-neg 79.0%

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

      11. remove-double-neg 79.0%

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

      12. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in t around 0 78.8%

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

      1. fma-def 78.8%

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

      2. fma-def 78.8%

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

      3. associate-*r* 78.8%

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

      4. neg-mul-1 78.8%

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

      5. +-commutative 78.8%

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

      6. *-commutative 78.8%

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

      7. *-commutative 78.8%

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

      8. mul-1-neg 78.8%

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

      9. distribute-lft-neg-in 78.8%

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

      10. cancel-sign-sub-inv 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in z around inf 65.4%

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

   if 1.07999999999999997e104 < x < 2.6000000000000001e138

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. fma-def 72.2%

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

      3. *-commutative 72.2%

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

      4. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in y around 0 99.8%

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

   5. Taylor expanded in b around 0 99.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(a \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+104}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 10: 28.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* i (* y (- j)))))
   (if (<= z -1.7e+111)
     (* y (* x z))
     (if (<= z -2.4e-21)
       t_1
       (if (<= z -2.3e-84)
         t_2
         (if (<= z 1.02e-138)
           (* c (* a j))
           (if (<= z 1.6e-69)
             (* i (* t b))
             (if (<= z 1.22e+131) 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 = z * (b * -c);
	double t_2 = i * (y * -j);
	double tmp;
	if (z <= -1.7e+111) {
		tmp = y * (x * z);
	} else if (z <= -2.4e-21) {
		tmp = t_1;
	} else if (z <= -2.3e-84) {
		tmp = t_2;
	} else if (z <= 1.02e-138) {
		tmp = c * (a * j);
	} else if (z <= 1.6e-69) {
		tmp = i * (t * b);
	} else if (z <= 1.22e+131) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (b * -c)
    t_2 = i * (y * -j)
    if (z <= (-1.7d+111)) then
        tmp = y * (x * z)
    else if (z <= (-2.4d-21)) then
        tmp = t_1
    else if (z <= (-2.3d-84)) then
        tmp = t_2
    else if (z <= 1.02d-138) then
        tmp = c * (a * j)
    else if (z <= 1.6d-69) then
        tmp = i * (t * b)
    else if (z <= 1.22d+131) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = i * (y * -j);
	double tmp;
	if (z <= -1.7e+111) {
		tmp = y * (x * z);
	} else if (z <= -2.4e-21) {
		tmp = t_1;
	} else if (z <= -2.3e-84) {
		tmp = t_2;
	} else if (z <= 1.02e-138) {
		tmp = c * (a * j);
	} else if (z <= 1.6e-69) {
		tmp = i * (t * b);
	} else if (z <= 1.22e+131) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = i * (y * -j)
	tmp = 0
	if z <= -1.7e+111:
		tmp = y * (x * z)
	elif z <= -2.4e-21:
		tmp = t_1
	elif z <= -2.3e-84:
		tmp = t_2
	elif z <= 1.02e-138:
		tmp = c * (a * j)
	elif z <= 1.6e-69:
		tmp = i * (t * b)
	elif z <= 1.22e+131:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (z <= -1.7e+111)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -2.4e-21)
		tmp = t_1;
	elseif (z <= -2.3e-84)
		tmp = t_2;
	elseif (z <= 1.02e-138)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 1.6e-69)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 1.22e+131)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (z <= -1.7e+111)
		tmp = y * (x * z);
	elseif (z <= -2.4e-21)
		tmp = t_1;
	elseif (z <= -2.3e-84)
		tmp = t_2;
	elseif (z <= 1.02e-138)
		tmp = c * (a * j);
	elseif (z <= 1.6e-69)
		tmp = i * (t * b);
	elseif (z <= 1.22e+131)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+111], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-21], t$95$1, If[LessEqual[z, -2.3e-84], t$95$2, If[LessEqual[z, 1.02e-138], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-69], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+131], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7000000000000001e111

   1. Initial program 71.1%

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

      1. sub-neg 71.1%

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

      2. +-commutative 71.1%

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

      3. associate-+l+ 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

      5. +-commutative 71.1%

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

      6. fma-def 73.7%

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

      7. sub-neg 73.7%

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

      8. +-commutative 73.7%

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

      9. distribute-neg-in 73.7%

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

      10. unsub-neg 73.7%

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

      11. remove-double-neg 73.7%

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

      12. *-commutative 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around 0 66.5%

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

      1. fma-def 66.5%

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

      2. fma-def 66.5%

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

      3. associate-*r* 66.5%

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

      4. neg-mul-1 66.5%

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

      5. +-commutative 66.5%

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

      6. *-commutative 66.5%

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

      7. *-commutative 66.5%

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

      8. mul-1-neg 66.5%

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

      9. distribute-lft-neg-in 66.5%

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

      10. cancel-sign-sub-inv 66.5%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in z around inf 58.9%

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

   8. Taylor expanded in y around inf 51.1%

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

   if -1.7000000000000001e111 < z < -2.3999999999999999e-21 or 1.22e131 < z

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. associate-+l+ 75.5%

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

      4. distribute-rgt-neg-in 75.5%

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

      5. +-commutative 75.5%

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

      6. fma-def 75.5%

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

      7. sub-neg 75.5%

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

      8. +-commutative 75.5%

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

      9. distribute-neg-in 75.5%

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

      10. unsub-neg 75.5%

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

      11. remove-double-neg 75.5%

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

      12. *-commutative 75.5%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in t around 0 75.3%

