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

Percentage Accurate: 72.9% → 81.1%

Time: 21.7s

Alternatives: 19

Speedup: 0.5×

• 58.1% 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: 72.9% 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: 81.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(x \cdot t - c \cdot j\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + t_3\\ \mathbf{if}\;t_4 \leq -1 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(t_1 - y \cdot \left(i \cdot j\right)\right) - t_2\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot y - b \cdot c, t \cdot \left(b \cdot i - x \cdot a\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z)))
        (t_2 (* a (- (* x t) (* c j))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* t i)))) t_3)))
   (if (<= t_4 -1e+307)
     (+ (- (- t_1 (* y (* i j))) t_2) (* b (- (* t i) (* z c))))
     (if (<= t_4 2e+304)
       t_4
       (if (<= t_4 INFINITY)
         (+ (fma z (- (* x y) (* b c)) (* t (- (* b i) (* x a)))) t_3)
         (- 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 = y * (x * z);
	double t_2 = a * ((x * t) - (c * j));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = ((x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))) + t_3;
	double tmp;
	if (t_4 <= -1e+307) {
		tmp = ((t_1 - (y * (i * j))) - t_2) + (b * ((t * i) - (z * c)));
	} else if (t_4 <= 2e+304) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = fma(z, ((x * y) - (b * c)), (t * ((b * i) - (x * a)))) + t_3;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(a * Float64(Float64(x * t) - Float64(c * j)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(t * i)))) + t_3)
	tmp = 0.0
	if (t_4 <= -1e+307)
		tmp = Float64(Float64(Float64(t_1 - Float64(y * Float64(i * j))) - t_2) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (t_4 <= 2e+304)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = Float64(fma(z, Float64(Float64(x * y) - Float64(b * c)), Float64(t * Float64(Float64(b * i) - Float64(x * a)))) + t_3);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+307], N[(N[(N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+304], t$95$4, If[LessEqual[t$95$4, Infinity], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 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)))) < -9.99999999999999986e306

   1. Initial program 84.4%

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

      1. cancel-sign-sub 84.4%

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

      2. cancel-sign-sub-inv 84.4%

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

      3. *-commutative 84.4%

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

      4. remove-double-neg 84.4%

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

      5. *-commutative 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in a around 0 94.5%

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

   if -9.99999999999999986e306 < (+.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)))) < 1.9999999999999999e304

   1. Initial program 97.5%

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

   if 1.9999999999999999e304 < (+.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 82.7%

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

      1. cancel-sign-sub 82.7%

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

      2. cancel-sign-sub-inv 82.7%

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

      3. *-commutative 82.7%

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

      4. remove-double-neg 82.7%

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

      5. *-commutative 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in z around 0 92.0%

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

      1. associate--l+ 92.0%

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

      2. *-commutative 92.0%

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

      3. fma-def 92.0%

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

      4. sub-neg 92.0%

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

      5. mul-1-neg 92.0%

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

      6. remove-double-neg 92.0%

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

      7. *-commutative 92.0%

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

      8. associate-*r* 92.0%

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

      9. associate-*l* 92.0%

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

      10. *-commutative 92.0%

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

      11. associate-*r* 92.1%

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

      12. distribute-rgt-in 92.1%

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

      13. +-commutative 92.1%

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

      14. mul-1-neg 92.1%

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

      15. unsub-neg 92.1%

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

   6. Simplified 92.1%

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

   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. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. remove-double-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around 0 26.9%

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

   5. Taylor expanded in i around 0 36.7%

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

      1. sub-neg 36.7%

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

      2. +-commutative 36.7%

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

      3. associate-+l+ 36.7%

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

      4. mul-1-neg 36.7%

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

      5. *-commutative 36.7%

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

      6. unsub-neg 36.7%

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

      7. *-commutative 36.7%

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

      8. *-commutative 36.7%

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

      9. associate-*r* 34.8%

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

      10. associate-*r* 36.6%

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

      11. distribute-lft-neg-in 36.6%

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

      12. mul-1-neg 36.6%

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

      13. distribute-rgt-in 42.4%

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

      14. mul-1-neg 42.4%

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

      15. sub-neg 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in b around 0 50.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -1 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\right) - a \cdot \left(x \cdot t - c \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z, x \cdot y - b \cdot c, t \cdot \left(b \cdot i - x \cdot a\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 2: 81.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(x \cdot t - c \cdot j\right)\\ t_3 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(t_1 - y \cdot \left(i \cdot j\right)\right) - t_2\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z)))
        (t_2 (* a (- (* x t) (* c j))))
        (t_3
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* t i))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_3 -1e+307)
     (+ (- (- t_1 (* y (* i j))) t_2) (* b (- (* t i) (* z c))))
     (if (<= t_3 INFINITY) t_3 (- 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 = y * (x * z);
	double t_2 = a * ((x * t) - (c * j));
	double t_3 = ((x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_3 <= -1e+307) {
		tmp = ((t_1 - (y * (i * j))) - t_2) + (b * ((t * i) - (z * c)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1 - t_2;
	}
	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 = y * (x * z);
	double t_2 = a * ((x * t) - (c * j));
	double t_3 = ((x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_3 <= -1e+307) {
		tmp = ((t_1 - (y * (i * j))) - t_2) + (b * ((t * i) - (z * c)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = a * ((x * t) - (c * j))
	t_3 = ((x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_3 <= -1e+307:
		tmp = ((t_1 - (y * (i * j))) - t_2) + (b * ((t * i) - (z * c)))
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1 - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(a * Float64(Float64(x * t) - Float64(c * j)))
	t_3 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(t * i)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= -1e+307)
		tmp = Float64(Float64(Float64(t_1 - Float64(y * Float64(i * j))) - t_2) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = a * ((x * t) - (c * j));
	t_3 = ((x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_3 <= -1e+307)
		tmp = ((t_1 - (y * (i * j))) - t_2) + (b * ((t * i) - (z * c)));
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+307], N[(N[(N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, N[(t$95$1 - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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)))) < -9.99999999999999986e306

   1. Initial program 84.4%

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

      1. cancel-sign-sub 84.4%

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

      2. cancel-sign-sub-inv 84.4%

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

      3. *-commutative 84.4%

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

      4. remove-double-neg 84.4%

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

      5. *-commutative 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in a around 0 94.5%

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

   if -9.99999999999999986e306 < (+.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 91.6%

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

   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. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. remove-double-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around 0 26.9%

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

   5. Taylor expanded in i around 0 36.7%

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

      1. sub-neg 36.7%

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

      2. +-commutative 36.7%

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

      3. associate-+l+ 36.7%

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

      4. mul-1-neg 36.7%

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

      5. *-commutative 36.7%

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

      6. unsub-neg 36.7%

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

      7. *-commutative 36.7%

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

      8. *-commutative 36.7%

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

      9. associate-*r* 34.8%

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

      10. associate-*r* 36.6%

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

      11. distribute-lft-neg-in 36.6%

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

      12. mul-1-neg 36.6%

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

      13. distribute-rgt-in 42.4%

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

      14. mul-1-neg 42.4%

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

      15. sub-neg 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in b around 0 50.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq -1 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\right) - a \cdot \left(x \cdot t - c \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 3: 82.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.6%

