Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.9% → 80.9%

Time: 30.1s

Alternatives: 22

Speedup: 0.5×

• 57.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, z \cdot b\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, a \cdot b\right), t_1\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* t c) (* y i))) (+ t_1 (* b (- (* a i) (* z c)))))))
   (if (<= t_2 (- INFINITY))
     (fma (- c) (fma (- j) t (* z b)) (fma i (fma (- j) y (* a b)) t_1))
     (if (<= t_2 5e+281)
       t_2
       (if (<= t_2 INFINITY)
         (+
          (* z (- (* x y) (* b c)))
          (+ (* i (- (* a b) (* y j))) (* t (- (* c j) (* x a)))))
         (- (* c (- (* t j) (* z b))) (* y (- (* i j) (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(-c, fma(-j, t, (z * b)), fma(i, fma(-j, y, (a * b)), t_1));
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(-c), fma(Float64(-j), t, Float64(z * b)), fma(i, fma(Float64(-j), y, Float64(a * b)), t_1));
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a)))));
	else
		tmp = Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[((-c) * N[((-j) * t + N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(i * N[((-j) * y + N[(a * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+281], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -inf.0

   1. Initial program 75.3%

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

   3. Taylor expanded in c around -inf 87.2%

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

   5. Simplified 87.3%

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 5.00000000000000016e281

   1. Initial program 99.5%

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

   if 5.00000000000000016e281 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 77.2%

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

   3. Taylor expanded in c around -inf 75.1%

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

   5. Simplified 78.1%

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

      1. add-cube-cbrt 78.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 78.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 78.1%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in z around -inf 84.8%

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

   10. Simplified 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around -inf 32.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in a around 0 40.2%

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

      1. +-commutative 40.2%

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

      2. +-commutative 40.2%

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

      3. *-commutative 40.2%

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

      4. *-commutative 40.2%

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

      5. *-commutative 40.2%

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

      6. associate-*r* 44.2%

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

      7. mul-1-neg 44.2%

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

      8. associate-*r* 46.2%

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

      9. *-commutative 46.2%

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

      10. distribute-lft-neg-out 46.2%

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

      11. *-commutative 46.2%

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

      12. distribute-lft-in 56.2%

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

      13. fma-udef 56.2%

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

      14. mul-1-neg 56.2%

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

      15. unsub-neg 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, z \cdot b\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, a \cdot b\right), x \cdot \left(y \cdot z - t \cdot a\right)\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* z (- (* x y) (* b c)))
          (+ (* i (- (* a b) (* y j))) (* t (- (* c j) (* x a))))))
        (t_2
         (+
          (* j (- (* t c) (* y i)))
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 5e+281)
       t_2
       (if (<= t_2 INFINITY)
         t_1
         (- (* c (- (* t j) (* z b))) (* y (- (* i j) (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	double t_2 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	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 = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	double t_2 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 5e+281) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))))
	t_2 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 5e+281:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a)))))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	t_2 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 5e+281)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+281], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$1, N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -inf.0 or 5.00000000000000016e281 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 76.3%

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

   3. Taylor expanded in c around -inf 81.3%

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

   5. Simplified 82.8%

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

      1. add-cube-cbrt 82.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 82.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 82.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 82.8%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in z around -inf 86.0%

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

   10. Simplified 88.4%

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 5.00000000000000016e281

   1. Initial program 99.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around -inf 32.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in a around 0 40.2%

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

      1. +-commutative 40.2%

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

      2. +-commutative 40.2%

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

      3. *-commutative 40.2%

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

      4. *-commutative 40.2%

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

      5. *-commutative 40.2%

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

      6. associate-*r* 44.2%

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

      7. mul-1-neg 44.2%

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

      8. associate-*r* 46.2%

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

      9. *-commutative 46.2%

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

      10. distribute-lft-neg-out 46.2%

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

      11. *-commutative 46.2%

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

      12. distribute-lft-in 56.2%

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

      13. fma-udef 56.2%

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

      14. mul-1-neg 56.2%

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

      15. unsub-neg 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(\left(t_2 + t_1\right) - i \cdot \left(y \cdot j\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (+ (* j (- (* t c) (* y i))) (+ t_1 (* b (- (* a i) (* z c)))))))
   (if (<= t_3 (- INFINITY))
     (+ (- (+ t_2 t_1) (* i (* y j))) (* a (* b i)))
     (if (<= t_3 5e+281)
       t_3
       (if (<= t_3 INFINITY)
         (+
          (* z (- (* x y) (* b c)))
          (+ (* i (- (* a b) (* y j))) (* t (- (* c j) (* x a)))))
         (- t_2 (* y (- (* i j) (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((t_2 + t_1) - (i * (y * j))) + (a * (b * i));
	} else if (t_3 <= 5e+281) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	} else {
		tmp = t_2 - (y * ((i * j) - (x * z)));
	}
	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));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = ((t_2 + t_1) - (i * (y * j))) + (a * (b * i));
	} else if (t_3 <= 5e+281) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	} else {
		tmp = t_2 - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = c * ((t * j) - (z * b))
	t_3 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = ((t_2 + t_1) - (i * (y * j))) + (a * (b * i))
	elif t_3 <= 5e+281:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))))
	else:
		tmp = t_2 - (y * ((i * j) - (x * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(t_2 + t_1) - Float64(i * Float64(y * j))) + Float64(a * Float64(b * i)));
	elseif (t_3 <= 5e+281)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) + Float64(t * Float64(Float64(c * j) - Float64(x * a)))));
	else
		tmp = Float64(t_2 - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	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));
	t_2 = c * ((t * j) - (z * b));
	t_3 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = ((t_2 + t_1) - (i * (y * j))) + (a * (b * i));
	elseif (t_3 <= 5e+281)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = (z * ((x * y) - (b * c))) + ((i * ((a * b) - (y * j))) + (t * ((c * j) - (x * a))));
	else
		tmp = t_2 - (y * ((i * j) - (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(t$95$2 + t$95$1), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+281], t$95$3, If[LessEqual[t$95$3, Infinity], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -inf.0

   1. Initial program 75.3%

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

   3. Taylor expanded in c around 0 87.2%

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

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 5.00000000000000016e281

   1. Initial program 99.5%

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

   if 5.00000000000000016e281 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 77.2%