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

      1. fma-def 76.7%

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

      2. fma-def 76.7%

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

      3. associate-*r* 76.7%

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

      4. neg-mul-1 76.7%

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

      5. +-commutative 76.7%

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

      6. *-commutative 76.7%

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

      7. *-commutative 76.7%

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

      8. mul-1-neg 76.7%

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

      9. distribute-lft-neg-in 76.7%

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

      10. cancel-sign-sub-inv 76.7%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in z around inf 68.9%

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

   8. Taylor expanded in c around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. neg-mul-1 51.5%

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

      3. distribute-lft-neg-in 51.5%

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

      4. *-commutative 51.5%

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

      5. associate-*l* 49.0%

         \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(-c\right)\right)} \]

      6. distribute-rgt-neg-in 49.0%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      7. *-commutative 49.0%

         \[\leadsto z \cdot \left(-\color{blue}{c \cdot b}\right) \]

   10. Simplified 49.0%

       \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

   if -2.3999999999999999e-21 < z < -2.29999999999999981e-84 or 1.59999999999999999e-69 < z < 1.22e131

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 75.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 75.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 75.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 75.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.5%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.5%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around inf 52.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 52.8%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 52.8%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around 0 35.5%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.5%

         \[\leadsto i \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot j\right)} \]

      2. neg-mul-1 35.5%

         \[\leadsto i \cdot \left(\color{blue}{\left(-y\right)} \cdot j\right) \]

   9. Simplified 35.5%

      \[\leadsto i \cdot \color{blue}{\left(\left(-y\right) \cdot j\right)} \]

   if -2.29999999999999981e-84 < z < 1.02000000000000007e-138

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 48.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 48.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 48.5%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 48.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   7. Taylor expanded in a around inf 42.9%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if 1.02000000000000007e-138 < z < 1.59999999999999999e-69

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 52.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 45.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-84}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+131}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 11: 29.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* y (* i (- j)))))
   (if (<= z -7.5e+111)
     (* y (* x z))
     (if (<= z -2.25e-20)
       t_1
       (if (<= z -3.4e-84)
         t_2
         (if (<= z 2.2e-138)
           (* c (* a j))
           (if (<= z 3.8e-101) (* i (* t b)) (if (<= z 6e+130) 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 = z * (b * -c);
	double t_2 = y * (i * -j);
	double tmp;
	if (z <= -7.5e+111) {
		tmp = y * (x * z);
	} else if (z <= -2.25e-20) {
		tmp = t_1;
	} else if (z <= -3.4e-84) {
		tmp = t_2;
	} else if (z <= 2.2e-138) {
		tmp = c * (a * j);
	} else if (z <= 3.8e-101) {
		tmp = i * (t * b);
	} else if (z <= 6e+130) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (b * -c)
    t_2 = y * (i * -j)
    if (z <= (-7.5d+111)) then
        tmp = y * (x * z)
    else if (z <= (-2.25d-20)) then
        tmp = t_1
    else if (z <= (-3.4d-84)) then
        tmp = t_2
    else if (z <= 2.2d-138) then
        tmp = c * (a * j)
    else if (z <= 3.8d-101) then
        tmp = i * (t * b)
    else if (z <= 6d+130) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = y * (i * -j);
	double tmp;
	if (z <= -7.5e+111) {
		tmp = y * (x * z);
	} else if (z <= -2.25e-20) {
		tmp = t_1;
	} else if (z <= -3.4e-84) {
		tmp = t_2;
	} else if (z <= 2.2e-138) {
		tmp = c * (a * j);
	} else if (z <= 3.8e-101) {
		tmp = i * (t * b);
	} else if (z <= 6e+130) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = y * (i * -j)
	tmp = 0
	if z <= -7.5e+111:
		tmp = y * (x * z)
	elif z <= -2.25e-20:
		tmp = t_1
	elif z <= -3.4e-84:
		tmp = t_2
	elif z <= 2.2e-138:
		tmp = c * (a * j)
	elif z <= 3.8e-101:
		tmp = i * (t * b)
	elif z <= 6e+130:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (z <= -7.5e+111)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -2.25e-20)
		tmp = t_1;
	elseif (z <= -3.4e-84)
		tmp = t_2;
	elseif (z <= 2.2e-138)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 3.8e-101)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 6e+130)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	t_2 = y * (i * -j);
	tmp = 0.0;
	if (z <= -7.5e+111)
		tmp = y * (x * z);
	elseif (z <= -2.25e-20)
		tmp = t_1;
	elseif (z <= -3.4e-84)
		tmp = t_2;
	elseif (z <= 2.2e-138)
		tmp = c * (a * j);
	elseif (z <= 3.8e-101)
		tmp = i * (t * b);
	elseif (z <= 6e+130)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+111], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-20], t$95$1, If[LessEqual[z, -3.4e-84], t$95$2, If[LessEqual[z, 2.2e-138], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-101], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+130], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.49999999999999948e111

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 71.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 71.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 71.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 71.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 73.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 73.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 73.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 73.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 73.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 73.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 66.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 66.5%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 66.5%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 58.9%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -7.49999999999999948e111 < z < -2.2500000000000001e-20 or 5.9999999999999999e130 < z

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 75.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 75.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 75.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 75.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 75.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 75.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 75.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 75.5%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 75.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 75.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 75.5%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 75.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 76.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 76.7%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 76.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 76.7%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 78.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 68.9%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(z \cdot b\right)}\right) \]

      2. neg-mul-1 51.5%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      3. distribute-lft-neg-in 51.5%

         \[\leadsto \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)} \]

      4. *-commutative 51.5%

         \[\leadsto \color{blue}{\left(z \cdot b\right) \cdot \left(-c\right)} \]