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

   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. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. remove-double-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in a around 0 26.9%

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

   5. Taylor expanded in i around 0 36.7%

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

      1. sub-neg 36.7%

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

      2. +-commutative 36.7%

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

      3. associate-+l+ 36.7%

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

      4. mul-1-neg 36.7%

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

      5. *-commutative 36.7%

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

      6. unsub-neg 36.7%

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

      7. *-commutative 36.7%

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

      8. *-commutative 36.7%

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

      9. associate-*r* 34.8%

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

      10. associate-*r* 36.6%

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

      11. distribute-lft-neg-in 36.6%

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

      12. mul-1-neg 36.6%

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

      13. distribute-rgt-in 42.4%

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

      14. mul-1-neg 42.4%

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

      15. sub-neg 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in b around 0 50.1%

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

4. Final simplification 81.6%

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

Alternative 4: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;j \leq -2600:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (* x z)) (* a (- (* x t) (* c j)))))
        (t_2 (+ (* t (- (* b i) (* x a))) (* z (- (* x y) (* b c)))))
        (t_3 (- (* j (- (* a c) (* y i))) (* c (* z b)))))
   (if (<= j -2600.0)
     t_3
     (if (<= j 1.7e-168)
       (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* t i))))
       (if (<= j 5.3e-20)
         t_2
         (if (<= j 5.8e+18)
           t_1
           (if (<= j 1.3e+62) t_2 (if (<= j 1.32e+129) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * (x * z)) - (a * ((x * t) - (c * j)));
	double t_2 = (t * ((b * i) - (x * a))) + (z * ((x * y) - (b * c)));
	double t_3 = (j * ((a * c) - (y * i))) - (c * (z * b));
	double tmp;
	if (j <= -2600.0) {
		tmp = t_3;
	} else if (j <= 1.7e-168) {
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	} else if (j <= 5.3e-20) {
		tmp = t_2;
	} else if (j <= 5.8e+18) {
		tmp = t_1;
	} else if (j <= 1.3e+62) {
		tmp = t_2;
	} else if (j <= 1.32e+129) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * (x * z)) - (a * ((x * t) - (c * j)))
    t_2 = (t * ((b * i) - (x * a))) + (z * ((x * y) - (b * c)))
    t_3 = (j * ((a * c) - (y * i))) - (c * (z * b))
    if (j <= (-2600.0d0)) then
        tmp = t_3
    else if (j <= 1.7d-168) then
        tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))
    else if (j <= 5.3d-20) then
        tmp = t_2
    else if (j <= 5.8d+18) then
        tmp = t_1
    else if (j <= 1.3d+62) then
        tmp = t_2
    else if (j <= 1.32d+129) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * (x * z)) - (a * ((x * t) - (c * j)));
	double t_2 = (t * ((b * i) - (x * a))) + (z * ((x * y) - (b * c)));
	double t_3 = (j * ((a * c) - (y * i))) - (c * (z * b));
	double tmp;
	if (j <= -2600.0) {
		tmp = t_3;
	} else if (j <= 1.7e-168) {
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	} else if (j <= 5.3e-20) {
		tmp = t_2;
	} else if (j <= 5.8e+18) {
		tmp = t_1;
	} else if (j <= 1.3e+62) {
		tmp = t_2;
	} else if (j <= 1.32e+129) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * (x * z)) - (a * ((x * t) - (c * j)))
	t_2 = (t * ((b * i) - (x * a))) + (z * ((x * y) - (b * c)))
	t_3 = (j * ((a * c) - (y * i))) - (c * (z * b))
	tmp = 0
	if j <= -2600.0:
		tmp = t_3
	elif j <= 1.7e-168:
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))
	elif j <= 5.3e-20:
		tmp = t_2
	elif j <= 5.8e+18:
		tmp = t_1
	elif j <= 1.3e+62:
		tmp = t_2
	elif j <= 1.32e+129:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))))
	t_2 = Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(c * Float64(z * b)))
	tmp = 0.0
	if (j <= -2600.0)
		tmp = t_3;
	elseif (j <= 1.7e-168)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	elseif (j <= 5.3e-20)
		tmp = t_2;
	elseif (j <= 5.8e+18)
		tmp = t_1;
	elseif (j <= 1.3e+62)
		tmp = t_2;
	elseif (j <= 1.32e+129)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * (x * z)) - (a * ((x * t) - (c * j)));
	t_2 = (t * ((b * i) - (x * a))) + (z * ((x * y) - (b * c)));
	t_3 = (j * ((a * c) - (y * i))) - (c * (z * b));
	tmp = 0.0;
	if (j <= -2600.0)
		tmp = t_3;
	elseif (j <= 1.7e-168)
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	elseif (j <= 5.3e-20)
		tmp = t_2;
	elseif (j <= 5.8e+18)
		tmp = t_1;
	elseif (j <= 1.3e+62)
		tmp = t_2;
	elseif (j <= 1.32e+129)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2600.0], t$95$3, If[LessEqual[j, 1.7e-168], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.3e-20], t$95$2, If[LessEqual[j, 5.8e+18], t$95$1, If[LessEqual[j, 1.3e+62], t$95$2, If[LessEqual[j, 1.32e+129], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2600 or 1.32e129 < j

   1. Initial program 70.0%

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

      1. cancel-sign-sub 70.0%

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

      2. cancel-sign-sub-inv 70.0%

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

      3. *-commutative 70.0%

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

      4. remove-double-neg 70.0%

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

      5. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in c around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. *-commutative 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

      4. distribute-rgt-neg-in 69.6%

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

   6. Simplified 69.6%

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

   if -2600 < j < 1.70000000000000011e-168

   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 j around 0 81.1%

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

   if 1.70000000000000011e-168 < j < 5.3000000000000002e-20 or 5.8e18 < j < 1.29999999999999992e62

   1. Initial program 65.6%

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

      1. cancel-sign-sub 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. *-commutative 65.6%

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

      4. remove-double-neg 65.6%

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

      5. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around 0 76.7%

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

      1. associate--l+ 76.7%

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

      2. *-commutative 76.7%

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

      3. fma-def 76.7%

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

      4. sub-neg 76.7%

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

      5. mul-1-neg 76.7%

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

      6. remove-double-neg 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*r* 81.6%

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

      9. associate-*l* 81.6%

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

      10. *-commutative 81.6%

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

      11. associate-*r* 84.4%

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

      12. distribute-rgt-in 84.4%

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

      13. +-commutative 84.4%

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

      14. mul-1-neg 84.4%

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

      15. unsub-neg 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in j around 0 84.3%