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

   3. Taylor expanded in c around -inf 75.1%

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

   5. Simplified 78.1%

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

      1. add-cube-cbrt 78.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 78.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 78.1%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in z around -inf 84.8%

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

   10. Simplified 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around -inf 32.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in a around 0 40.2%

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

      1. +-commutative 40.2%

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

      2. +-commutative 40.2%

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

      3. *-commutative 40.2%

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

      4. *-commutative 40.2%

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

      5. *-commutative 40.2%

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

      6. associate-*r* 44.2%

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

      7. mul-1-neg 44.2%

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

      8. associate-*r* 46.2%

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

      9. *-commutative 46.2%

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

      10. distribute-lft-neg-out 46.2%

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

      11. *-commutative 46.2%

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

      12. distribute-lft-in 56.2%

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

      13. fma-udef 56.2%

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

      14. mul-1-neg 56.2%

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

      15. unsub-neg 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq -\infty:\\ \;\;\;\;\left(\left(c \cdot \left(t \cdot j - z \cdot b\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - i \cdot \left(y \cdot j\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) \leq \infty:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + \left(i \cdot \left(a \cdot b - y \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 84.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around -inf 32.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in a around 0 40.2%

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

      1. +-commutative 40.2%

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

      2. +-commutative 40.2%

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

      3. *-commutative 40.2%

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

      4. *-commutative 40.2%

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

      5. *-commutative 40.2%

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

      6. associate-*r* 44.2%

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

      7. mul-1-neg 44.2%

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

      8. associate-*r* 46.2%

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

      9. *-commutative 46.2%

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

      10. distribute-lft-neg-out 46.2%

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

      11. *-commutative 46.2%

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

      12. distribute-lft-in 56.2%

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

      13. fma-udef 56.2%

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

      14. mul-1-neg 56.2%

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

      15. unsub-neg 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 78.8%

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

Alternative 5: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ \mathbf{if}\;j \leq -4.1 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + t_1\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-35} \lor \neg \left(j \leq 2.95 \cdot 10^{+138}\right) \land j \leq 1.78 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (+ t_1 t_2)))
   (if (<= j -4.1e+68)
     (+ (* a (* b i)) t_1)
     (if (<= j -2.3e-161)
       t_3
       (if (<= j -4.4e-226)
         (* a (- (* b i) (* x t)))
         (if (or (<= j 1.1e-35) (and (not (<= j 2.95e+138)) (<= j 1.78e+199)))
           (+ (* x (- (* y z) (* t a))) t_2)
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (j <= -4.1e+68) {
		tmp = (a * (b * i)) + t_1;
	} else if (j <= -2.3e-161) {
		tmp = t_3;
	} else if (j <= -4.4e-226) {
		tmp = a * ((b * i) - (x * t));
	} else if ((j <= 1.1e-35) || (!(j <= 2.95e+138) && (j <= 1.78e+199))) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t_1 + t_2
    if (j <= (-4.1d+68)) then
        tmp = (a * (b * i)) + t_1
    else if (j <= (-2.3d-161)) then
        tmp = t_3
    else if (j <= (-4.4d-226)) then
        tmp = a * ((b * i) - (x * t))
    else if ((j <= 1.1d-35) .or. (.not. (j <= 2.95d+138)) .and. (j <= 1.78d+199)) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (j <= -4.1e+68) {
		tmp = (a * (b * i)) + t_1;
	} else if (j <= -2.3e-161) {
		tmp = t_3;
	} else if (j <= -4.4e-226) {
		tmp = a * ((b * i) - (x * t));
	} else if ((j <= 1.1e-35) || (!(j <= 2.95e+138) && (j <= 1.78e+199))) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t_1 + t_2
	tmp = 0
	if j <= -4.1e+68:
		tmp = (a * (b * i)) + t_1
	elif j <= -2.3e-161:
		tmp = t_3
	elif j <= -4.4e-226:
		tmp = a * ((b * i) - (x * t))
	elif (j <= 1.1e-35) or (not (j <= 2.95e+138) and (j <= 1.78e+199)):
		tmp = (x * ((y * z) - (t * a))) + t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	tmp = 0.0
	if (j <= -4.1e+68)
		tmp = Float64(Float64(a * Float64(b * i)) + t_1);
	elseif (j <= -2.3e-161)
		tmp = t_3;
	elseif (j <= -4.4e-226)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif ((j <= 1.1e-35) || (!(j <= 2.95e+138) && (j <= 1.78e+199)))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t_1 + t_2;
	tmp = 0.0;
	if (j <= -4.1e+68)
		tmp = (a * (b * i)) + t_1;
	elseif (j <= -2.3e-161)
		tmp = t_3;
	elseif (j <= -4.4e-226)
		tmp = a * ((b * i) - (x * t));
	elseif ((j <= 1.1e-35) || (~((j <= 2.95e+138)) && (j <= 1.78e+199)))
		tmp = (x * ((y * z) - (t * a))) + t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, If[LessEqual[j, -4.1e+68], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, -2.3e-161], t$95$3, If[LessEqual[j, -4.4e-226], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 1.1e-35], And[N[Not[LessEqual[j, 2.95e+138]], $MachinePrecision], LessEqual[j, 1.78e+199]]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.0999999999999999e68

   1. Initial program 64.4%

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

   3. Taylor expanded in x around 0 64.5%

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

   4. Taylor expanded in z around 0 84.4%

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

      1. *-commutative 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*r* 84.4%

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

      4. neg-mul-1 84.4%

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

      5. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   if -4.0999999999999999e68 < j < -2.3e-161 or 1.09999999999999997e-35 < j < 2.9499999999999999e138 or 1.7800000000000001e199 < j

   1. Initial program 74.2%

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

   3. Taylor expanded in x around 0 72.2%

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

   if -2.3e-161 < j < -4.4e-226

   1. Initial program 55.0%

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

   3. Taylor expanded in c around -inf 88.3%

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

   5. Simplified 92.9%

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

      1. add-cube-cbrt 92.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 92.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 92.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 92.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

      4. *-commutative 61.5%

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

   10. Simplified 61.5%

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

   if -4.4e-226 < j < 1.09999999999999997e-35 or 2.9499999999999999e138 < j < 1.7800000000000001e199