      5. associate-*l* 49.0%

         \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(-c\right)\right)} \]

      6. distribute-rgt-neg-in 49.0%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      7. *-commutative 49.0%

         \[\leadsto z \cdot \left(-\color{blue}{c \cdot b}\right) \]

   10. Simplified 49.0%

       \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

   if -2.2500000000000001e-20 < z < -3.40000000000000021e-84 or 3.8000000000000001e-101 < z < 5.9999999999999999e130

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 78.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 78.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 78.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 78.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 82.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 82.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 83.7%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 83.7%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in j around inf 52.5%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   8. Taylor expanded in c around 0 36.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(i \cdot j\right)} \]

      2. neg-mul-1 36.8%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(i \cdot j\right) \]

   10. Simplified 36.8%

       \[\leadsto \color{blue}{\left(-y\right) \cdot \left(i \cdot j\right)} \]

   if -3.40000000000000021e-84 < z < 2.1999999999999999e-138

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 48.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 48.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 48.5%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 48.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   7. Taylor expanded in a around inf 42.9%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if 2.1999999999999999e-138 < z < 3.8000000000000001e-101

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 72.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 72.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 72.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 72.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 64.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 12: 29.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= z -2.2e+111)
     (* y (* x z))
     (if (<= z -1e-20)
       (* z (* b (- c)))
       (if (<= z -3.8e-86)
         t_1
         (if (<= z 2.35e-138)
           (* c (* a j))
           (if (<= z 7.8e-101)
             (* i (* t b))
             (if (<= z 5.3e+130) t_1 (* b (* z (- c)))))))))))

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 * (i * -j);
	double tmp;
	if (z <= -2.2e+111) {
		tmp = y * (x * z);
	} else if (z <= -1e-20) {
		tmp = z * (b * -c);
	} else if (z <= -3.8e-86) {
		tmp = t_1;
	} else if (z <= 2.35e-138) {
		tmp = c * (a * j);
	} else if (z <= 7.8e-101) {
		tmp = i * (t * b);
	} else if (z <= 5.3e+130) {
		tmp = t_1;
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (i * -j)
    if (z <= (-2.2d+111)) then
        tmp = y * (x * z)
    else if (z <= (-1d-20)) then
        tmp = z * (b * -c)
    else if (z <= (-3.8d-86)) then
        tmp = t_1
    else if (z <= 2.35d-138) then
        tmp = c * (a * j)
    else if (z <= 7.8d-101) then
        tmp = i * (t * b)
    else if (z <= 5.3d+130) then
        tmp = t_1
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (z <= -2.2e+111) {
		tmp = y * (x * z);
	} else if (z <= -1e-20) {
		tmp = z * (b * -c);
	} else if (z <= -3.8e-86) {
		tmp = t_1;
	} else if (z <= 2.35e-138) {
		tmp = c * (a * j);
	} else if (z <= 7.8e-101) {
		tmp = i * (t * b);
	} else if (z <= 5.3e+130) {
		tmp = t_1;
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if z <= -2.2e+111:
		tmp = y * (x * z)
	elif z <= -1e-20:
		tmp = z * (b * -c)
	elif z <= -3.8e-86:
		tmp = t_1
	elif z <= 2.35e-138:
		tmp = c * (a * j)
	elif z <= 7.8e-101:
		tmp = i * (t * b)
	elif z <= 5.3e+130:
		tmp = t_1
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (z <= -2.2e+111)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -1e-20)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (z <= -3.8e-86)
		tmp = t_1;
	elseif (z <= 2.35e-138)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 7.8e-101)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 5.3e+130)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (z <= -2.2e+111)
		tmp = y * (x * z);
	elseif (z <= -1e-20)
		tmp = z * (b * -c);
	elseif (z <= -3.8e-86)
		tmp = t_1;
	elseif (z <= 2.35e-138)
		tmp = c * (a * j);
	elseif (z <= 7.8e-101)
		tmp = i * (t * b);
	elseif (z <= 5.3e+130)
		tmp = t_1;
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+111], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-20], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-86], t$95$1, If[LessEqual[z, 2.35e-138], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-101], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+130], t$95$1, N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.19999999999999999e111

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 71.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 71.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 71.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 71.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 73.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 73.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 73.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 73.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 73.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 73.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 73.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 66.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 66.5%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 66.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 66.5%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 58.9%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -2.19999999999999999e111 < z < -9.99999999999999945e-21

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 72.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 72.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 72.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 72.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 72.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 72.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 72.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 75.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 78.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 78.7%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 78.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 78.7%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 82.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 68.2%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in c around inf 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(z \cdot b\right)}\right) \]

      2. neg-mul-1 47.1%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      3. distribute-lft-neg-in 47.1%

         \[\leadsto \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)} \]

      4. *-commutative 47.1%

         \[\leadsto \color{blue}{\left(z \cdot b\right) \cdot \left(-c\right)} \]

      5. associate-*l* 47.2%

         \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(-c\right)\right)} \]

      6. distribute-rgt-neg-in 47.2%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      7. *-commutative 47.2%

         \[\leadsto z \cdot \left(-\color{blue}{c \cdot b}\right) \]

   10. Simplified 47.2%

       \[\leadsto \color{blue}{z \cdot \left(-c \cdot b\right)} \]

   if -9.99999999999999945e-21 < z < -3.8e-86 or 7.80000000000000031e-101 < z < 5.2999999999999997e130