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

   if 5.3000000000000002e-20 < j < 5.8e18 or 1.29999999999999992e62 < j < 1.32e129

   1. Initial program 52.6%

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

      1. cancel-sign-sub 52.6%

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

      2. cancel-sign-sub-inv 52.6%

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

      3. *-commutative 52.6%

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

      4. remove-double-neg 52.6%

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

      5. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   4. Taylor expanded in a around 0 70.1%

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

   5. Taylor expanded in i around 0 70.1%

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

      1. sub-neg 70.1%

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

      2. +-commutative 70.1%

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

      3. associate-+l+ 70.1%

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

      4. mul-1-neg 70.1%

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

      5. *-commutative 70.1%

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

      6. unsub-neg 70.1%

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

      7. *-commutative 70.1%

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

      8. *-commutative 70.1%

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

      9. associate-*r* 65.8%

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

      10. associate-*r* 65.4%

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

      11. distribute-lft-neg-in 65.4%

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

      12. mul-1-neg 65.4%

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

      13. distribute-rgt-in 69.7%

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

      14. mul-1-neg 69.7%

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

      15. sub-neg 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in b around 0 82.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2600:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;j \leq 5.3 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 5: 67.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+100} \lor \neg \left(i \leq 9.2 \cdot 10^{+86}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.4e+100) (not (<= i 9.2e+86)))
   (* i (- (* t b) (* y j)))
   (- (* z (- (* x y) (* b c))) (* a (- (* x t) (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.4e+100) || !(i <= 9.2e+86)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.4d+100)) .or. (.not. (i <= 9.2d+86))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.4e+100) || !(i <= 9.2e+86)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.4e+100) or not (i <= 9.2e+86):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.4e+100) || !(i <= 9.2e+86))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.4e+100) || ~((i <= 9.2e+86)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.4e+100], N[Not[LessEqual[i, 9.2e+86]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.3999999999999999e100 or 9.19999999999999958e86 < i

   1. Initial program 58.3%

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

      1. cancel-sign-sub 58.3%

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

      2. cancel-sign-sub-inv 58.3%

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

      3. *-commutative 58.3%

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

      4. remove-double-neg 58.3%

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

      5. *-commutative 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in i around inf 69.8%

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

      1. associate-*r* 69.8%

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

      2. neg-mul-1 69.8%

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

      3. cancel-sign-sub 69.8%

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

      4. +-commutative 69.8%

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

      5. mul-1-neg 69.8%

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

      6. unsub-neg 69.8%

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

      7. *-commutative 69.8%

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

   6. Simplified 69.8%

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

   if -1.3999999999999999e100 < i < 9.19999999999999958e86

   1. Initial program 77.2%

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

      1. cancel-sign-sub 77.2%

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

      2. cancel-sign-sub-inv 77.2%

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

      3. *-commutative 77.2%

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

      4. remove-double-neg 77.2%

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

      5. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in a around 0 76.1%

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

   5. Taylor expanded in i around 0 68.0%

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

      1. sub-neg 68.0%

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

      2. +-commutative 68.0%

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

      3. associate-+l+ 68.0%

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

      4. mul-1-neg 68.0%

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

      5. *-commutative 68.0%

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

      6. unsub-neg 68.0%

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

      7. *-commutative 68.0%

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

      8. *-commutative 68.0%

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

      9. associate-*r* 68.9%

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

      10. associate-*r* 67.7%

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

      11. distribute-lft-neg-in 67.7%

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

      12. mul-1-neg 67.7%

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

      13. distribute-rgt-in 69.3%

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

      14. mul-1-neg 69.3%

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

      15. sub-neg 69.3%

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

   7. Simplified 69.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+100} \lor \neg \left(i \leq 9.2 \cdot 10^{+86}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 6: 65.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t - c \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-26}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* x t) (* c j)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= a -2.5e-26)
     (- t_2 t_1)
     (if (<= a 2.3e+75)
       (+ (* t (- (* b i) (* x a))) t_2)
       (- (* 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 = a * ((x * t) - (c * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (a <= -2.5e-26) {
		tmp = t_2 - t_1;
	} else if (a <= 2.3e+75) {
		tmp = (t * ((b * i) - (x * a))) + t_2;
	} else {
		tmp = (y * (x * z)) - 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 = a * ((x * t) - (c * j))
    t_2 = z * ((x * y) - (b * c))
    if (a <= (-2.5d-26)) then
        tmp = t_2 - t_1
    else if (a <= 2.3d+75) then
        tmp = (t * ((b * i) - (x * a))) + t_2
    else
        tmp = (y * (x * z)) - 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 = a * ((x * t) - (c * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (a <= -2.5e-26) {
		tmp = t_2 - t_1;
	} else if (a <= 2.3e+75) {
		tmp = (t * ((b * i) - (x * a))) + t_2;
	} else {
		tmp = (y * (x * z)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((x * t) - (c * j))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if a <= -2.5e-26:
		tmp = t_2 - t_1
	elif a <= 2.3e+75:
		tmp = (t * ((b * i) - (x * a))) + t_2
	else:
		tmp = (y * (x * z)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(x * t) - Float64(c * j)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (a <= -2.5e-26)
		tmp = Float64(t_2 - t_1);
	elseif (a <= 2.3e+75)
		tmp = Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) + t_2);
	else
		tmp = Float64(Float64(y * Float64(x * z)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((x * t) - (c * j));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (a <= -2.5e-26)
		tmp = t_2 - t_1;
	elseif (a <= 2.3e+75)
		tmp = (t * ((b * i) - (x * a))) + t_2;
	else
		tmp = (y * (x * z)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-26], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[a, 2.3e+75], N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5000000000000001e-26

   1. Initial program 66.0%

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

      1. cancel-sign-sub 66.0%

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

      2. cancel-sign-sub-inv 66.0%

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

      3. *-commutative 66.0%

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

      4. remove-double-neg 66.0%

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

      5. *-commutative 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in a around 0 77.1%

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

   5. Taylor expanded in i around 0 70.1%

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

      1. sub-neg 70.1%

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

      2. +-commutative 70.1%

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

      3. associate-+l+ 70.1%

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

      4. mul-1-neg 70.1%

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

      5. *-commutative 70.1%

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

      6. unsub-neg 70.1%

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

      7. *-commutative 70.1%

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

      8. *-commutative 70.1%

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

      9. associate-*r* 71.1%

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

      10. associate-*r* 70.1%

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

      11. distribute-lft-neg-in 70.1%

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

      12. mul-1-neg 70.1%

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

      13. distribute-rgt-in 71.2%

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

      14. mul-1-neg 71.2%

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

      15. sub-neg 71.2%

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

   7. Simplified 71.2%

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

   if -2.5000000000000001e-26 < a < 2.2999999999999999e75

   1. Initial program 76.4%

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

      1. cancel-sign-sub 76.4%

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

      2. cancel-sign-sub-inv 76.4%

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

      3. *-commutative 76.4%

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

      4. remove-double-neg 76.4%

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

      5. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in z around 0 70.1%

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

      1. associate--l+ 70.1%

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

      2. *-commutative 70.1%

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

      3. fma-def 70.1%

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

      4. sub-neg 70.1%

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

      5. mul-1-neg 70.1%

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

      6. remove-double-neg 70.1%

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

      7. *-commutative 70.1%

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

      8. associate-*r* 73.8%

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

      9. associate-*l* 73.8%

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

      10. *-commutative 73.8%

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

      11. associate-*r* 76.8%

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

      12. distribute-rgt-in 76.8%

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

      13. +-commutative 76.8%

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

      14. mul-1-neg 76.8%

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

      15. unsub-neg 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in j around 0 65.1%