   1. Initial program 64.9%

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

   3. Taylor expanded in j around 0 71.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-35} \lor \neg \left(j \leq 2.95 \cdot 10^{+138}\right) \land j \leq 1.78 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+116} \lor \neg \left(a \leq -4.7 \cdot 10^{+67} \lor \neg \left(a \leq -2.75 \cdot 10^{-21}\right) \land a \leq 2.4 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -5.2e+116)
         (not
          (or (<= a -4.7e+67) (and (not (<= a -2.75e-21)) (<= a 2.4e+93)))))
   (* a (- (* b i) (* x t)))
   (- (* c (- (* t j) (* z b))) (* y (- (* i j) (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -5.2e+116) || !((a <= -4.7e+67) || (!(a <= -2.75e-21) && (a <= 2.4e+93)))) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-5.2d+116)) .or. (.not. (a <= (-4.7d+67)) .or. (.not. (a <= (-2.75d-21))) .and. (a <= 2.4d+93))) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -5.2e+116) || !((a <= -4.7e+67) || (!(a <= -2.75e-21) && (a <= 2.4e+93)))) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -5.2e+116) or not ((a <= -4.7e+67) or (not (a <= -2.75e-21) and (a <= 2.4e+93))):
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -5.2e+116) || !((a <= -4.7e+67) || (!(a <= -2.75e-21) && (a <= 2.4e+93))))
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -5.2e+116) || ~(((a <= -4.7e+67) || (~((a <= -2.75e-21)) && (a <= 2.4e+93)))))
		tmp = a * ((b * i) - (x * t));
	else
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -5.2e+116], N[Not[Or[LessEqual[a, -4.7e+67], And[N[Not[LessEqual[a, -2.75e-21]], $MachinePrecision], LessEqual[a, 2.4e+93]]]], $MachinePrecision]], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.19999999999999973e116 or -4.70000000000000017e67 < a < -2.74999999999999989e-21 or 2.4000000000000001e93 < a

   1. Initial program 60.9%

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

   3. Taylor expanded in c around -inf 70.3%

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

   5. Simplified 72.0%

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

      1. add-cube-cbrt 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 71.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

   10. Simplified 72.2%

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

   if -5.19999999999999973e116 < a < -4.70000000000000017e67 or -2.74999999999999989e-21 < a < 2.4000000000000001e93

   1. Initial program 72.7%

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

   3. Taylor expanded in c around -inf 75.1%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in a around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. +-commutative 72.1%

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

      3. *-commutative 72.1%

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

      4. *-commutative 72.1%

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

      5. *-commutative 72.1%

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

      6. associate-*r* 73.3%

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

      7. mul-1-neg 73.3%

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

      8. associate-*r* 75.2%

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

      9. *-commutative 75.2%

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

      10. distribute-lft-neg-out 75.2%

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

      11. *-commutative 75.2%

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

      12. distribute-lft-in 77.8%

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

      13. fma-udef 77.8%

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

      14. mul-1-neg 77.8%

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

      15. unsub-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+116} \lor \neg \left(a \leq -4.7 \cdot 10^{+67} \lor \neg \left(a \leq -2.75 \cdot 10^{-21}\right) \land a \leq 2.4 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.3e+51)
     t_2
     (if (<= y -2.5e-196)
       t_1
       (if (<= y 7.2e-235)
         (* a (- (* b i) (* x t)))
         (if (<= y 2.4e+31)
           (+ (* a (* b i)) (* j (- (* t c) (* y i))))
           (if (<= y 5.5e+153) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.3e+51) {
		tmp = t_2;
	} else if (y <= -2.5e-196) {
		tmp = t_1;
	} else if (y <= 7.2e-235) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 2.4e+31) {
		tmp = (a * (b * i)) + (j * ((t * c) - (y * i)));
	} else if (y <= 5.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.3d+51)) then
        tmp = t_2
    else if (y <= (-2.5d-196)) then
        tmp = t_1
    else if (y <= 7.2d-235) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 2.4d+31) then
        tmp = (a * (b * i)) + (j * ((t * c) - (y * i)))
    else if (y <= 5.5d+153) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.3e+51) {
		tmp = t_2;
	} else if (y <= -2.5e-196) {
		tmp = t_1;
	} else if (y <= 7.2e-235) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 2.4e+31) {
		tmp = (a * (b * i)) + (j * ((t * c) - (y * i)));
	} else if (y <= 5.5e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.3e+51:
		tmp = t_2
	elif y <= -2.5e-196:
		tmp = t_1
	elif y <= 7.2e-235:
		tmp = a * ((b * i) - (x * t))
	elif y <= 2.4e+31:
		tmp = (a * (b * i)) + (j * ((t * c) - (y * i)))
	elif y <= 5.5e+153:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.3e+51)
		tmp = t_2;
	elseif (y <= -2.5e-196)
		tmp = t_1;
	elseif (y <= 7.2e-235)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 2.4e+31)
		tmp = Float64(Float64(a * Float64(b * i)) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	elseif (y <= 5.5e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.3e+51)
		tmp = t_2;
	elseif (y <= -2.5e-196)
		tmp = t_1;
	elseif (y <= 7.2e-235)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 2.4e+31)
		tmp = (a * (b * i)) + (j * ((t * c) - (y * i)));
	elseif (y <= 5.5e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+51], t$95$2, If[LessEqual[y, -2.5e-196], t$95$1, If[LessEqual[y, 7.2e-235], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+31], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+153], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3000000000000001e51 or 5.5000000000000003e153 < y

   1. Initial program 53.7%

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

   3. Taylor expanded in c around -inf 58.4%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 74.9%

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

      1. +-commutative 74.9%

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

      2. *-commutative 74.9%

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

      3. mul-1-neg 74.9%

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

      4. *-commutative 74.9%

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

      5. unsub-neg 74.9%

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

      6. *-commutative 74.9%

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

      7. *-commutative 74.9%

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

   8. Simplified 74.9%

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

   if -1.3000000000000001e51 < y < -2.5000000000000002e-196 or 2.39999999999999982e31 < y < 5.5000000000000003e153

   1. Initial program 69.2%

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

   3. Taylor expanded in c around inf 53.4%

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

   if -2.5000000000000002e-196 < y < 7.19999999999999998e-235

   1. Initial program 81.0%

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

   3. Taylor expanded in c around -inf 86.4%

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

   5. Simplified 81.0%

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

      1. add-cube-cbrt 80.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 80.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 80.8%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

