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

Percentage Accurate: 73.0% → 76.7%

Time: 44.4s

Alternatives: 30

Speedup: 0.5×

• 59.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 76.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.28 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, z \cdot \left(x \cdot y - c \cdot b\right) + t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x 1.28e+123)
   (fma
    j
    (- (* a c) (* y i))
    (+ (* z (- (* x y) (* c b))) (* t (fma (- a) x (* i b)))))
   (+ (* x (- (* y z) (* a t))) (* b (- (* i t) (* c 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 (x <= 1.28e+123) {
		tmp = fma(j, ((a * c) - (y * i)), ((z * ((x * y) - (c * b))) + (t * fma(-a, x, (i * b)))));
	} else {
		tmp = (x * ((y * z) - (a * t))) + (b * ((i * t) - (c * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= 1.28e+123)
		tmp = fma(j, Float64(Float64(a * c) - Float64(y * i)), Float64(Float64(z * Float64(Float64(x * y) - Float64(c * b))) + Float64(t * fma(Float64(-a), x, Float64(i * b)))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(a * t))) + Float64(b * Float64(Float64(i * t) - Float64(c * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, 1.28e+123], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.28000000000000005e123

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. fma-define 76.4%

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

      3. *-commutative 76.4%

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

      4. *-commutative 76.4%

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

      5. *-commutative 76.4%

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

      6. *-commutative 76.4%

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

      7. *-commutative 76.4%

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

      8. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 80.3%

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

   7. Simplified 84.1%

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

   if 1.28000000000000005e123 < x

   1. Initial program 85.4%

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

   3. Taylor expanded in j around 0 93.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.28 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, z \cdot \left(x \cdot y - c \cdot b\right) + t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot t - c \cdot z\\ t_2 := x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot t\_1\\ t_3 := a \cdot c - y \cdot i\\ \mathbf{if}\;t\_2 + j \cdot t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_3, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \sqrt[3]{{t\_1}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i t) (* c z)))
        (t_2 (+ (* x (- (* y z) (* a t))) (* b t_1)))
        (t_3 (- (* a c) (* y i))))
   (if (<= (+ t_2 (* j t_3)) INFINITY)
     (fma j t_3 t_2)
     (* b (cbrt (pow t_1 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * t) - (c * z);
	double t_2 = (x * ((y * z) - (a * t))) + (b * t_1);
	double t_3 = (a * c) - (y * i);
	double tmp;
	if ((t_2 + (j * t_3)) <= ((double) INFINITY)) {
		tmp = fma(j, t_3, t_2);
	} else {
		tmp = b * cbrt(pow(t_1, 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * t) - Float64(c * z))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(a * t))) + Float64(b * t_1))
	t_3 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_2 + Float64(j * t_3)) <= Inf)
		tmp = fma(j, t_3, t_2);
	else
		tmp = Float64(b * cbrt((t_1 ^ 3.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$3 + t$95$2), $MachinePrecision], N[(b * N[Power[N[Power[t$95$1, 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. fma-define 90.2%

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

      3. *-commutative 90.2%

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

      4. *-commutative 90.2%

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

      5. *-commutative 90.2%

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

      6. *-commutative 90.2%

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

      7. *-commutative 90.2%

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

      8. *-commutative 90.2%

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

   3. Simplified 90.2%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 16.7%

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

      3. *-commutative 16.7%

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

      4. *-commutative 16.7%

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

      5. *-commutative 16.7%

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

      6. *-commutative 16.7%

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

      7. *-commutative 16.7%

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

      8. *-commutative 16.7%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in z around 0 35.7%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in b around inf 43.5%

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

      1. +-commutative 43.5%

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

      2. mul-1-neg 43.5%

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

      3. sub-neg 43.5%

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

      4. *-commutative 43.5%

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

      5. *-commutative 43.5%

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

   10. Simplified 43.5%

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

       1. add-cbrt-cube 57.2%

          \[\leadsto b \cdot \color{blue}{\sqrt[3]{\left(\left(t \cdot i - z \cdot c\right) \cdot \left(t \cdot i - z \cdot c\right)\right) \cdot \left(t \cdot i - z \cdot c\right)}} \]