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 78.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 78.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 78.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 78.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 82.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 82.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 83.7%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 83.7%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 83.7%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in j around inf 52.5%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   8. Taylor expanded in c around 0 36.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(i \cdot j\right)} \]

      2. neg-mul-1 36.8%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(i \cdot j\right) \]

   10. Simplified 36.8%

       \[\leadsto \color{blue}{\left(-y\right) \cdot \left(i \cdot j\right)} \]

   if -3.8e-86 < z < 2.3500000000000001e-138

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 48.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 48.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 48.5%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 48.5%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 48.5%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   7. Taylor expanded in a around inf 42.9%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if 2.3500000000000001e-138 < z < 7.80000000000000031e-101

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 72.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 72.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 72.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 72.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 72.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 72.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 72.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 72.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 72.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 64.9%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 5.2999999999999997e130 < z

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.4%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.4%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 75.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 75.4%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 75.4%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 62.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   8. Taylor expanded in i around 0 54.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \cdot b \]
   9. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(z \cdot c\right)}\right) \cdot b \]

      2. neg-mul-1 54.3%

         \[\leadsto \color{blue}{\left(-z \cdot c\right)} \cdot b \]

   10. Simplified 54.3%

       \[\leadsto \color{blue}{\left(-z \cdot c\right)} \cdot b \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 13: 52.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -8.8e-30)
     t_2
     (if (<= y -7.5e-168)
       t_1
       (if (<= y 6.5e-237)
         (* a (- (* c j) (* x t)))
         (if (<= y 4.8e+52) 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 * ((a * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8.8e-30) {
		tmp = t_2;
	} else if (y <= -7.5e-168) {
		tmp = t_1;
	} else if (y <= 6.5e-237) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 4.8e+52) {
		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 * ((a * j) - (z * b))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-8.8d-30)) then
        tmp = t_2
    else if (y <= (-7.5d-168)) then
        tmp = t_1
    else if (y <= 6.5d-237) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 4.8d+52) 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 * ((a * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8.8e-30) {
		tmp = t_2;
	} else if (y <= -7.5e-168) {
		tmp = t_1;
	} else if (y <= 6.5e-237) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 4.8e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -8.8e-30:
		tmp = t_2
	elif y <= -7.5e-168:
		tmp = t_1
	elif y <= 6.5e-237:
		tmp = a * ((c * j) - (x * t))
	elif y <= 4.8e+52:
		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(a * j) - Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -8.8e-30)
		tmp = t_2;
	elseif (y <= -7.5e-168)
		tmp = t_1;
	elseif (y <= 6.5e-237)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 4.8e+52)
		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 * ((a * j) - (z * b));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -8.8e-30)
		tmp = t_2;
	elseif (y <= -7.5e-168)
		tmp = t_1;
	elseif (y <= 6.5e-237)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 4.8e+52)
		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[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e-30], t$95$2, If[LessEqual[y, -7.5e-168], t$95$1, If[LessEqual[y, 6.5e-237], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.79999999999999933e-30 or 4.8e52 < y

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 70.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 70.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 70.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 70.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 71.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 71.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 71.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 71.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 71.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 71.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 71.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 73.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 74.6%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 75.4%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 75.4%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 75.4%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 77.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in y around inf 67.9%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 67.9%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   9. Simplified 67.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -8.79999999999999933e-30 < y < -7.4999999999999995e-168 or 6.5000000000000001e-237 < y < 4.8e52

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 56.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 56.7%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 56.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 56.7%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 56.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 56.7%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 56.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 56.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -7.4999999999999995e-168 < y < 6.5000000000000001e-237

   1. Initial program 88.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 88.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 88.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 88.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 88.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 88.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 88.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 88.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 88.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 88.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 88.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 88.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 78.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 78.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 78.2%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 78.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 78.2%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 78.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in a around inf 62.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   8. Step-by-step derivation

      1. +-commutative 62.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 62.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 62.8%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   9. Simplified 62.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-168}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 14: 30.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+167} \lor \neg \left(y \leq 2.05 \cdot 10^{+220}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= y -2e-20)
     t_1
     (if (<= y 3.7e-68)
       (* j (* a c))
       (if (<= y 1.8e+84)
         (* i (* t b))
         (if (or (<= y 1.75e+167) (not (<= y 2.05e+220)))
           t_1
           (* 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 t_1 = i * (y * -j);
	double tmp;
	if (y <= -2e-20) {
		tmp = t_1;
	} else if (y <= 3.7e-68) {
		tmp = j * (a * c);
	} else if (y <= 1.8e+84) {
		tmp = i * (t * b);
	} else if ((y <= 1.75e+167) || !(y <= 2.05e+220)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = i * (y * -j)
    if (y <= (-2d-20)) then
        tmp = t_1
    else if (y <= 3.7d-68) then
        tmp = j * (a * c)
    else if (y <= 1.8d+84) then
        tmp = i * (t * b)
    else if ((y <= 1.75d+167) .or. (.not. (y <= 2.05d+220))) then
        tmp = t_1
    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 t_1 = i * (y * -j);
	double tmp;
	if (y <= -2e-20) {
		tmp = t_1;
	} else if (y <= 3.7e-68) {
		tmp = j * (a * c);
	} else if (y <= 1.8e+84) {
		tmp = i * (t * b);
	} else if ((y <= 1.75e+167) || !(y <= 2.05e+220)) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if y <= -2e-20:
		tmp = t_1
	elif y <= 3.7e-68:
		tmp = j * (a * c)
	elif y <= 1.8e+84:
		tmp = i * (t * b)
	elif (y <= 1.75e+167) or not (y <= 2.05e+220):
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -2e-20)
		tmp = t_1;
	elseif (y <= 3.7e-68)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1.8e+84)
		tmp = Float64(i * Float64(t * b));
	elseif ((y <= 1.75e+167) || !(y <= 2.05e+220))
		tmp = t_1;
	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)
	t_1 = i * (y * -j);
	tmp = 0.0;
	if (y <= -2e-20)
		tmp = t_1;
	elseif (y <= 3.7e-68)
		tmp = j * (a * c);
	elseif (y <= 1.8e+84)
		tmp = i * (t * b);
	elseif ((y <= 1.75e+167) || ~((y <= 2.05e+220)))
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-20], t$95$1, If[LessEqual[y, 3.7e-68], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+84], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.75e+167], N[Not[LessEqual[y, 2.05e+220]], $MachinePrecision]], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.99999999999999989e-20 or 1.8e84 < y < 1.74999999999999994e167 or 2.0499999999999999e220 < y