   10. Simplified 59.2%

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

   if 7.19999999999999998e-235 < y < 2.39999999999999982e31

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0 63.5%

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

   4. Taylor expanded in z around 0 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*r* 67.4%

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

      4. neg-mul-1 67.4%

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

      5. *-commutative 67.4%

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

   6. Simplified 67.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+153}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-117}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -7.5e-83)
     t_1
     (if (<= a 3.5e-230)
       (* y (- (* x z) (* i j)))
       (if (<= a 5e-117)
         (* j (- (* t c) (* y i)))
         (if (<= a 5.7e+29)
           (* x (- (* y z) (* t a)))
           (if (<= a 1.05e+44) (* c (- (* t j) (* z b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e-83) {
		tmp = t_1;
	} else if (a <= 3.5e-230) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 5e-117) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5.7e+29) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 1.05e+44) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-7.5d-83)) then
        tmp = t_1
    else if (a <= 3.5d-230) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 5d-117) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 5.7d+29) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= 1.05d+44) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e-83) {
		tmp = t_1;
	} else if (a <= 3.5e-230) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 5e-117) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 5.7e+29) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 1.05e+44) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7.5e-83:
		tmp = t_1
	elif a <= 3.5e-230:
		tmp = y * ((x * z) - (i * j))
	elif a <= 5e-117:
		tmp = j * ((t * c) - (y * i))
	elif a <= 5.7e+29:
		tmp = x * ((y * z) - (t * a))
	elif a <= 1.05e+44:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.5e-83)
		tmp = t_1;
	elseif (a <= 3.5e-230)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 5e-117)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 5.7e+29)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= 1.05e+44)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7.5e-83)
		tmp = t_1;
	elseif (a <= 3.5e-230)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 5e-117)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 5.7e+29)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= 1.05e+44)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e-83], t$95$1, If[LessEqual[a, 3.5e-230], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-117], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.7e+29], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+44], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.4999999999999997e-83 or 1.04999999999999993e44 < a

   1. Initial program 63.1%

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

   3. Taylor expanded in c around -inf 72.0%

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

   5. Simplified 73.4%

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

      1. add-cube-cbrt 73.3%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 73.3%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 73.3%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 73.3%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

   10. Simplified 66.4%

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

   if -7.4999999999999997e-83 < a < 3.49999999999999988e-230

   1. Initial program 66.4%

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

   3. Taylor expanded in c around -inf 70.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in y around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. mul-1-neg 58.5%

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

      4. *-commutative 58.5%

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

      5. unsub-neg 58.5%

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

      6. *-commutative 58.5%

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

      7. *-commutative 58.5%

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

   8. Simplified 58.5%

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

   if 3.49999999999999988e-230 < a < 5e-117

   1. Initial program 90.3%

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

   3. Taylor expanded in c around -inf 72.2%

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

   5. Simplified 76.9%

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

      1. add-cube-cbrt 76.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 76.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 76.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in j around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-lft-neg-out 58.7%

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

      3. *-commutative 58.7%

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

      4. +-commutative 58.7%

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

      5. cancel-sign-sub-inv 58.7%

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

      6. *-commutative 58.7%

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

   10. Simplified 58.7%

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

   if 5e-117 < a < 5.6999999999999999e29

   1. Initial program 80.9%

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

   3. Taylor expanded in c around -inf 90.6%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in x around inf 62.8%

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

   if 5.6999999999999999e29 < a < 1.04999999999999993e44

   1. Initial program 66.7%

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

   3. Taylor expanded in c around inf 99.5%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-117}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -2.8e-82)
     t_1
     (if (<= a 1.3e-228)
       (* y (- (* x z) (* i j)))
       (if (<= a 2.5e-117)
         (* j (- (* t c) (* y i)))
         (if (<= a 8.5e-36)
           (* z (- (* x y) (* b c)))
           (if (<= a 5e+46) (* c (- (* t j) (* z b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.8e-82) {
		tmp = t_1;
	} else if (a <= 1.3e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 2.5e-117) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 8.5e-36) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 5e+46) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-2.8d-82)) then
        tmp = t_1
    else if (a <= 1.3d-228) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 2.5d-117) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 8.5d-36) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 5d+46) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.8e-82) {
		tmp = t_1;
	} else if (a <= 1.3e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 2.5e-117) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 8.5e-36) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 5e+46) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.8e-82:
		tmp = t_1
	elif a <= 1.3e-228:
		tmp = y * ((x * z) - (i * j))
	elif a <= 2.5e-117:
		tmp = j * ((t * c) - (y * i))
	elif a <= 8.5e-36:
		tmp = z * ((x * y) - (b * c))
	elif a <= 5e+46:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.8e-82)
		tmp = t_1;
	elseif (a <= 1.3e-228)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 2.5e-117)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 8.5e-36)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 5e+46)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2.8e-82)
		tmp = t_1;
	elseif (a <= 1.3e-228)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 2.5e-117)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 8.5e-36)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 5e+46)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e-82], t$95$1, If[LessEqual[a, 1.3e-228], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-117], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-36], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+46], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.80000000000000024e-82 or 5.0000000000000002e46 < a

   1. Initial program 63.1%

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

   3. Taylor expanded in c around -inf 72.0%

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

   5. Simplified 73.4%

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

      1. add-cube-cbrt 73.3%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 73.3%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 73.3%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 73.3%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

   10. Simplified 66.4%

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

   if -2.80000000000000024e-82 < a < 1.3e-228

   1. Initial program 66.4%

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

   3. Taylor expanded in c around -inf 70.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in y around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. mul-1-neg 58.5%

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

      4. *-commutative 58.5%

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

      5. unsub-neg 58.5%

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

      6. *-commutative 58.5%

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

      7. *-commutative 58.5%

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

   8. Simplified 58.5%

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

   if 1.3e-228 < a < 2.5e-117

   1. Initial program 90.3%

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

   3. Taylor expanded in c around -inf 72.2%

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

   5. Simplified 76.9%

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

      1. add-cube-cbrt 76.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 76.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 76.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in j around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. distribute-lft-neg-out 58.7%

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

      3. *-commutative 58.7%

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

      4. +-commutative 58.7%

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

      5. cancel-sign-sub-inv 58.7%

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

      6. *-commutative 58.7%

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

   10. Simplified 58.7%

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

   if 2.5e-117 < a < 8.5000000000000007e-36

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   if 8.5000000000000007e-36 < a < 5.0000000000000002e46