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

   if 2.2999999999999999e75 < a

   1. Initial program 67.0%

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

      1. cancel-sign-sub 67.0%

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

      2. cancel-sign-sub-inv 67.0%

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

      3. *-commutative 67.0%

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

      4. remove-double-neg 67.0%

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

      5. *-commutative 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in a around 0 79.5%

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

   5. Taylor expanded in i around 0 80.0%

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

      1. sub-neg 80.0%

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

      2. +-commutative 80.0%

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

      3. associate-+l+ 80.0%

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

      4. mul-1-neg 80.0%

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

      5. *-commutative 80.0%

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

      6. unsub-neg 80.0%

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

      7. *-commutative 80.0%

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

      8. *-commutative 80.0%

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

      9. associate-*r* 77.7%

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

      10. associate-*r* 79.8%

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

      11. distribute-lft-neg-in 79.8%

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

      12. mul-1-neg 79.8%

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

      13. distribute-rgt-in 79.8%

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

      14. mul-1-neg 79.8%

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

      15. sub-neg 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in b around 0 87.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 7: 60.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{+99} \lor \neg \left(i \leq 2.9 \cdot 10^{+86}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -7e+99) (not (<= i 2.9e+86)))
   (* i (- (* t b) (* y j)))
   (- (* y (* x z)) (* a (- (* x t) (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -7e+99) || !(i <= 2.9e+86)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (y * (x * z)) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-7d+99)) .or. (.not. (i <= 2.9d+86))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (y * (x * z)) - (a * ((x * t) - (c * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -7e+99) || !(i <= 2.9e+86)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (y * (x * z)) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -7e+99) or not (i <= 2.9e+86):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (y * (x * z)) - (a * ((x * t) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -7e+99) || !(i <= 2.9e+86))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -7e+99) || ~((i <= 2.9e+86)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (y * (x * z)) - (a * ((x * t) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -7e+99], N[Not[LessEqual[i, 2.9e+86]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.9999999999999995e99 or 2.8999999999999999e86 < i

   1. Initial program 58.3%

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

      1. cancel-sign-sub 58.3%

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

      2. cancel-sign-sub-inv 58.3%

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

      3. *-commutative 58.3%

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

      4. remove-double-neg 58.3%

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

      5. *-commutative 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in i around inf 69.8%

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

      1. associate-*r* 69.8%

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

      2. neg-mul-1 69.8%

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

      3. cancel-sign-sub 69.8%

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

      4. +-commutative 69.8%

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

      5. mul-1-neg 69.8%

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

      6. unsub-neg 69.8%

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

      7. *-commutative 69.8%

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

   6. Simplified 69.8%

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

   if -6.9999999999999995e99 < i < 2.8999999999999999e86

   1. Initial program 77.2%

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

      1. cancel-sign-sub 77.2%

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

      2. cancel-sign-sub-inv 77.2%

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

      3. *-commutative 77.2%

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

      4. remove-double-neg 77.2%

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

      5. *-commutative 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in a around 0 76.1%

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

   5. Taylor expanded in i around 0 68.0%

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

      1. sub-neg 68.0%

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

      2. +-commutative 68.0%

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

      3. associate-+l+ 68.0%

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

      4. mul-1-neg 68.0%

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

      5. *-commutative 68.0%

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

      6. unsub-neg 68.0%

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

      7. *-commutative 68.0%

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

      8. *-commutative 68.0%

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

      9. associate-*r* 68.9%

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

      10. associate-*r* 67.7%

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

      11. distribute-lft-neg-in 67.7%

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

      12. mul-1-neg 67.7%

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

      13. distribute-rgt-in 69.3%

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

      14. mul-1-neg 69.3%

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

      15. sub-neg 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in b around 0 61.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{+99} \lor \neg \left(i \leq 2.9 \cdot 10^{+86}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 8: 39.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -29000000000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 96000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -29000000000000.0)
   (* y (* i (- j)))
   (if (<= y 5e-275)
     (* c (- (* a j) (* z b)))
     (if (<= y 96000000000.0) (* a (- (* c j) (* x t))) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -29000000000000.0) {
		tmp = y * (i * -j);
	} else if (y <= 5e-275) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 96000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-29000000000000.0d0)) then
        tmp = y * (i * -j)
    else if (y <= 5d-275) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 96000000000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -29000000000000.0) {
		tmp = y * (i * -j);
	} else if (y <= 5e-275) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 96000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -29000000000000.0:
		tmp = y * (i * -j)
	elif y <= 5e-275:
		tmp = c * ((a * j) - (z * b))
	elif y <= 96000000000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -29000000000000.0)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (y <= 5e-275)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 96000000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -29000000000000.0)
		tmp = y * (i * -j);
	elseif (y <= 5e-275)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 96000000000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -29000000000000.0], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-275], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 96000000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9e13

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in j around inf 39.0%

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

   5. Taylor expanded in c around 0 41.2%

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

      1. associate-*r* 37.5%

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

      2. associate-*r* 37.5%

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

      3. neg-mul-1 37.5%

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

      4. distribute-rgt-neg-in 37.5%

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

      5. associate-*r* 41.2%

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

   7. Simplified 41.2%

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

   if -2.9e13 < y < 4.99999999999999983e-275

   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. cancel-sign-sub 83.7%

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

      2. cancel-sign-sub-inv 83.7%

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

      3. *-commutative 83.7%

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

      4. remove-double-neg 83.7%

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

      5. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. *-commutative 60.3%

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

   6. Simplified 60.3%

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

   if 4.99999999999999983e-275 < y < 9.6e10

   1. Initial program 76.2%

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

      1. cancel-sign-sub 76.2%

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

      2. cancel-sign-sub-inv 76.2%

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

      3. *-commutative 76.2%

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

      4. remove-double-neg 76.2%

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

      5. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in a around 0 66.4%

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

   5. Taylor expanded in a around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. *-commutative 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if 9.6e10 < y