       2. pow3 57.2%

          \[\leadsto b \cdot \sqrt[3]{\color{blue}{{\left(t \cdot i - z \cdot c\right)}^{3}}} \]

       3. *-commutative 57.2%

          \[\leadsto b \cdot \sqrt[3]{{\left(\color{blue}{i \cdot t} - z \cdot c\right)}^{3}} \]

       4. *-commutative 57.2%

          \[\leadsto b \cdot \sqrt[3]{{\left(i \cdot t - \color{blue}{c \cdot z}\right)}^{3}} \]

   12. Applied egg-rr 57.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \sqrt[3]{{\left(i \cdot t - c \cdot z\right)}^{3}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. fma-define 90.2%

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

      3. *-commutative 90.2%

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

      4. *-commutative 90.2%

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

      5. *-commutative 90.2%

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

      6. *-commutative 90.2%

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

      7. *-commutative 90.2%

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

      8. *-commutative 90.2%

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

   3. Simplified 90.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 28.6%

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

   4. Taylor expanded in c around -inf 42.9%

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

      1. associate--l+ 42.9%

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

      2. mul-1-neg 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

      4. associate-*r* 42.9%

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

      5. neg-mul-1 42.9%

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

      6. cancel-sign-sub 42.9%

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

      7. +-commutative 42.9%

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

      8. mul-1-neg 42.9%

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

      9. unsub-neg 42.9%

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

      10. *-commutative 42.9%

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

      11. associate-*r* 42.9%

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

      12. neg-mul-1 42.9%

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

      13. cancel-sign-sub 42.9%

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

   6. Simplified 52.6%

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

   7. Taylor expanded in a around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. *-commutative 48.2%

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

      5. *-commutative 48.2%

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

      6. associate-*l* 52.9%

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

   9. Simplified 52.9%

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

4. Final simplification 84.1%

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

Alternative 4: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 28.6%

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

   4. Taylor expanded in c around -inf 42.9%

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

      1. associate--l+ 42.9%

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

      2. mul-1-neg 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

      4. associate-*r* 42.9%

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

      5. neg-mul-1 42.9%

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

      6. cancel-sign-sub 42.9%

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

      7. +-commutative 42.9%

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

      8. mul-1-neg 42.9%

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

      9. unsub-neg 42.9%

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

      10. *-commutative 42.9%

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

      11. associate-*r* 42.9%

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

      12. neg-mul-1 42.9%

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

      13. cancel-sign-sub 42.9%

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

   6. Simplified 52.6%

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

   7. Taylor expanded in a around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. *-commutative 48.2%

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

      5. *-commutative 48.2%

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

      6. associate-*l* 52.9%

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

   9. Simplified 52.9%

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

4. Final simplification 84.1%

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