   1. Initial program 73.5%

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

   3. Taylor expanded in c around inf 67.1%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-117}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-21} \lor \neg \left(a \leq 1.02 \cdot 10^{+68}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.1e-21) (not (<= a 1.02e+68)))
   (+ (* a (* b i)) (- (* j (- (* t c) (* y i))) (* a (* x t))))
   (- (* c (- (* t j) (* z b))) (* y (- (* i j) (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.1e-21) || !(a <= 1.02e+68)) {
		tmp = (a * (b * i)) + ((j * ((t * c) - (y * i))) - (a * (x * t)));
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-2.1d-21)) .or. (.not. (a <= 1.02d+68))) then
        tmp = (a * (b * i)) + ((j * ((t * c) - (y * i))) - (a * (x * t)))
    else
        tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.1e-21) || !(a <= 1.02e+68)) {
		tmp = (a * (b * i)) + ((j * ((t * c) - (y * i))) - (a * (x * t)));
	} else {
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.1e-21) or not (a <= 1.02e+68):
		tmp = (a * (b * i)) + ((j * ((t * c) - (y * i))) - (a * (x * t)))
	else:
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.1e-21) || !(a <= 1.02e+68))
		tmp = Float64(Float64(a * Float64(b * i)) + Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t))));
	else
		tmp = Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.1e-21) || ~((a <= 1.02e+68)))
		tmp = (a * (b * i)) + ((j * ((t * c) - (y * i))) - (a * (x * t)));
	else
		tmp = (c * ((t * j) - (z * b))) - (y * ((i * j) - (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.1e-21], N[Not[LessEqual[a, 1.02e+68]], $MachinePrecision]], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.10000000000000013e-21 or 1.02e68 < a

   1. Initial program 62.1%

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

   3. Taylor expanded in z around 0 72.6%

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

   if -2.10000000000000013e-21 < a < 1.02e68

   1. Initial program 72.8%

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

   3. Taylor expanded in c around -inf 75.4%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in a around 0 72.8%

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

      1. +-commutative 72.8%

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

      2. +-commutative 72.8%

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

      3. *-commutative 72.8%

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

      4. *-commutative 72.8%

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

      5. *-commutative 72.8%

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

      6. associate-*r* 74.1%

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

      7. mul-1-neg 74.1%

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

      8. associate-*r* 75.5%

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

      9. *-commutative 75.5%

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

      10. distribute-lft-neg-out 75.5%

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

      11. *-commutative 75.5%

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

      12. distribute-lft-in 78.4%

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

      13. fma-udef 78.4%

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

      14. mul-1-neg 78.4%

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

      15. unsub-neg 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-21} \lor \neg \left(a \leq 1.02 \cdot 10^{+68}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -2e-83)
     t_1
     (if (<= a -2.4e-165)
       (* y (* x z))
       (if (<= a -2.15e-228)
         (* b (- (* a i) (* z c)))
         (if (<= a 2.9e-12) (* z (* x y)) 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 * ((b * i) - (x * t));
	double tmp;
	if (a <= -2e-83) {
		tmp = t_1;
	} else if (a <= -2.4e-165) {
		tmp = y * (x * z);
	} else if (a <= -2.15e-228) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 2.9e-12) {
		tmp = z * (x * y);
	} 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 = a * ((b * i) - (x * t))
    if (a <= (-2d-83)) then
        tmp = t_1
    else if (a <= (-2.4d-165)) then
        tmp = y * (x * z)
    else if (a <= (-2.15d-228)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 2.9d-12) then
        tmp = z * (x * y)
    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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2e-83) {
		tmp = t_1;
	} else if (a <= -2.4e-165) {
		tmp = y * (x * z);
	} else if (a <= -2.15e-228) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 2.9e-12) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2e-83:
		tmp = t_1
	elif a <= -2.4e-165:
		tmp = y * (x * z)
	elif a <= -2.15e-228:
		tmp = b * ((a * i) - (z * c))
	elif a <= 2.9e-12:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2e-83)
		tmp = t_1;
	elseif (a <= -2.4e-165)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -2.15e-228)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 2.9e-12)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2e-83)
		tmp = t_1;
	elseif (a <= -2.4e-165)
		tmp = y * (x * z);
	elseif (a <= -2.15e-228)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 2.9e-12)
		tmp = z * (x * y);
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e-83], t$95$1, If[LessEqual[a, -2.4e-165], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.15e-228], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-12], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.0000000000000001e-83 or 2.9000000000000002e-12 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in c around -inf 72.7%

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

   5. Simplified 74.7%

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

      1. add-cube-cbrt 74.5%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 74.5%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 74.5%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   10. Simplified 64.1%

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

   if -2.0000000000000001e-83 < a < -2.4000000000000002e-165

   1. Initial program 69.0%

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

   3. Taylor expanded in y around inf 54.2%

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

   4. Taylor expanded in i around 0 39.1%

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

   if -2.4000000000000002e-165 < a < -2.15e-228

   1. Initial program 59.3%

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

   3. Taylor expanded in b around inf 43.0%

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

   if -2.15e-228 < a < 2.9000000000000002e-12

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf 53.9%

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

      1. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in y around inf 41.0%

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

      1. *-commutative 41.0%

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

   8. Simplified 41.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -6.5e-25)
     t_2
     (if (<= a 6e-117)
       t_1
       (if (<= a 2.1e-44) (* z (* x y)) (if (<= a 2.95e+44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.5e-25) {
		tmp = t_2;
	} else if (a <= 6e-117) {
		tmp = t_1;
	} else if (a <= 2.1e-44) {
		tmp = z * (x * y);
	} else if (a <= 2.95e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-6.5d-25)) then
        tmp = t_2
    else if (a <= 6d-117) then
        tmp = t_1
    else if (a <= 2.1d-44) then
        tmp = z * (x * y)
    else if (a <= 2.95d+44) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.5e-25) {
		tmp = t_2;
	} else if (a <= 6e-117) {
		tmp = t_1;
	} else if (a <= 2.1e-44) {
		tmp = z * (x * y);
	} else if (a <= 2.95e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -6.5e-25:
		tmp = t_2
	elif a <= 6e-117:
		tmp = t_1
	elif a <= 2.1e-44:
		tmp = z * (x * y)
	elif a <= 2.95e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.5e-25)
		tmp = t_2;
	elseif (a <= 6e-117)
		tmp = t_1;
	elseif (a <= 2.1e-44)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 2.95e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -6.5e-25)
		tmp = t_2;
	elseif (a <= 6e-117)
		tmp = t_1;
	elseif (a <= 2.1e-44)
		tmp = z * (x * y);
	elseif (a <= 2.95e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-25], t$95$2, If[LessEqual[a, 6e-117], t$95$1, If[LessEqual[a, 2.1e-44], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.95e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e-25 or 2.94999999999999982e44 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in c around -inf 70.6%