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -29000000000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 96000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 9: 43.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7800000000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 90000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7800000000000.0)
   (* i (- (* t b) (* y j)))
   (if (<= y 3.6e-276)
     (* c (- (* a j) (* z b)))
     (if (<= y 90000000000.0) (* a (- (* c j) (* x t))) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7800000000000.0) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 3.6e-276) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 90000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7800000000000.0d0)) then
        tmp = i * ((t * b) - (y * j))
    else if (y <= 3.6d-276) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 90000000000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7800000000000.0) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 3.6e-276) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 90000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7800000000000.0:
		tmp = i * ((t * b) - (y * j))
	elif y <= 3.6e-276:
		tmp = c * ((a * j) - (z * b))
	elif y <= 90000000000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7800000000000.0)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (y <= 3.6e-276)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 90000000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7800000000000.0)
		tmp = i * ((t * b) - (y * j));
	elseif (y <= 3.6e-276)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 90000000000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7800000000000.0], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-276], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 90000000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.8e12

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in i around inf 56.4%

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

      1. associate-*r* 56.4%

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

      2. neg-mul-1 56.4%

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

      3. cancel-sign-sub 56.4%

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

      4. +-commutative 56.4%

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

      5. mul-1-neg 56.4%

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

      6. unsub-neg 56.4%

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

      7. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if -7.8e12 < y < 3.59999999999999994e-276

   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. cancel-sign-sub 83.7%

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

      2. cancel-sign-sub-inv 83.7%

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

      3. *-commutative 83.7%

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

      4. remove-double-neg 83.7%

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

      5. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. *-commutative 60.3%

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

   6. Simplified 60.3%

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

   if 3.59999999999999994e-276 < y < 9e10

   1. Initial program 76.2%

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

      1. cancel-sign-sub 76.2%

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

      2. cancel-sign-sub-inv 76.2%

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

      3. *-commutative 76.2%

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

      4. remove-double-neg 76.2%

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

      5. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in a around 0 66.4%

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

   5. Taylor expanded in a around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. *-commutative 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if 9e10 < y

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7800000000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 90000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 10: 51.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1350000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 62000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1350000000000.0)
     t_1
     (if (<= y 4.5e-276)
       (* c (- (* a j) (* z b)))
       (if (<= y 62000000000.0) (* a (- (* c j) (* 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1350000000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e-276) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 62000000000.0) {
		tmp = a * ((c * j) - (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 = y * ((x * z) - (i * j))
    if (y <= (-1350000000000.0d0)) then
        tmp = t_1
    else if (y <= 4.5d-276) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 62000000000.0d0) then
        tmp = a * ((c * j) - (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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1350000000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e-276) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 62000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1350000000000.0:
		tmp = t_1
	elif y <= 4.5e-276:
		tmp = c * ((a * j) - (z * b))
	elif y <= 62000000000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1350000000000.0)
		tmp = t_1;
	elseif (y <= 4.5e-276)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 62000000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - 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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1350000000000.0)
		tmp = t_1;
	elseif (y <= 4.5e-276)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 62000000000.0)
		tmp = a * ((c * j) - (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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1350000000000.0], t$95$1, If[LessEqual[y, 4.5e-276], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 62000000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e12 or 6.2e10 < y

   1. Initial program 59.7%

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

      1. cancel-sign-sub 59.7%

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

      2. cancel-sign-sub-inv 59.7%

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

      3. *-commutative 59.7%

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

      4. remove-double-neg 59.7%

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

      5. *-commutative 59.7%

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

   3. Simplified 59.7%

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

   4. Taylor expanded in a around 0 72.4%

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

   5. Taylor expanded in y around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. *-commutative 65.5%

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

      4. unsub-neg 65.5%

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

      5. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -1.35e12 < y < 4.49999999999999962e-276

   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. cancel-sign-sub 83.7%

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

      2. cancel-sign-sub-inv 83.7%

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

      3. *-commutative 83.7%

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

      4. remove-double-neg 83.7%

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

      5. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. *-commutative 60.3%

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

   6. Simplified 60.3%

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

   if 4.49999999999999962e-276 < y < 6.2e10

   1. Initial program 76.2%

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

      1. cancel-sign-sub 76.2%

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

      2. cancel-sign-sub-inv 76.2%

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

      3. *-commutative 76.2%

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

      4. remove-double-neg 76.2%

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

      5. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in a around 0 66.4%

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

   5. Taylor expanded in a around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. *-commutative 56.1%

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

      3. unsub-neg 56.1%

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

      4. *-commutative 56.1%

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

   7. Simplified 56.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1350000000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 62000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 11: 29.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-109}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 23000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x t) (- a))))
   (if (<= y -5.1e+153)
     (* y (* x z))
     (if (<= y -1.15e-11)
       t_1
       (if (<= y 2.2e-109)
         (* j (* a c))
         (if (<= y 23000000000.0) t_1 (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * t) * -a;
	double tmp;
	if (y <= -5.1e+153) {
		tmp = y * (x * z);
	} else if (y <= -1.15e-11) {
		tmp = t_1;
	} else if (y <= 2.2e-109) {
		tmp = j * (a * c);
	} else if (y <= 23000000000.0) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * t) * -a
    if (y <= (-5.1d+153)) then
        tmp = y * (x * z)
    else if (y <= (-1.15d-11)) then
        tmp = t_1
    else if (y <= 2.2d-109) then
        tmp = j * (a * c)
    else if (y <= 23000000000.0d0) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * t) * -a;
	double tmp;
	if (y <= -5.1e+153) {
		tmp = y * (x * z);
	} else if (y <= -1.15e-11) {
		tmp = t_1;
	} else if (y <= 2.2e-109) {
		tmp = j * (a * c);
	} else if (y <= 23000000000.0) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * t) * -a
	tmp = 0
	if y <= -5.1e+153:
		tmp = y * (x * z)
	elif y <= -1.15e-11:
		tmp = t_1
	elif y <= 2.2e-109:
		tmp = j * (a * c)
	elif y <= 23000000000.0:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * t) * Float64(-a))
	tmp = 0.0
	if (y <= -5.1e+153)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -1.15e-11)
		tmp = t_1;
	elseif (y <= 2.2e-109)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 23000000000.0)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * t) * -a;
	tmp = 0.0;
	if (y <= -5.1e+153)
		tmp = y * (x * z);
	elseif (y <= -1.15e-11)
		tmp = t_1;
	elseif (y <= 2.2e-109)
		tmp = j * (a * c);
	elseif (y <= 23000000000.0)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, If[LessEqual[y, -5.1e+153], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-11], t$95$1, If[LessEqual[y, 2.2e-109], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 23000000000.0], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.10000000000000035e153

   1. Initial program 45.3%

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

      1. cancel-sign-sub 45.3%

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

      2. cancel-sign-sub-inv 45.3%

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

      3. *-commutative 45.3%

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

      4. remove-double-neg 45.3%

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

      5. *-commutative 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in x around inf 42.6%

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

   5. Taylor expanded in y around inf 45.7%

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

   if -5.10000000000000035e153 < y < -1.15000000000000007e-11 or 2.1999999999999999e-109 < y < 2.3e10