Alternative 5: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - j \cdot i\right)\\ t_3 := b \cdot \left(i \cdot t - c \cdot z\right)\\ t_4 := c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.96 \cdot 10^{+184}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -1.85:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+183}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* i b) (* x a))))
        (t_2 (* y (- (* x z) (* j i))))
        (t_3 (* b (- (* i t) (* c z))))
        (t_4 (* c (- (* j a) (* z b)))))
   (if (<= c -3.96e+184)
     t_4
     (if (<= c -1.85)
       t_2
       (if (<= c -8.6e-57)
         (* a (- (* j c) (* x t)))
         (if (<= c -1.95e-97)
           t_3
           (if (<= c -1e-290)
             t_1
             (if (<= c 3.5e-192)
               t_2
               (if (<= c 3.8e-5)
                 t_1
                 (if (<= c 8.5e+125)
                   t_2
                   (if (<= c 1.25e+183) t_3 t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (x * a));
	double t_2 = y * ((x * z) - (j * i));
	double t_3 = b * ((i * t) - (c * z));
	double t_4 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -3.96e+184) {
		tmp = t_4;
	} else if (c <= -1.85) {
		tmp = t_2;
	} else if (c <= -8.6e-57) {
		tmp = a * ((j * c) - (x * t));
	} else if (c <= -1.95e-97) {
		tmp = t_3;
	} else if (c <= -1e-290) {
		tmp = t_1;
	} else if (c <= 3.5e-192) {
		tmp = t_2;
	} else if (c <= 3.8e-5) {
		tmp = t_1;
	} else if (c <= 8.5e+125) {
		tmp = t_2;
	} else if (c <= 1.25e+183) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((i * b) - (x * a))
    t_2 = y * ((x * z) - (j * i))
    t_3 = b * ((i * t) - (c * z))
    t_4 = c * ((j * a) - (z * b))
    if (c <= (-3.96d+184)) then
        tmp = t_4
    else if (c <= (-1.85d0)) then
        tmp = t_2
    else if (c <= (-8.6d-57)) then
        tmp = a * ((j * c) - (x * t))
    else if (c <= (-1.95d-97)) then
        tmp = t_3
    else if (c <= (-1d-290)) then
        tmp = t_1
    else if (c <= 3.5d-192) then
        tmp = t_2
    else if (c <= 3.8d-5) then
        tmp = t_1
    else if (c <= 8.5d+125) then
        tmp = t_2
    else if (c <= 1.25d+183) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (x * a));
	double t_2 = y * ((x * z) - (j * i));
	double t_3 = b * ((i * t) - (c * z));
	double t_4 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -3.96e+184) {
		tmp = t_4;
	} else if (c <= -1.85) {
		tmp = t_2;
	} else if (c <= -8.6e-57) {
		tmp = a * ((j * c) - (x * t));
	} else if (c <= -1.95e-97) {
		tmp = t_3;
	} else if (c <= -1e-290) {
		tmp = t_1;
	} else if (c <= 3.5e-192) {
		tmp = t_2;
	} else if (c <= 3.8e-5) {
		tmp = t_1;
	} else if (c <= 8.5e+125) {
		tmp = t_2;
	} else if (c <= 1.25e+183) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((i * b) - (x * a))
	t_2 = y * ((x * z) - (j * i))
	t_3 = b * ((i * t) - (c * z))
	t_4 = c * ((j * a) - (z * b))
	tmp = 0
	if c <= -3.96e+184:
		tmp = t_4
	elif c <= -1.85:
		tmp = t_2
	elif c <= -8.6e-57:
		tmp = a * ((j * c) - (x * t))
	elif c <= -1.95e-97:
		tmp = t_3
	elif c <= -1e-290:
		tmp = t_1
	elif c <= 3.5e-192:
		tmp = t_2
	elif c <= 3.8e-5:
		tmp = t_1
	elif c <= 8.5e+125:
		tmp = t_2
	elif c <= 1.25e+183:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(i * b) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(j * i)))
	t_3 = Float64(b * Float64(Float64(i * t) - Float64(c * z)))
	t_4 = Float64(c * Float64(Float64(j * a) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.96e+184)
		tmp = t_4;
	elseif (c <= -1.85)
		tmp = t_2;
	elseif (c <= -8.6e-57)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	elseif (c <= -1.95e-97)
		tmp = t_3;
	elseif (c <= -1e-290)
		tmp = t_1;
	elseif (c <= 3.5e-192)
		tmp = t_2;
	elseif (c <= 3.8e-5)
		tmp = t_1;
	elseif (c <= 8.5e+125)
		tmp = t_2;
	elseif (c <= 1.25e+183)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((i * b) - (x * a));
	t_2 = y * ((x * z) - (j * i));
	t_3 = b * ((i * t) - (c * z));
	t_4 = c * ((j * a) - (z * b));
	tmp = 0.0;
	if (c <= -3.96e+184)
		tmp = t_4;
	elseif (c <= -1.85)
		tmp = t_2;
	elseif (c <= -8.6e-57)
		tmp = a * ((j * c) - (x * t));
	elseif (c <= -1.95e-97)
		tmp = t_3;
	elseif (c <= -1e-290)
		tmp = t_1;
	elseif (c <= 3.5e-192)
		tmp = t_2;
	elseif (c <= 3.8e-5)
		tmp = t_1;
	elseif (c <= 8.5e+125)
		tmp = t_2;
	elseif (c <= 1.25e+183)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.96e+184], t$95$4, If[LessEqual[c, -1.85], t$95$2, If[LessEqual[c, -8.6e-57], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.95e-97], t$95$3, If[LessEqual[c, -1e-290], t$95$1, If[LessEqual[c, 3.5e-192], t$95$2, If[LessEqual[c, 3.8e-5], t$95$1, If[LessEqual[c, 8.5e+125], t$95$2, If[LessEqual[c, 1.25e+183], t$95$3, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.95999999999999993e184 or 1.25000000000000002e183 < c