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 66.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 66.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 66.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 66.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 66.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 68.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 68.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 68.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 68.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 68.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 68.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 68.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around inf 53.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 53.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around 0 44.8%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.8%

         \[\leadsto i \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot j\right)} \]

      2. neg-mul-1 44.8%

         \[\leadsto i \cdot \left(\color{blue}{\left(-y\right)} \cdot j\right) \]

   9. Simplified 44.8%

      \[\leadsto i \cdot \color{blue}{\left(\left(-y\right) \cdot j\right)} \]

   if -1.99999999999999989e-20 < y < 3.70000000000000002e-68

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 82.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 82.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 82.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 82.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 82.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 82.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 82.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 82.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 78.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 78.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 79.6%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 79.6%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in j around inf 42.6%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   8. Taylor expanded in c around inf 36.8%

      \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   if 3.70000000000000002e-68 < y < 1.8e84

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.8%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.8%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.8%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.8%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 76.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 76.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 76.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 76.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 76.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 76.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 48.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 31.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.74999999999999994e167 < y < 2.0499999999999999e220

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 77.6%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 77.6%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 77.6%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 77.6%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 85.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 85.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 85.3%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 85.3%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 85.3%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 85.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 84.5%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in y around inf 76.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-68}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+84}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+167} \lor \neg \left(y \leq 2.05 \cdot 10^{+220}\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 15: 29.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= y -2e-20)
     t_1
     (if (<= y 9.5e-67)
       (* j (* a c))
       (if (<= y 8.5e+69)
         (* i (* t b))
         (if (<= y 3.8e+139)
           (* t (- (* x a)))
           (if (<= y 7e+220) (* y (* x z)) 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 = i * (y * -j);
	double tmp;
	if (y <= -2e-20) {
		tmp = t_1;
	} else if (y <= 9.5e-67) {
		tmp = j * (a * c);
	} else if (y <= 8.5e+69) {
		tmp = i * (t * b);
	} else if (y <= 3.8e+139) {
		tmp = t * -(x * a);
	} else if (y <= 7e+220) {
		tmp = y * (x * z);
	} 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 = i * (y * -j)
    if (y <= (-2d-20)) then
        tmp = t_1
    else if (y <= 9.5d-67) then
        tmp = j * (a * c)
    else if (y <= 8.5d+69) then
        tmp = i * (t * b)
    else if (y <= 3.8d+139) then
        tmp = t * -(x * a)
    else if (y <= 7d+220) then
        tmp = y * (x * z)
    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 = i * (y * -j);
	double tmp;
	if (y <= -2e-20) {
		tmp = t_1;
	} else if (y <= 9.5e-67) {
		tmp = j * (a * c);
	} else if (y <= 8.5e+69) {
		tmp = i * (t * b);
	} else if (y <= 3.8e+139) {
		tmp = t * -(x * a);
	} else if (y <= 7e+220) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if y <= -2e-20:
		tmp = t_1
	elif y <= 9.5e-67:
		tmp = j * (a * c)
	elif y <= 8.5e+69:
		tmp = i * (t * b)
	elif y <= 3.8e+139:
		tmp = t * -(x * a)
	elif y <= 7e+220:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -2e-20)
		tmp = t_1;
	elseif (y <= 9.5e-67)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 8.5e+69)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 3.8e+139)
		tmp = Float64(t * Float64(-Float64(x * a)));
	elseif (y <= 7e+220)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	tmp = 0.0;
	if (y <= -2e-20)
		tmp = t_1;
	elseif (y <= 9.5e-67)
		tmp = j * (a * c);
	elseif (y <= 8.5e+69)
		tmp = i * (t * b);
	elseif (y <= 3.8e+139)
		tmp = t * -(x * a);
	elseif (y <= 7e+220)
		tmp = y * (x * z);
	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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-20], t$95$1, If[LessEqual[y, 9.5e-67], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+69], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+139], N[(t * (-N[(x * a), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 7e+220], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.99999999999999989e-20 or 6.99999999999999972e220 < y

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 65.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 65.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 65.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 65.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 67.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 67.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 67.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 67.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 67.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 67.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 67.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around inf 55.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.2%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 55.2%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 55.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   7. Taylor expanded in t around 0 45.6%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.6%

         \[\leadsto i \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot j\right)} \]

      2. neg-mul-1 45.6%

         \[\leadsto i \cdot \left(\color{blue}{\left(-y\right)} \cdot j\right) \]