   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 a around 0 78.2%

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

   5. Taylor expanded in a around inf 50.2%

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

      1. mul-1-neg 50.2%

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

      2. *-commutative 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in j around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. distribute-rgt-neg-in 36.6%

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

   10. Simplified 36.6%

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

   if -1.15000000000000007e-11 < y < 2.1999999999999999e-109

   1. Initial program 82.2%

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

      1. cancel-sign-sub 82.2%

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

      2. cancel-sign-sub-inv 82.2%

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

      3. *-commutative 82.2%

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

      4. remove-double-neg 82.2%

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

      5. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in j around inf 45.6%

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

   5. Taylor expanded in c around inf 38.0%

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

   if 2.3e10 < y

   1. Initial program 62.3%

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

      1. cancel-sign-sub 62.3%

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

      2. cancel-sign-sub-inv 62.3%

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

      3. *-commutative 62.3%

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

      4. remove-double-neg 62.3%

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

      5. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in z around inf 58.0%

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

   5. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-11}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-109}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 23000000000:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 30.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8200000000000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-50}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 65000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -8200000000000.0)
   (* i (* y (- j)))
   (if (<= y 4.5e-110)
     (* j (* a c))
     (if (<= y 8.6e-50)
       (* (* x t) (- a))
       (if (<= y 65000000000.0) (* a (* c j)) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -8200000000000.0) {
		tmp = i * (y * -j);
	} else if (y <= 4.5e-110) {
		tmp = j * (a * c);
	} else if (y <= 8.6e-50) {
		tmp = (x * t) * -a;
	} else if (y <= 65000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-8200000000000.0d0)) then
        tmp = i * (y * -j)
    else if (y <= 4.5d-110) then
        tmp = j * (a * c)
    else if (y <= 8.6d-50) then
        tmp = (x * t) * -a
    else if (y <= 65000000000.0d0) then
        tmp = a * (c * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -8200000000000.0) {
		tmp = i * (y * -j);
	} else if (y <= 4.5e-110) {
		tmp = j * (a * c);
	} else if (y <= 8.6e-50) {
		tmp = (x * t) * -a;
	} else if (y <= 65000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -8200000000000.0:
		tmp = i * (y * -j)
	elif y <= 4.5e-110:
		tmp = j * (a * c)
	elif y <= 8.6e-50:
		tmp = (x * t) * -a
	elif y <= 65000000000.0:
		tmp = a * (c * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -8200000000000.0)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 4.5e-110)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 8.6e-50)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (y <= 65000000000.0)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -8200000000000.0)
		tmp = i * (y * -j);
	elseif (y <= 4.5e-110)
		tmp = j * (a * c);
	elseif (y <= 8.6e-50)
		tmp = (x * t) * -a;
	elseif (y <= 65000000000.0)
		tmp = a * (c * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -8200000000000.0], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-110], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-50], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[y, 65000000000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.2e12

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in j around inf 39.0%

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

   5. Taylor expanded in c around 0 41.2%

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

      1. associate-*r* 37.5%

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

      2. *-commutative 37.5%

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

      3. associate-*r* 39.5%

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

      4. mul-1-neg 39.5%

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

      5. distribute-rgt-neg-in 39.5%

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

      6. distribute-rgt-neg-in 39.5%

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

   7. Simplified 39.5%

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

   if -8.2e12 < y < 4.5000000000000001e-110

   1. Initial program 81.8%

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

      1. cancel-sign-sub 81.8%

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

      2. cancel-sign-sub-inv 81.8%

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

      3. *-commutative 81.8%

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

      4. remove-double-neg 81.8%

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

      5. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in j around inf 43.6%

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

   5. Taylor expanded in c around inf 36.5%

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

   if 4.5000000000000001e-110 < y < 8.59999999999999995e-50

   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. cancel-sign-sub 77.4%

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

      2. cancel-sign-sub-inv 77.4%

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

      3. *-commutative 77.4%

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

      4. remove-double-neg 77.4%

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

      5. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in a around 0 56.1%

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

   5. Taylor expanded in a around inf 43.2%

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

      1. mul-1-neg 43.2%

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

      2. *-commutative 43.2%

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

      3. unsub-neg 43.2%

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

      4. *-commutative 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in j around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

   10. Simplified 54.3%

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

   if 8.59999999999999995e-50 < y < 6.5e10

   1. Initial program 73.9%

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

      1. cancel-sign-sub 73.9%

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

      2. cancel-sign-sub-inv 73.9%

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

      3. *-commutative 73.9%

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

      4. remove-double-neg 73.9%

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

      5. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in c around inf 29.5%

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

      1. *-commutative 29.5%

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

   6. Simplified 29.5%

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

   7. Taylor expanded in j around inf 23.1%

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

      1. *-commutative 23.1%

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

   9. Simplified 23.1%

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

   10. Taylor expanded in c around 0 23.1%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 29.1%

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

       2. *-commutative 29.1%

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

       3. associate-*r* 35.3%

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

   12. Simplified 35.3%

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

   if 6.5e10 < y

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in y around inf 51.1%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8200000000000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-50}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 65000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 29.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6200000000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-49}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -6200000000000.0)
   (* y (* i (- j)))
   (if (<= y 6e-110)
     (* j (* a c))
     (if (<= y 1.08e-49)
       (* (* x t) (- a))
       (if (<= y 95000000000.0) (* a (* c j)) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6200000000000.0) {
		tmp = y * (i * -j);
	} else if (y <= 6e-110) {
		tmp = j * (a * c);
	} else if (y <= 1.08e-49) {
		tmp = (x * t) * -a;
	} else if (y <= 95000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-6200000000000.0d0)) then
        tmp = y * (i * -j)
    else if (y <= 6d-110) then
        tmp = j * (a * c)
    else if (y <= 1.08d-49) then
        tmp = (x * t) * -a
    else if (y <= 95000000000.0d0) then
        tmp = a * (c * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6200000000000.0) {
		tmp = y * (i * -j);
	} else if (y <= 6e-110) {
		tmp = j * (a * c);
	} else if (y <= 1.08e-49) {
		tmp = (x * t) * -a;
	} else if (y <= 95000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -6200000000000.0:
		tmp = y * (i * -j)
	elif y <= 6e-110:
		tmp = j * (a * c)
	elif y <= 1.08e-49:
		tmp = (x * t) * -a
	elif y <= 95000000000.0:
		tmp = a * (c * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -6200000000000.0)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (y <= 6e-110)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1.08e-49)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (y <= 95000000000.0)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -6200000000000.0)
		tmp = y * (i * -j);
	elseif (y <= 6e-110)
		tmp = j * (a * c);
	elseif (y <= 1.08e-49)
		tmp = (x * t) * -a;
	elseif (y <= 95000000000.0)
		tmp = a * (c * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -6200000000000.0], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-110], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e-49], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[y, 95000000000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.2e12