   1. Initial program 66.4%

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

   3. Taylor expanded in c around inf 82.1%

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

   if -3.95999999999999993e184 < c < -1.8500000000000001 or -1.0000000000000001e-290 < c < 3.50000000000000014e-192 or 3.8000000000000002e-5 < c < 8.49999999999999974e125

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf 60.2%

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

      1. +-commutative 60.2%

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

      2. mul-1-neg 60.2%

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

      3. unsub-neg 60.2%

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

      4. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if -1.8500000000000001 < c < -8.60000000000000043e-57

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 73.7%

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

      1. +-commutative 73.7%

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

      2. mul-1-neg 73.7%

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

      3. unsub-neg 73.7%

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

      4. *-commutative 73.7%

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

      5. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -8.60000000000000043e-57 < c < -1.9499999999999999e-97 or 8.49999999999999974e125 < c < 1.25000000000000002e183

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf 56.7%

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

   if -1.9499999999999999e-97 < c < -1.0000000000000001e-290 or 3.50000000000000014e-192 < c < 3.8000000000000002e-5

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. fma-define 82.3%

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

      3. *-commutative 82.3%

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

      4. *-commutative 82.3%

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

      5. *-commutative 82.3%

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

      6. *-commutative 82.3%

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

      7. *-commutative 82.3%

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

      8. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in z around 0 74.9%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in t around inf 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-lft-neg-out 65.6%

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

      3. +-commutative 65.6%

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

      4. distribute-lft-neg-out 65.6%

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

      5. unsub-neg 65.6%

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

      6. *-commutative 65.6%

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

   10. Simplified 65.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.96 \cdot 10^{+184}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.85:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-97}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t - c \cdot z\right)\\ t_2 := a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-135}:\\ \;\;\;\;\left(j \cdot y\right) \cdot \left(-i\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 0.000115:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* i t) (* c z)))) (t_2 (* a (- (* j c) (* x t)))))
   (if (<= a -1.25e+84)
     t_2
     (if (<= a -1.06e+14)
       t_1
       (if (<= a -1.5e-50)
         t_2
         (if (<= a -9.8e-135)
           (* (* j y) (- i))
           (if (<= a 7.2e-188)
             t_1
             (if (<= a 1.52e-120)
               (* y (* x z))
               (if (<= a 0.000115) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (c * z));
	double t_2 = a * ((j * c) - (x * t));
	double tmp;
	if (a <= -1.25e+84) {
		tmp = t_2;
	} else if (a <= -1.06e+14) {
		tmp = t_1;
	} else if (a <= -1.5e-50) {
		tmp = t_2;
	} else if (a <= -9.8e-135) {
		tmp = (j * y) * -i;
	} else if (a <= 7.2e-188) {
		tmp = t_1;
	} else if (a <= 1.52e-120) {
		tmp = y * (x * z);
	} else if (a <= 0.000115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((i * t) - (c * z))
    t_2 = a * ((j * c) - (x * t))
    if (a <= (-1.25d+84)) then
        tmp = t_2
    else if (a <= (-1.06d+14)) then
        tmp = t_1
    else if (a <= (-1.5d-50)) then
        tmp = t_2
    else if (a <= (-9.8d-135)) then
        tmp = (j * y) * -i
    else if (a <= 7.2d-188) then
        tmp = t_1
    else if (a <= 1.52d-120) then
        tmp = y * (x * z)
    else if (a <= 0.000115d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (c * z));
	double t_2 = a * ((j * c) - (x * t));
	double tmp;
	if (a <= -1.25e+84) {
		tmp = t_2;
	} else if (a <= -1.06e+14) {
		tmp = t_1;
	} else if (a <= -1.5e-50) {
		tmp = t_2;
	} else if (a <= -9.8e-135) {
		tmp = (j * y) * -i;
	} else if (a <= 7.2e-188) {
		tmp = t_1;
	} else if (a <= 1.52e-120) {
		tmp = y * (x * z);
	} else if (a <= 0.000115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((i * t) - (c * z))
	t_2 = a * ((j * c) - (x * t))
	tmp = 0
	if a <= -1.25e+84:
		tmp = t_2
	elif a <= -1.06e+14:
		tmp = t_1
	elif a <= -1.5e-50:
		tmp = t_2
	elif a <= -9.8e-135:
		tmp = (j * y) * -i
	elif a <= 7.2e-188:
		tmp = t_1
	elif a <= 1.52e-120:
		tmp = y * (x * z)
	elif a <= 0.000115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(i * t) - Float64(c * z)))
	t_2 = Float64(a * Float64(Float64(j * c) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.25e+84)
		tmp = t_2;
	elseif (a <= -1.06e+14)
		tmp = t_1;
	elseif (a <= -1.5e-50)
		tmp = t_2;
	elseif (a <= -9.8e-135)
		tmp = Float64(Float64(j * y) * Float64(-i));
	elseif (a <= 7.2e-188)
		tmp = t_1;
	elseif (a <= 1.52e-120)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 0.000115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((i * t) - (c * z));
	t_2 = a * ((j * c) - (x * t));
	tmp = 0.0;
	if (a <= -1.25e+84)
		tmp = t_2;
	elseif (a <= -1.06e+14)
		tmp = t_1;
	elseif (a <= -1.5e-50)
		tmp = t_2;
	elseif (a <= -9.8e-135)
		tmp = (j * y) * -i;
	elseif (a <= 7.2e-188)
		tmp = t_1;
	elseif (a <= 1.52e-120)
		tmp = y * (x * z);
	elseif (a <= 0.000115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+84], t$95$2, If[LessEqual[a, -1.06e+14], t$95$1, If[LessEqual[a, -1.5e-50], t$95$2, If[LessEqual[a, -9.8e-135], N[(N[(j * y), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[a, 7.2e-188], t$95$1, If[LessEqual[a, 1.52e-120], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.000115], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.25e84 or -1.06e14 < a < -1.49999999999999995e-50 or 1.15e-4 < a