   9. Simplified 45.6%

      \[\leadsto i \cdot \color{blue}{\left(\left(-y\right) \cdot j\right)} \]

   if -1.99999999999999989e-20 < y < 9.4999999999999994e-67

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 82.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 82.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 82.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 82.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 82.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 82.9%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 82.9%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 82.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 82.9%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 82.9%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 78.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 78.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 79.6%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 79.6%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in j around inf 42.6%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   8. Taylor expanded in c around inf 36.8%

      \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   if 9.4999999999999994e-67 < y < 8.5000000000000002e69

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 75.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 75.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 75.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 75.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 75.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 75.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 75.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 75.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 45.4%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 33.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 8.5000000000000002e69 < y < 3.79999999999999999e139

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 83.1%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 83.1%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 83.1%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 83.1%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 83.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 83.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 83.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 83.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 83.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 55.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 46.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 46.9%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. *-commutative 46.9%

         \[\leadsto t \cdot \left(-\color{blue}{x \cdot a}\right) \]

      3. distribute-rgt-neg-in 46.9%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   7. Simplified 46.9%

      \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   if 3.79999999999999999e139 < y < 6.99999999999999972e220

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 71.3%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 71.3%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 71.3%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 71.3%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 71.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 71.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 71.3%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 71.3%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 71.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 71.3%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 71.3%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 77.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 77.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 77.2%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 77.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 77.2%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 76.8%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in y around inf 65.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 16: 44.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+113} \lor \neg \left(a \leq 2.7 \cdot 10^{+97}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -5.6e+113) (not (<= a 2.7e+97)))
   (* a (- (* c j) (* x t)))
   (* c (- (* a 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 ((a <= -5.6e+113) || !(a <= 2.7e+97)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = c * ((a * 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 ((a <= (-5.6d+113)) .or. (.not. (a <= 2.7d+97))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = c * ((a * 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 ((a <= -5.6e+113) || !(a <= 2.7e+97)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -5.6e+113) or not (a <= 2.7e+97):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -5.6e+113) || !(a <= 2.7e+97))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(c * Float64(Float64(a * 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 ((a <= -5.6e+113) || ~((a <= 2.7e+97)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -5.6e+113], N[Not[LessEqual[a, 2.7e+97]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.59999999999999995e113 or 2.69999999999999993e97 < a

   1. Initial program 65.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 65.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 65.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 65.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 65.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 65.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 65.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 65.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 65.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 65.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 65.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 65.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 65.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 74.0%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 75.2%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 75.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 75.2%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in a around inf 71.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   8. Step-by-step derivation

      1. +-commutative 71.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 71.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 71.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 71.9%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   9. Simplified 71.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if -5.59999999999999995e113 < a < 2.69999999999999993e97

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 81.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 81.2%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 81.2%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 81.2%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 81.2%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 82.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 82.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 82.4%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 82.4%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 82.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 82.4%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 82.4%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 41.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 41.9%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 41.9%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 41.9%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 41.9%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 41.9%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 41.9%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+113} \lor \neg \left(a \leq 2.7 \cdot 10^{+97}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 17: 51.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{-62} \lor \neg \left(i \leq 1.25 \cdot 10^{+39}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1e-62) (not (<= i 1.25e+39)))
   (* i (- (* t b) (* y j)))
   (* c (- (* a 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 <= -1e-62) || !(i <= 1.25e+39)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = c * ((a * 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 <= (-1d-62)) .or. (.not. (i <= 1.25d+39))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = c * ((a * 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 <= -1e-62) || !(i <= 1.25e+39)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1e-62) or not (i <= 1.25e+39):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1e-62) || !(i <= 1.25e+39))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(Float64(a * 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 <= -1e-62) || ~((i <= 1.25e+39)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1e-62], N[Not[LessEqual[i, 1.25e+39]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1e-62 or 1.25000000000000004e39 < i

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 68.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 68.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 68.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 68.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 68.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 69.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 69.1%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 69.1%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 69.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 69.1%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 69.1%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in i around inf 60.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      2. unsub-neg 60.4%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

   6. Simplified 60.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - y \cdot j\right)} \]

   if -1e-62 < i < 1.25000000000000004e39

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 83.9%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 83.9%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 83.9%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 83.9%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 84.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 84.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 84.7%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 84.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 84.7%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 84.7%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 55.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 55.0%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 55.0%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 55.0%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 55.0%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 55.0%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 55.0%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 55.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{-62} \lor \neg \left(i \leq 1.25 \cdot 10^{+39}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 18: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{-22} \lor \neg \left(j \leq 6.5 \cdot 10^{-63}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -9e-22) (not (<= j 6.5e-63))) (* c (* a j)) (* i (* t 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 ((j <= -9e-22) || !(j <= 6.5e-63)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * 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 ((j <= (-9d-22)) .or. (.not. (j <= 6.5d-63))) then
        tmp = c * (a * j)
    else
        tmp = i * (t * 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 ((j <= -9e-22) || !(j <= 6.5e-63)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -9e-22) or not (j <= 6.5e-63):
		tmp = c * (a * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -9e-22) || !(j <= 6.5e-63))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -9e-22) || ~((j <= 6.5e-63)))
		tmp = c * (a * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -9e-22], N[Not[LessEqual[j, 6.5e-63]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -8.99999999999999973e-22 or 6.4999999999999998e-63 < j

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 81.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 81.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 81.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 81.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 81.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 81.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 81.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 81.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 81.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 81.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 81.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 49.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 49.1%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 49.1%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 49.1%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 49.1%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 49.1%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 49.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 49.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   7. Taylor expanded in a around inf 38.6%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if -8.99999999999999973e-22 < j < 6.4999999999999998e-63