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in j around inf 39.0%

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

   5. Taylor expanded in c around 0 41.2%

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

      1. associate-*r* 37.5%

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

      2. associate-*r* 37.5%

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

      3. neg-mul-1 37.5%

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

      4. distribute-rgt-neg-in 37.5%

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

      5. associate-*r* 41.2%

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

   7. Simplified 41.2%

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

   if -6.2e12 < y < 5.99999999999999972e-110

   1. Initial program 81.8%

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

      1. cancel-sign-sub 81.8%

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

      2. cancel-sign-sub-inv 81.8%

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

      3. *-commutative 81.8%

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

      4. remove-double-neg 81.8%

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

      5. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in j around inf 43.6%

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

   5. Taylor expanded in c around inf 36.5%

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

   if 5.99999999999999972e-110 < y < 1.08e-49

   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. cancel-sign-sub 77.4%

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

      2. cancel-sign-sub-inv 77.4%

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

      3. *-commutative 77.4%

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

      4. remove-double-neg 77.4%

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

      5. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in a around 0 56.1%

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

   5. Taylor expanded in a around inf 43.2%

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

      1. mul-1-neg 43.2%

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

      2. *-commutative 43.2%

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

      3. unsub-neg 43.2%

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

      4. *-commutative 43.2%

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

   7. Simplified 43.2%

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

   8. Taylor expanded in j around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

   10. Simplified 54.3%

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

   if 1.08e-49 < y < 9.5e10

   1. Initial program 73.9%

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

      1. cancel-sign-sub 73.9%

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

      2. cancel-sign-sub-inv 73.9%

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

      3. *-commutative 73.9%

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

      4. remove-double-neg 73.9%

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

      5. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in c around inf 29.5%

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

      1. *-commutative 29.5%

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

   6. Simplified 29.5%

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

   7. Taylor expanded in j around inf 23.1%

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

      1. *-commutative 23.1%

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

   9. Simplified 23.1%

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

   10. Taylor expanded in c around 0 23.1%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 29.1%

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

       2. *-commutative 29.1%

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

       3. associate-*r* 35.3%

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

   12. Simplified 35.3%

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

   if 9.5e10 < y

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in y around inf 51.1%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6200000000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-49}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 41.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 96000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.9e+139)
   (* i (* y (- j)))
   (if (<= y 96000000000.0) (* a (- (* c j) (* x t))) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.9e+139) {
		tmp = i * (y * -j);
	} else if (y <= 96000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-3.9d+139)) then
        tmp = i * (y * -j)
    else if (y <= 96000000000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.9e+139) {
		tmp = i * (y * -j);
	} else if (y <= 96000000000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.9e+139:
		tmp = i * (y * -j)
	elif y <= 96000000000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.9e+139)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 96000000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.9e+139)
		tmp = i * (y * -j);
	elseif (y <= 96000000000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.9e+139], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 96000000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.90000000000000006e139

   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. cancel-sign-sub 47.6%

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

      2. cancel-sign-sub-inv 47.6%

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

      3. *-commutative 47.6%

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

      4. remove-double-neg 47.6%

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

      5. *-commutative 47.6%

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

   3. Simplified 47.6%

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

   4. Taylor expanded in j around inf 36.0%

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

   5. Taylor expanded in c around 0 42.6%

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

      1. associate-*r* 36.6%

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

      2. *-commutative 36.6%

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

      3. associate-*r* 42.8%

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

      4. mul-1-neg 42.8%

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

      5. distribute-rgt-neg-in 42.8%

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

      6. distribute-rgt-neg-in 42.8%

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

   7. Simplified 42.8%

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

   if -3.90000000000000006e139 < y < 9.6e10

   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. cancel-sign-sub 79.3%

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

      2. cancel-sign-sub-inv 79.3%

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

      3. *-commutative 79.3%

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

      4. remove-double-neg 79.3%

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

      5. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in a around 0 73.9%

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

   5. Taylor expanded in a around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. *-commutative 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if 9.6e10 < y

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in y around inf 51.1%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 96000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 15: 30.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30000000000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1150000000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -30000000000000.0)
   (* y (* i (- j)))
   (if (<= y 1.6e-108)
     (* j (* a c))
     (if (<= y 1150000000.0) (* (* t a) (- x)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -30000000000000.0) {
		tmp = y * (i * -j);
	} else if (y <= 1.6e-108) {
		tmp = j * (a * c);
	} else if (y <= 1150000000.0) {
		tmp = (t * a) * -x;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-30000000000000.0d0)) then
        tmp = y * (i * -j)
    else if (y <= 1.6d-108) then
        tmp = j * (a * c)
    else if (y <= 1150000000.0d0) then
        tmp = (t * a) * -x
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -30000000000000.0) {
		tmp = y * (i * -j);
	} else if (y <= 1.6e-108) {
		tmp = j * (a * c);
	} else if (y <= 1150000000.0) {
		tmp = (t * a) * -x;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -30000000000000.0:
		tmp = y * (i * -j)
	elif y <= 1.6e-108:
		tmp = j * (a * c)
	elif y <= 1150000000.0:
		tmp = (t * a) * -x
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -30000000000000.0)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (y <= 1.6e-108)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1150000000.0)
		tmp = Float64(Float64(t * a) * Float64(-x));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -30000000000000.0)
		tmp = y * (i * -j);
	elseif (y <= 1.6e-108)
		tmp = j * (a * c);
	elseif (y <= 1150000000.0)
		tmp = (t * a) * -x;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -30000000000000.0], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-108], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1150000000.0], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3e13