   1. Initial program 72.1%

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

   3. Taylor expanded in a around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

      5. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   if -1.25e84 < a < -1.06e14 or -9.8000000000000005e-135 < a < 7.1999999999999994e-188 or 1.52e-120 < a < 1.15e-4

   1. Initial program 80.1%

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

   3. Taylor expanded in b around inf 53.8%

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

   if -1.49999999999999995e-50 < a < -9.8000000000000005e-135

   1. Initial program 79.6%

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

   3. Taylor expanded in c around inf 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-*l* 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in i around inf 38.5%

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

   if 7.1999999999999994e-188 < a < 1.52e-120

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. fma-define 69.0%

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

      3. *-commutative 69.0%

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

      4. *-commutative 69.0%

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

      5. *-commutative 69.0%

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

      6. *-commutative 69.0%

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

      7. *-commutative 69.0%

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

      8. *-commutative 69.0%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in z around 0 81.7%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in y around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. *-commutative 75.5%

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

   10. Simplified 75.5%

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

   11. Taylor expanded in z around inf 56.8%

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

       1. *-commutative 56.8%

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

   13. Simplified 56.8%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-135}:\\ \;\;\;\;\left(j \cdot y\right) \cdot \left(-i\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-188}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 0.000115:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-189}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+154}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* i b) (* x a)))) (t_2 (* z (- (* x y) (* c b)))))
   (if (<= z -3.5e+41)
     t_2
     (if (<= z 7.2e-230)
       t_1
       (if (<= z 1.06e-189)
         (* j (- (* a c) (* y i)))
         (if (<= z 1.85e-115)
           t_1
           (if (<= z 5.5e-90)
             (* i (- (* b t) (* j y)))
             (if (<= z 1.06e+136)
               (* x (- (* y z) (* a t)))
               (if (<= z 1.06e+154) (* c (- (* j a) (* z b))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (x * a));
	double t_2 = z * ((x * y) - (c * b));
	double tmp;
	if (z <= -3.5e+41) {
		tmp = t_2;
	} else if (z <= 7.2e-230) {
		tmp = t_1;
	} else if (z <= 1.06e-189) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.85e-115) {
		tmp = t_1;
	} else if (z <= 5.5e-90) {
		tmp = i * ((b * t) - (j * y));
	} else if (z <= 1.06e+136) {
		tmp = x * ((y * z) - (a * t));
	} else if (z <= 1.06e+154) {
		tmp = c * ((j * a) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((i * b) - (x * a))
    t_2 = z * ((x * y) - (c * b))
    if (z <= (-3.5d+41)) then
        tmp = t_2
    else if (z <= 7.2d-230) then
        tmp = t_1
    else if (z <= 1.06d-189) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 1.85d-115) then
        tmp = t_1
    else if (z <= 5.5d-90) then
        tmp = i * ((b * t) - (j * y))
    else if (z <= 1.06d+136) then
        tmp = x * ((y * z) - (a * t))
    else if (z <= 1.06d+154) then
        tmp = c * ((j * a) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (x * a));
	double t_2 = z * ((x * y) - (c * b));
	double tmp;
	if (z <= -3.5e+41) {
		tmp = t_2;
	} else if (z <= 7.2e-230) {
		tmp = t_1;
	} else if (z <= 1.06e-189) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.85e-115) {
		tmp = t_1;
	} else if (z <= 5.5e-90) {
		tmp = i * ((b * t) - (j * y));
	} else if (z <= 1.06e+136) {
		tmp = x * ((y * z) - (a * t));