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

   5. Simplified 72.0%

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

      1. add-cube-cbrt 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 71.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

   10. Simplified 68.3%

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

   if -6.5e-25 < a < 5.99999999999999982e-117 or 2.10000000000000001e-44 < a < 2.94999999999999982e44

   1. Initial program 72.4%

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

   3. Taylor expanded in c around inf 53.3%

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

   if 5.99999999999999982e-117 < a < 2.10000000000000001e-44

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in y around inf 67.4%

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

      1. *-commutative 67.4%

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

   8. Simplified 67.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.1e-21)
     t_2
     (if (<= a 1.45e-211)
       t_1
       (if (<= a 6.8e-8)
         (* j (- (* t c) (* y i)))
         (if (<= a 1.05e+44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.1e-21) {
		tmp = t_2;
	} else if (a <= 1.45e-211) {
		tmp = t_1;
	} else if (a <= 6.8e-8) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 1.05e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1.1d-21)) then
        tmp = t_2
    else if (a <= 1.45d-211) then
        tmp = t_1
    else if (a <= 6.8d-8) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 1.05d+44) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.1e-21) {
		tmp = t_2;
	} else if (a <= 1.45e-211) {
		tmp = t_1;
	} else if (a <= 6.8e-8) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 1.05e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.1e-21:
		tmp = t_2
	elif a <= 1.45e-211:
		tmp = t_1
	elif a <= 6.8e-8:
		tmp = j * ((t * c) - (y * i))
	elif a <= 1.05e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.1e-21)
		tmp = t_2;
	elseif (a <= 1.45e-211)
		tmp = t_1;
	elseif (a <= 6.8e-8)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 1.05e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.1e-21)
		tmp = t_2;
	elseif (a <= 1.45e-211)
		tmp = t_1;
	elseif (a <= 6.8e-8)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 1.05e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e-21], t$95$2, If[LessEqual[a, 1.45e-211], t$95$1, If[LessEqual[a, 6.8e-8], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e-21 or 1.04999999999999993e44 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in c around -inf 70.6%

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

   5. Simplified 72.0%

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

      1. add-cube-cbrt 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 71.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

   10. Simplified 68.3%

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

   if -1.1e-21 < a < 1.45000000000000007e-211 or 6.8e-8 < a < 1.04999999999999993e44

   1. Initial program 69.7%

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

   3. Taylor expanded in c around inf 55.0%

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

   if 1.45000000000000007e-211 < a < 6.8e-8

   1. Initial program 86.5%

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

   3. Taylor expanded in c around -inf 80.7%

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

   5. Simplified 84.1%

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

      1. add-cube-cbrt 84.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 84.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 84.1%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in j around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-lft-neg-out 54.7%

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

      3. *-commutative 54.7%

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

      4. +-commutative 54.7%

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

      5. cancel-sign-sub-inv 54.7%

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

      6. *-commutative 54.7%

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

   10. Simplified 54.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-211}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.029:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -3.5e-24)
     t_2
     (if (<= a 4.8e-117)
       t_1
       (if (<= a 0.029)
         (* x (- (* y z) (* t a)))
         (if (<= a 2.3e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.5e-24) {
		tmp = t_2;
	} else if (a <= 4.8e-117) {
		tmp = t_1;
	} else if (a <= 0.029) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 2.3e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-3.5d-24)) then
        tmp = t_2
    else if (a <= 4.8d-117) then
        tmp = t_1
    else if (a <= 0.029d0) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= 2.3d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.5e-24) {
		tmp = t_2;
	} else if (a <= 4.8e-117) {
		tmp = t_1;
	} else if (a <= 0.029) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 2.3e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3.5e-24:
		tmp = t_2
	elif a <= 4.8e-117:
		tmp = t_1
	elif a <= 0.029:
		tmp = x * ((y * z) - (t * a))
	elif a <= 2.3e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.5e-24)
		tmp = t_2;
	elseif (a <= 4.8e-117)
		tmp = t_1;
	elseif (a <= 0.029)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= 2.3e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3.5e-24)
		tmp = t_2;
	elseif (a <= 4.8e-117)
		tmp = t_1;
	elseif (a <= 0.029)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= 2.3e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e-24], t$95$2, If[LessEqual[a, 4.8e-117], t$95$1, If[LessEqual[a, 0.029], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4999999999999996e-24 or 2.30000000000000012e45 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in c around -inf 70.6%

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

   5. Simplified 72.0%

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

      1. add-cube-cbrt 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 71.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 71.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

   10. Simplified 68.3%

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

   if -3.4999999999999996e-24 < a < 4.80000000000000028e-117 or 0.0290000000000000015 < a < 2.30000000000000012e45

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 54.2%

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

   if 4.80000000000000028e-117 < a < 0.0290000000000000015

   1. Initial program 79.9%

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

   3. Taylor expanded in c around -inf 93.6%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in x around inf 61.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 0.029:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+61} \lor \neg \left(y \leq 2.6 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -2.5e+61) (not (<= y 2.6e+156)))
   (* y (- (* x z) (* i j)))
   (+ (* j (- (* t c) (* y i))) (* b (- (* a i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.5e+61) || !(y <= 2.6e+156)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-2.5d+61)) .or. (.not. (y <= 2.6d+156))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.5e+61) || !(y <= 2.6e+156)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -2.5e+61) or not (y <= 2.6e+156):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -2.5e+61) || !(y <= 2.6e+156))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -2.5e+61) || ~((y <= 2.6e+156)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -2.5e+61], N[Not[LessEqual[y, 2.6e+156]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000009e61 or 2.60000000000000019e156 < y

   1. Initial program 53.1%

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

   3. Taylor expanded in c around -inf 57.9%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in y around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. *-commutative 74.6%