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 68.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 68.7%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 68.7%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 68.7%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 68.7%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 70.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 70.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 70.5%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 70.5%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 70.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 70.5%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 70.5%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 70.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 46.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around inf 26.7%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{-22} \lor \neg \left(j \leq 6.5 \cdot 10^{-63}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 19: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.9 \cdot 10^{+28} \lor \neg \left(j \leq 4.8 \cdot 10^{+22}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -4.9e+28) (not (<= j 4.8e+22))) (* c (* a 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 ((j <= -4.9e+28) || !(j <= 4.8e+22)) {
		tmp = c * (a * 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 ((j <= (-4.9d+28)) .or. (.not. (j <= 4.8d+22))) then
        tmp = c * (a * 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 ((j <= -4.9e+28) || !(j <= 4.8e+22)) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -4.9e+28) or not (j <= 4.8e+22):
		tmp = c * (a * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -4.9e+28) || !(j <= 4.8e+22))
		tmp = Float64(c * Float64(a * 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 ((j <= -4.9e+28) || ~((j <= 4.8e+22)))
		tmp = c * (a * 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[j, -4.9e+28], N[Not[LessEqual[j, 4.8e+22]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.8999999999999996e28 or 4.8e22 < j

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 82.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 82.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 82.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 82.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 82.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 82.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 82.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 82.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 82.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 82.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in c around inf 53.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-in 52.8%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

      2. *-commutative 52.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

      3. mul-1-neg 52.8%

         \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

      4. cancel-sign-sub-inv 52.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

      5. *-commutative 52.8%

         \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

      6. distribute-rgt-out-- 53.7%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   7. Taylor expanded in a around inf 43.6%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if -4.8999999999999996e28 < j < 4.8e22

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 70.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 70.4%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 70.4%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 70.4%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 70.4%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 71.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 71.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 71.8%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 71.8%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 71.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 71.8%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 71.8%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 74.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 74.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 75.5%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 75.5%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 75.5%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in z around inf 69.5%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{y \cdot \left(z \cdot x\right)} - c \cdot \left(z \cdot b\right)\right) \]

   8. Taylor expanded in y around inf 28.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.9 \cdot 10^{+28} \lor \neg \left(j \leq 4.8 \cdot 10^{+22}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 20: 21.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x 7.2e+145) (* a (* c j)) (* 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 tmp;
	if (x <= 7.2e+145) {
		tmp = a * (c * j);
	} else {
		tmp = 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) :: tmp
    if (x <= 7.2d+145) then
        tmp = a * (c * j)
    else
        tmp = 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 tmp;
	if (x <= 7.2e+145) {
		tmp = a * (c * j);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= 7.2e+145:
		tmp = a * (c * j)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= 7.2e+145)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= 7.2e+145)
		tmp = a * (c * j);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, 7.2e+145], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.19999999999999948e145

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 76.5%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 76.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 76.5%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 76.5%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 77.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 77.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 77.0%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 77.0%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 77.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 77.0%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 77.0%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around 0 80.2%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

      2. fma-def 81.2%

         \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      3. associate-*r* 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      4. neg-mul-1 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

      5. +-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

      6. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      7. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

      8. mul-1-neg 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

      9. distribute-lft-neg-in 81.2%

         \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

      10. cancel-sign-sub-inv 81.2%

          \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

   6. Simplified 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

   7. Taylor expanded in a around inf 41.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   8. Step-by-step derivation

      1. +-commutative 41.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 41.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 41.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 41.9%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   9. Simplified 41.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   10. Taylor expanded in c around inf 27.5%

       \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if 7.19999999999999948e145 < x

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. +-commutative 71.0%

         \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-+l+ 71.0%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      4. distribute-rgt-neg-in 71.0%

         \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      5. +-commutative 71.0%

         \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      6. fma-def 73.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

      7. sub-neg 73.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      8. +-commutative 73.6%

         \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      9. distribute-neg-in 73.6%

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      10. unsub-neg 73.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      11. remove-double-neg 73.6%

          \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

      12. *-commutative 73.6%

          \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 50.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right)} \]

   5. Taylor expanded in i around 0 34.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 35.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(a \cdot t\right) \cdot x\right)} \]

      2. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x} \]

      3. *-commutative 35.6%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right)\right)} \]

      4. mul-1-neg 35.6%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      5. distribute-rgt-neg-in 35.6%

         \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]

   7. Simplified 35.6%

      \[\leadsto \color{blue}{x \cdot \left(a \cdot \left(-t\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 16.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(a \cdot \left(-t\right)\right)\right)\right)} \]

      2. expm1-udef 16.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(a \cdot \left(-t\right)\right)\right)} - 1} \]

      3. *-commutative 16.4%

         \[\leadsto e^{\mathsf{log1p}\left(x \cdot \color{blue}{\left(\left(-t\right) \cdot a\right)}\right)} - 1 \]

      4. add-sqr-sqrt 10.7%

         \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)} \cdot a\right)\right)} - 1 \]

      5. sqrt-unprod 21.7%

         \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}} \cdot a\right)\right)} - 1 \]

      6. sqr-neg 21.7%

         \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\sqrt{\color{blue}{t \cdot t}} \cdot a\right)\right)} - 1 \]

      7. sqrt-unprod 10.9%

         \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)} \cdot a\right)\right)} - 1 \]

      8. add-sqr-sqrt 13.9%

         \[\leadsto e^{\mathsf{log1p}\left(x \cdot \left(\color{blue}{t} \cdot a\right)\right)} - 1 \]