	} else if (z <= 1.06e+154) {
		tmp = c * ((j * a) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((i * b) - (x * a))
	t_2 = z * ((x * y) - (c * b))
	tmp = 0
	if z <= -3.5e+41:
		tmp = t_2
	elif z <= 7.2e-230:
		tmp = t_1
	elif z <= 1.06e-189:
		tmp = j * ((a * c) - (y * i))
	elif z <= 1.85e-115:
		tmp = t_1
	elif z <= 5.5e-90:
		tmp = i * ((b * t) - (j * y))
	elif z <= 1.06e+136:
		tmp = x * ((y * z) - (a * t))
	elif z <= 1.06e+154:
		tmp = c * ((j * a) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(i * b) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(c * b)))
	tmp = 0.0
	if (z <= -3.5e+41)
		tmp = t_2;
	elseif (z <= 7.2e-230)
		tmp = t_1;
	elseif (z <= 1.06e-189)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 1.85e-115)
		tmp = t_1;
	elseif (z <= 5.5e-90)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(j * y)));
	elseif (z <= 1.06e+136)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(a * t)));
	elseif (z <= 1.06e+154)
		tmp = Float64(c * Float64(Float64(j * a) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((i * b) - (x * a));
	t_2 = z * ((x * y) - (c * b));
	tmp = 0.0;
	if (z <= -3.5e+41)
		tmp = t_2;
	elseif (z <= 7.2e-230)
		tmp = t_1;
	elseif (z <= 1.06e-189)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 1.85e-115)
		tmp = t_1;
	elseif (z <= 5.5e-90)
		tmp = i * ((b * t) - (j * y));
	elseif (z <= 1.06e+136)
		tmp = x * ((y * z) - (a * t));
	elseif (z <= 1.06e+154)
		tmp = c * ((j * a) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+41], t$95$2, If[LessEqual[z, 7.2e-230], t$95$1, If[LessEqual[z, 1.06e-189], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-115], t$95$1, If[LessEqual[z, 5.5e-90], N[(i * N[(N[(b * t), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+136], N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+154], N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.4999999999999999e41 or 1.06e154 < z

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -3.4999999999999999e41 < z < 7.1999999999999997e-230 or 1.06e-189 < z < 1.85e-115

   1. Initial program 79.0%

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

      1. +-commutative 79.0%

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

      2. fma-define 81.0%

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

      3. *-commutative 81.0%

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

      4. *-commutative 81.0%

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

      5. *-commutative 81.0%

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

      6. *-commutative 81.0%

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

      7. *-commutative 81.0%

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

      8. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in z around 0 74.9%

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

   7. Simplified 78.9%

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

   8. Taylor expanded in t around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. distribute-lft-neg-out 62.4%

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

      3. +-commutative 62.4%

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

      4. distribute-lft-neg-out 62.4%

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

      5. unsub-neg 62.4%

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

      6. *-commutative 62.4%

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

   10. Simplified 62.4%

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

   if 7.1999999999999997e-230 < z < 1.06e-189

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. fma-define 90.5%

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

      3. *-commutative 90.5%

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

      4. *-commutative 90.5%

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

      5. *-commutative 90.5%

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

      6. *-commutative 90.5%

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

      7. *-commutative 90.5%

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

      8. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around 0 81.6%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in j around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