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

      3. mul-1-neg 74.6%

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

      4. *-commutative 74.6%

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

      5. unsub-neg 74.6%

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

      6. *-commutative 74.6%

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

      7. *-commutative 74.6%

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

   8. Simplified 74.6%

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

   if -2.50000000000000009e61 < y < 2.60000000000000019e156

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 61.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+61} \lor \neg \left(y \leq 2.6 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -3.6e-46)
     t_1
     (if (<= j -1.3e-225)
       (* i (* a b))
       (if (<= j 6.2e-35) (* 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 = c * (t * j);
	double tmp;
	if (j <= -3.6e-46) {
		tmp = t_1;
	} else if (j <= -1.3e-225) {
		tmp = i * (a * b);
	} else if (j <= 6.2e-35) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (j <= (-3.6d-46)) then
        tmp = t_1
    else if (j <= (-1.3d-225)) then
        tmp = i * (a * b)
    else if (j <= 6.2d-35) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -3.6e-46) {
		tmp = t_1;
	} else if (j <= -1.3e-225) {
		tmp = i * (a * b);
	} else if (j <= 6.2e-35) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -3.6e-46:
		tmp = t_1
	elif j <= -1.3e-225:
		tmp = i * (a * b)
	elif j <= 6.2e-35:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -3.6e-46)
		tmp = t_1;
	elseif (j <= -1.3e-225)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 6.2e-35)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (j <= -3.6e-46)
		tmp = t_1;
	elseif (j <= -1.3e-225)
		tmp = i * (a * b);
	elseif (j <= 6.2e-35)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.6e-46], t$95$1, If[LessEqual[j, -1.3e-225], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-35], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.6e-46 or 6.20000000000000024e-35 < j

   1. Initial program 69.4%

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

   3. Taylor expanded in c around -inf 65.4%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

      4. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in j around inf 39.3%

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

       1. *-commutative 39.3%

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

   11. Simplified 39.3%

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

   if -3.6e-46 < j < -1.30000000000000007e-225

   1. Initial program 62.0%

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

   3. Taylor expanded in c around -inf 79.1%

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

   5. Simplified 83.0%

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

      1. add-cube-cbrt 82.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 82.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 82.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 82.8%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in i around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   10. Simplified 52.1%

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

   11. Taylor expanded in a around inf 44.5%

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

       1. *-commutative 44.5%

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

   13. Simplified 44.5%

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

   if -1.30000000000000007e-225 < j < 6.20000000000000024e-35

   1. Initial program 68.2%

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

   3. Taylor expanded in y around inf 39.3%

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

   4. Taylor expanded in i around 0 34.8%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -3.8e+189)
     t_1
     (if (<= x -9.8e-32)
       (* j (* t c))
       (if (<= x 6.5e-72) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -3.8e+189) {
		tmp = t_1;
	} else if (x <= -9.8e-32) {
		tmp = j * (t * c);
	} else if (x <= 6.5e-72) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-3.8d+189)) then
        tmp = t_1
    else if (x <= (-9.8d-32)) then
        tmp = j * (t * c)
    else if (x <= 6.5d-72) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -3.8e+189) {
		tmp = t_1;
	} else if (x <= -9.8e-32) {
		tmp = j * (t * c);
	} else if (x <= 6.5e-72) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -3.8e+189:
		tmp = t_1
	elif x <= -9.8e-32:
		tmp = j * (t * c)
	elif x <= 6.5e-72:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -3.8e+189)
		tmp = t_1;
	elseif (x <= -9.8e-32)
		tmp = Float64(j * Float64(t * c));
	elseif (x <= 6.5e-72)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -3.8e+189)
		tmp = t_1;
	elseif (x <= -9.8e-32)
		tmp = j * (t * c);
	elseif (x <= 6.5e-72)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+189], t$95$1, If[LessEqual[x, -9.8e-32], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-72], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998e189 or 6.4999999999999997e-72 < x

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around inf 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if -3.7999999999999998e189 < x < -9.7999999999999996e-32

   1. Initial program 75.6%

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

   3. Taylor expanded in c around -inf 86.3%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. *-commutative 49.8%

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

   8. Simplified 49.8%

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

   9. Taylor expanded in j around inf 26.0%

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

       1. *-commutative 26.0%

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

       2. associate-*r* 28.6%

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

   11. Simplified 28.6%

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

   if -9.7999999999999996e-32 < x < 6.4999999999999997e-72

   1. Initial program 68.0%

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

   3. Taylor expanded in c around -inf 73.4%

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

   5. Simplified 76.8%

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

      1. add-cube-cbrt 76.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 76.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 76.8%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in i around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. *-commutative 53.7%

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

   10. Simplified 53.7%

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

   11. Taylor expanded in a around inf 41.8%

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

       1. *-commutative 41.8%

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

   13. Simplified 41.8%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+189}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-82} \lor \neg \left(a \leq 1.02 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.8e-82) (not (<= a 1.02e-10)))
   (* a (- (* b i) (* 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 ((a <= -2.8e-82) || !(a <= 1.02e-10)) {
		tmp = a * ((b * i) - (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 ((a <= (-2.8d-82)) .or. (.not. (a <= 1.02d-10))) then
        tmp = a * ((b * i) - (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 ((a <= -2.8e-82) || !(a <= 1.02e-10)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.8e-82) or not (a <= 1.02e-10):
		tmp = a * ((b * i) - (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 ((a <= -2.8e-82) || !(a <= 1.02e-10))
		tmp = Float64(a * Float64(Float64(b * i) - 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 ((a <= -2.8e-82) || ~((a <= 1.02e-10)))
		tmp = a * ((b * i) - (x * t));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.8e-82], N[Not[LessEqual[a, 1.02e-10]], $MachinePrecision]], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.80000000000000024e-82 or 1.01999999999999997e-10 < a

   1. Initial program 64.5%

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

   3. Taylor expanded in c around -inf 72.7%

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

   5. Simplified 74.7%

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

      1. add-cube-cbrt 74.5%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 74.5%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 74.5%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in a around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   10. Simplified 64.1%

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

   if -2.80000000000000024e-82 < a < 1.01999999999999997e-10

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 37.3%

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

      1. *-commutative 37.3%

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

   8. Simplified 37.3%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-82} \lor \neg \left(a \leq 1.02 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+84} \lor \neg \left(c \leq 7.2 \cdot 10^{+55}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -9.5e+84) (not (<= c 7.2e+55))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -9.5e+84) || !(c <= 7.2e+55)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-9.5d+84)) .or. (.not. (c <= 7.2d+55))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -9.5e+84) || !(c <= 7.2e+55)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -9.5e+84) or not (c <= 7.2e+55):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -9.5e+84) || !(c <= 7.2e+55))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -9.5e+84) || ~((c <= 7.2e+55)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -9.5e+84], N[Not[LessEqual[c, 7.2e+55]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.49999999999999979e84 or 7.19999999999999975e55 < c