   9. Applied egg-rr 13.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(t \cdot a\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 14.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(t \cdot a\right)\right)\right)} \]

       2. expm1-log1p 19.4%

          \[\leadsto \color{blue}{x \cdot \left(t \cdot a\right)} \]

       3. associate-*r* 21.9%

          \[\leadsto \color{blue}{\left(x \cdot t\right) \cdot a} \]

       4. *-commutative 21.9%

          \[\leadsto \color{blue}{a \cdot \left(x \cdot t\right)} \]

   11. Simplified 21.9%

       \[\leadsto \color{blue}{a \cdot \left(x \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 21: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

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 * (c * j)
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 * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. sub-neg 75.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. +-commutative 75.7%

      \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. associate-+l+ 75.7%

      \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   4. distribute-rgt-neg-in 75.7%

      \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   5. +-commutative 75.7%

      \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

   6. fma-def 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

   7. sub-neg 76.5%

      \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   8. +-commutative 76.5%

      \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   9. distribute-neg-in 76.5%

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   10. unsub-neg 76.5%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   11. remove-double-neg 76.5%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   12. *-commutative 76.5%

       \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

3. Simplified 78.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

4. Taylor expanded in t around 0 76.9%

   \[\leadsto \color{blue}{t \cdot \left(i \cdot b + -1 \cdot \left(a \cdot x\right)\right) + \left(-1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]
5. Step-by-step derivation

   1. fma-def 77.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, i \cdot b + -1 \cdot \left(a \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right)} \]

   2. fma-def 77.7%

      \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{fma}\left(i, b, -1 \cdot \left(a \cdot x\right)\right)}, -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

   3. associate-*r* 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-1 \cdot a\right) \cdot x}\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

   4. neg-mul-1 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \color{blue}{\left(-a\right)} \cdot x\right), -1 \cdot \left(c \cdot \left(z \cdot b\right)\right) + \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)\right) \]

   5. +-commutative 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)}\right) \]

   6. *-commutative 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + j \cdot \left(c \cdot a - \color{blue}{i \cdot y}\right)\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

   7. *-commutative 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j}\right) + -1 \cdot \left(c \cdot \left(z \cdot b\right)\right)\right) \]

   8. mul-1-neg 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c \cdot \left(z \cdot b\right)\right)}\right) \]

   9. distribute-lft-neg-in 77.7%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) + \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)}\right) \]

   10. cancel-sign-sub-inv 77.7%

       \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \color{blue}{\left(y \cdot \left(z \cdot x\right) + \left(c \cdot a - i \cdot y\right) \cdot j\right) - c \cdot \left(z \cdot b\right)}\right) \]

6. Simplified 78.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(i, b, \left(-a\right) \cdot x\right), \mathsf{fma}\left(y, z \cdot x, j \cdot \left(a \cdot c - y \cdot i\right)\right) - c \cdot \left(z \cdot b\right)\right)} \]

7. Taylor expanded in a around inf 41.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
8. Step-by-step derivation

   1. +-commutative 41.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 41.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 41.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 41.0%

      \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

9. Simplified 41.0%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

10. Taylor expanded in c around inf 24.9%

    \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

11. Final simplification 24.9%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 22: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* c (* a j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

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 = c * (a * j)
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 c * (a * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return c * (a * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(c * Float64(a * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = c * (a * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. sub-neg 75.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - t \cdot i\right)\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. +-commutative 75.7%

      \[\leadsto \color{blue}{\left(\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. associate-+l+ 75.7%

      \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   4. distribute-rgt-neg-in 75.7%

      \[\leadsto \color{blue}{b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right)} + \left(x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   5. +-commutative 75.7%

      \[\leadsto b \cdot \left(-\left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

   6. fma-def 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, -\left(c \cdot z - t \cdot i\right), j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right)} \]

   7. sub-neg 76.5%

      \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   8. +-commutative 76.5%

      \[\leadsto \mathsf{fma}\left(b, -\color{blue}{\left(\left(-t \cdot i\right) + c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   9. distribute-neg-in 76.5%

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) + \left(-c \cdot z\right)}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   10. unsub-neg 76.5%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(-\left(-t \cdot i\right)\right) - c \cdot z}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   11. remove-double-neg 76.5%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{t \cdot i} - c \cdot z, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

   12. *-commutative 76.5%

       \[\leadsto \mathsf{fma}\left(b, t \cdot i - \color{blue}{z \cdot c}, j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) \]

3. Simplified 78.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, t \cdot i - z \cdot c, \mathsf{fma}\left(x, y \cdot z - t \cdot a, j \cdot \left(a \cdot c - y \cdot i\right)\right)\right)} \]

4. Taylor expanded in c around inf 43.3%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j + -1 \cdot \left(z \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. distribute-rgt-in 42.9%

      \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c} \]

   2. *-commutative 42.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} + \left(-1 \cdot \left(z \cdot b\right)\right) \cdot c \]

   3. mul-1-neg 42.9%

      \[\leadsto c \cdot \left(a \cdot j\right) + \color{blue}{\left(-z \cdot b\right)} \cdot c \]

   4. cancel-sign-sub-inv 42.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right) - \left(z \cdot b\right) \cdot c} \]

   5. *-commutative 42.9%

      \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} - \left(z \cdot b\right) \cdot c \]

   6. distribute-rgt-out-- 43.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

6. Simplified 43.3%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

7. Taylor expanded in a around inf 26.1%

   \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

8. Final simplification 26.1%

   \[\leadsto c \cdot \left(a \cdot j\right) \]

Developer target: 58.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - 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 * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))