   1. Initial program 55.5%

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

      1. cancel-sign-sub 55.5%

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

      2. cancel-sign-sub-inv 55.5%

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

      3. *-commutative 55.5%

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

      4. remove-double-neg 55.5%

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

      5. *-commutative 55.5%

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

   3. Simplified 55.5%

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

   4. Taylor expanded in j around inf 39.0%

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

   5. Taylor expanded in c around 0 41.2%

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

      1. associate-*r* 37.5%

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

      2. associate-*r* 37.5%

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

      3. neg-mul-1 37.5%

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

      4. distribute-rgt-neg-in 37.5%

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

      5. associate-*r* 41.2%

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

   7. Simplified 41.2%

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

   if -3e13 < y < 1.6e-108

   1. Initial program 81.8%

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

      1. cancel-sign-sub 81.8%

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

      2. cancel-sign-sub-inv 81.8%

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

      3. *-commutative 81.8%

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

      4. remove-double-neg 81.8%

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

      5. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in j around inf 43.6%

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

   5. Taylor expanded in c around inf 36.5%

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

   if 1.6e-108 < y < 1.15e9

   1. Initial program 78.5%

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

      1. cancel-sign-sub 78.5%

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

      2. cancel-sign-sub-inv 78.5%

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

      3. *-commutative 78.5%

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

      4. remove-double-neg 78.5%

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

      5. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around inf 49.0%

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

   5. Taylor expanded in y around 0 42.5%

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

      1. neg-mul-1 42.5%

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

      2. distribute-lft-neg-in 42.5%

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

      3. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if 1.15e9 < y

   1. Initial program 62.3%

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

      1. cancel-sign-sub 62.3%

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

      2. cancel-sign-sub-inv 62.3%

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

      3. *-commutative 62.3%

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

      4. remove-double-neg 62.3%

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

      5. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in z around inf 58.0%

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

   5. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30000000000000:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1150000000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+89} \lor \neg \left(y \leq 66000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -6.5e+89) (not (<= y 66000000000.0)))
   (* y (* x z))
   (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -6.5e+89) || !(y <= 66000000000.0)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-6.5d+89)) .or. (.not. (y <= 66000000000.0d0))) then
        tmp = y * (x * z)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -6.5e+89) || !(y <= 66000000000.0)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -6.5e+89) or not (y <= 66000000000.0):
		tmp = y * (x * z)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -6.5e+89) || !(y <= 66000000000.0))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -6.5e+89) || ~((y <= 66000000000.0)))
		tmp = y * (x * z);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -6.5e+89], N[Not[LessEqual[y, 66000000000.0]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999996e89 or 6.6e10 < y

   1. Initial program 58.4%

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

      1. cancel-sign-sub 58.4%

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

      2. cancel-sign-sub-inv 58.4%

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

      3. *-commutative 58.4%

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

      4. remove-double-neg 58.4%

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

      5. *-commutative 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in x around inf 50.4%

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

   5. Taylor expanded in y around inf 44.4%

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

   if -6.4999999999999996e89 < y < 6.6e10

   1. Initial program 80.1%

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

      1. cancel-sign-sub 80.1%

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

      2. cancel-sign-sub-inv 80.1%

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

      3. *-commutative 80.1%

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

      4. remove-double-neg 80.1%

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

      5. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in c around inf 47.9%

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

      1. *-commutative 47.9%

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

   6. Simplified 47.9%

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

   7. Taylor expanded in j around inf 31.8%

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

      1. *-commutative 31.8%

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

   9. Simplified 31.8%

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

   10. Taylor expanded in c around 0 31.8%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.6%

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

       2. *-commutative 32.6%

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

       3. associate-*r* 33.1%

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

   12. Simplified 33.1%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+89} \lor \neg \left(y \leq 66000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 17: 29.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 65000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5e+89)
   (* y (* x z))
   (if (<= y 65000000000.0) (* a (* c j)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5e+89) {
		tmp = y * (x * z);
	} else if (y <= 65000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-5d+89)) then
        tmp = y * (x * z)
    else if (y <= 65000000000.0d0) then
        tmp = a * (c * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5e+89) {
		tmp = y * (x * z);
	} else if (y <= 65000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5e+89:
		tmp = y * (x * z)
	elif y <= 65000000000.0:
		tmp = a * (c * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5e+89)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 65000000000.0)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5e+89)
		tmp = y * (x * z);
	elseif (y <= 65000000000.0)
		tmp = a * (c * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5e+89], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 65000000000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999983e89

   1. Initial program 50.8%

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

      1. cancel-sign-sub 50.8%

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

      2. cancel-sign-sub-inv 50.8%

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

      3. *-commutative 50.8%

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

      4. remove-double-neg 50.8%

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

      5. *-commutative 50.8%

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

   3. Simplified 50.8%

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

   4. Taylor expanded in x around inf 44.0%

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

   5. Taylor expanded in y around inf 36.4%

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

   if -4.99999999999999983e89 < y < 6.5e10

   1. Initial program 80.1%

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

      1. cancel-sign-sub 80.1%

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

      2. cancel-sign-sub-inv 80.1%

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

      3. *-commutative 80.1%

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

      4. remove-double-neg 80.1%

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

      5. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in c around inf 47.9%

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

      1. *-commutative 47.9%

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

   6. Simplified 47.9%

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

   7. Taylor expanded in j around inf 31.8%

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

      1. *-commutative 31.8%

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

   9. Simplified 31.8%

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

   10. Taylor expanded in c around 0 31.8%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.6%

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

       2. *-commutative 32.6%

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

       3. associate-*r* 33.1%

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

   12. Simplified 33.1%

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

   if 6.5e10 < y

   1. Initial program 63.3%

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

      1. cancel-sign-sub 63.3%

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

      2. cancel-sign-sub-inv 63.3%

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

      3. *-commutative 63.3%

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

      4. remove-double-neg 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in y around inf 51.1%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 65000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 18: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -4.8e+89)
   (* x (* y z))
   (if (<= y 95000000000.0) (* a (* c j)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -4.8e+89) {
		tmp = x * (y * z);
	} else if (y <= 95000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-4.8d+89)) then
        tmp = x * (y * z)
    else if (y <= 95000000000.0d0) then
        tmp = a * (c * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -4.8e+89) {
		tmp = x * (y * z);
	} else if (y <= 95000000000.0) {
		tmp = a * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -4.8e+89:
		tmp = x * (y * z)
	elif y <= 95000000000.0:
		tmp = a * (c * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -4.8e+89)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 95000000000.0)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -4.8e+89)
		tmp = x * (y * z);
	elseif (y <= 95000000000.0)
		tmp = a * (c * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -4.8e+89], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 95000000000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000009e89

   1. Initial program 50.8%

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

      1. cancel-sign-sub 50.8%

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

      2. cancel-sign-sub-inv 50.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 50.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 50.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 50.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 50.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 44.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]

   if -4.80000000000000009e89 < y < 9.5e10

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 80.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 47.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

   7. Taylor expanded in j around inf 31.8%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 31.8%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   10. Taylor expanded in c around 0 31.8%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.6%

          \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

       2. *-commutative 32.6%

          \[\leadsto \color{blue}{\left(a \cdot c\right)} \cdot j \]

       3. associate-*r* 33.1%

          \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   12. Simplified 33.1%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 9.5e10 < y

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 63.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 63.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 95000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 19: 22.4% 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 71.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 71.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   2. cancel-sign-sub-inv 71.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

   3. *-commutative 71.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

   4. remove-double-neg 71.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

   5. *-commutative 71.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 71.4%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

4. Taylor expanded in c around inf 41.1%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
5. Step-by-step derivation

   1. *-commutative 41.1%

      \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

6. Simplified 41.1%

   \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]

7. Taylor expanded in j around inf 24.9%

   \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 24.9%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

9. Simplified 24.9%

   \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

10. Taylor expanded in c around 0 24.9%

    \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
11. Step-by-step derivation

    1. associate-*r* 25.7%

       \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

    2. *-commutative 25.7%

       \[\leadsto \color{blue}{\left(a \cdot c\right)} \cdot j \]

    3. associate-*r* 25.6%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

12. Simplified 25.6%

    \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

13. Final simplification 25.6%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.8% 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 2023240 
(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)))))