   1. Initial program 55.0%

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

   3. Taylor expanded in c around -inf 74.3%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in t around inf 49.4%

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

      1. +-commutative 49.4%

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

      2. mul-1-neg 49.4%

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

      3. unsub-neg 49.4%

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

      4. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in j around inf 42.8%

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

       1. *-commutative 42.8%

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

   11. Simplified 42.8%

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

   if -9.49999999999999979e84 < c < 7.19999999999999975e55

   1. Initial program 77.4%

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

   3. Taylor expanded in b around inf 35.4%

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

   4. Taylor expanded in a around inf 28.9%

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

      1. *-commutative 28.9%

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

   6. Simplified 28.9%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+84} \lor \neg \left(c \leq 7.2 \cdot 10^{+55}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+85} \lor \neg \left(c \leq 5.2 \cdot 10^{+64}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.35e+85) (not (<= c 5.2e+64))) (* c (* t j)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.35e+85) || !(c <= 5.2e+64)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.35d+85)) .or. (.not. (c <= 5.2d+64))) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.35e+85) || !(c <= 5.2e+64)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.35e+85) or not (c <= 5.2e+64):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.35e+85) || !(c <= 5.2e+64))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.35e+85) || ~((c <= 5.2e+64)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.35e+85], N[Not[LessEqual[c, 5.2e+64]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.34999999999999992e85 or 5.19999999999999994e64 < c

   1. Initial program 55.1%

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

   3. Taylor expanded in c around -inf 75.7%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in t around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in j around inf 42.7%

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

       1. *-commutative 42.7%

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

   11. Simplified 42.7%

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

   if -1.34999999999999992e85 < c < 5.19999999999999994e64

   1. Initial program 77.0%

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

   3. Taylor expanded in c around -inf 71.3%

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

   5. Simplified 73.0%

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

      1. add-cube-cbrt 72.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 72.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 72.9%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in i around inf 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. *-commutative 48.2%

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

   10. Simplified 48.2%

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

   11. Taylor expanded in a around inf 29.3%

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

       1. *-commutative 29.3%

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

   13. Simplified 29.3%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+85} \lor \neg \left(c \leq 5.2 \cdot 10^{+64}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-82}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.55e-82)
   (- (* t (* x a)))
   (if (<= a 6.8e+34) (* z (* x y)) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.55e-82) {
		tmp = -(t * (x * a));
	} else if (a <= 6.8e+34) {
		tmp = z * (x * y);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.55d-82)) then
        tmp = -(t * (x * a))
    else if (a <= 6.8d+34) then
        tmp = z * (x * y)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.55e-82) {
		tmp = -(t * (x * a));
	} else if (a <= 6.8e+34) {
		tmp = z * (x * y);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.55e-82:
		tmp = -(t * (x * a))
	elif a <= 6.8e+34:
		tmp = z * (x * y)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.55e-82)
		tmp = Float64(-Float64(t * Float64(x * a)));
	elseif (a <= 6.8e+34)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.55e-82)
		tmp = -(t * (x * a));
	elseif (a <= 6.8e+34)
		tmp = z * (x * y);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.55e-82], (-N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), If[LessEqual[a, 6.8e+34], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.54999999999999996e-82

   1. Initial program 54.8%

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

   3. Taylor expanded in c around -inf 68.0%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around inf 43.8%

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

      1. +-commutative 43.8%

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

      2. mul-1-neg 43.8%

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

      3. unsub-neg 43.8%

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

      4. *-commutative 43.8%

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

   8. Simplified 43.8%

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

   9. Taylor expanded in j around 0 35.1%

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

       1. neg-mul-1 35.1%

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

       2. distribute-rgt-neg-in 35.1%

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

   11. Simplified 35.1%

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

   if -2.54999999999999996e-82 < a < 6.7999999999999999e34

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in y around inf 36.8%

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

      1. *-commutative 36.8%

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

   8. Simplified 36.8%

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

   if 6.7999999999999999e34 < a

   1. Initial program 72.9%

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

   3. Taylor expanded in c around -inf 76.0%

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

   5. Simplified 76.1%

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

      1. add-cube-cbrt 76.0%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

      2. pow3 76.0%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

      3. *-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

   7. Applied egg-rr 76.0%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

   8. Taylor expanded in i around inf 59.6%

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

      1. +-commutative 59.6%

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

      2. mul-1-neg 59.6%

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

      3. unsub-neg 59.6%

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

      4. *-commutative 59.6%

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

   10. Simplified 59.6%

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

   11. Taylor expanded in a around inf 49.1%

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

       1. *-commutative 49.1%

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

   13. Simplified 49.1%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-82}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.8%

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

3. Taylor expanded in c around -inf 73.1%

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

5. Simplified 76.1%

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

   1. add-cube-cbrt 76.0%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)}\right)\right) \]

   2. pow3 76.0%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - a \cdot t}\right)}^{3}}\right)\right) \]

   3. *-commutative 76.0%

      \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot {\left(\sqrt[3]{z \cdot y - \color{blue}{t \cdot a}}\right)}^{3}\right)\right) \]

7. Applied egg-rr 76.0%

   \[\leadsto \mathsf{fma}\left(-c, \mathsf{fma}\left(-j, t, b \cdot z\right), \mathsf{fma}\left(i, \mathsf{fma}\left(-j, y, b \cdot a\right), x \cdot \color{blue}{{\left(\sqrt[3]{z \cdot y - t \cdot a}\right)}^{3}}\right)\right) \]

8. Taylor expanded in i around inf 37.8%

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

   1. +-commutative 37.8%

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

   2. mul-1-neg 37.8%

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

   3. unsub-neg 37.8%

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

   4. *-commutative 37.8%

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

10. Simplified 37.8%

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

11. Taylor expanded in a around inf 23.2%

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

12. Final simplification 23.2%

    \[\leadsto a \cdot \left(b \cdot i\right) \]
13. Add Preprocessing

Developer target: 69.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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