   10. Simplified 73.9%

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

   if 1.85e-115 < z < 5.5000000000000003e-90

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-define 98.0%

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

      3. *-commutative 98.0%

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

      4. *-commutative 98.0%

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

      5. *-commutative 98.0%

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

      6. *-commutative 98.0%

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

      7. *-commutative 98.0%

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

      8. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 80.3%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in i around inf 80.1%

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

      1. +-commutative 80.1%

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

      2. mul-1-neg 80.1%

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

      3. unsub-neg 80.1%

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

      4. *-commutative 80.1%

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

   10. Simplified 80.1%

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

   if 5.5000000000000003e-90 < z < 1.06000000000000003e136

   1. Initial program 85.1%

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

      1. +-commutative 85.1%

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

      2. fma-define 85.1%

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

      3. *-commutative 85.1%

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

      4. *-commutative 85.1%

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

      5. *-commutative 85.1%

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

      6. *-commutative 85.1%

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

      7. *-commutative 85.1%

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

      8. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in z around 0 83.1%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in x around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

      5. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   if 1.06000000000000003e136 < z < 1.06e154

   1. Initial program 49.7%

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

   3. Taylor expanded in c around inf 83.5%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-189}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+154}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= x -1.02e+20)
     (* z (* x y))
     (if (<= x -6.5e-214)
       t_1
       (if (<= x 3.6e-197)
         (* a (* j c))
         (if (<= x 2.45e-147)
           (* c (- (* z b)))
           (if (<= x 1.0)
             (* c (* j a))
             (if (<= x 4e+47)
               t_1
               (if (<= x 7e+126) (* y (* x z)) (* x (* a (- t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (x <= -1.02e+20) {
		tmp = z * (x * y);
	} else if (x <= -6.5e-214) {
		tmp = t_1;
	} else if (x <= 3.6e-197) {
		tmp = a * (j * c);
	} else if (x <= 2.45e-147) {
		tmp = c * -(z * b);
	} else if (x <= 1.0) {
		tmp = c * (j * a);
	} else if (x <= 4e+47) {
		tmp = t_1;
	} else if (x <= 7e+126) {
		tmp = y * (x * z);
	} else {
		tmp = x * (a * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (i * b)
    if (x <= (-1.02d+20)) then
        tmp = z * (x * y)
    else if (x <= (-6.5d-214)) then
        tmp = t_1
    else if (x <= 3.6d-197) then
        tmp = a * (j * c)
    else if (x <= 2.45d-147) then
        tmp = c * -(z * b)
    else if (x <= 1.0d0) then
        tmp = c * (j * a)
    else if (x <= 4d+47) then
        tmp = t_1
    else if (x <= 7d+126) then
        tmp = y * (x * z)
    else
        tmp = x * (a * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (x <= -1.02e+20) {
		tmp = z * (x * y);
	} else if (x <= -6.5e-214) {
		tmp = t_1;
	} else if (x <= 3.6e-197) {
		tmp = a * (j * c);
	} else if (x <= 2.45e-147) {
		tmp = c * -(z * b);
	} else if (x <= 1.0) {
		tmp = c * (j * a);
	} else if (x <= 4e+47) {
		tmp = t_1;
	} else if (x <= 7e+126) {
		tmp = y * (x * z);
	} else {
		tmp = x * (a * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if x <= -1.02e+20:
		tmp = z * (x * y)
	elif x <= -6.5e-214:
		tmp = t_1
	elif x <= 3.6e-197:
		tmp = a * (j * c)
	elif x <= 2.45e-147:
		tmp = c * -(z * b)
	elif x <= 1.0:
		tmp = c * (j * a)
	elif x <= 4e+47:
		tmp = t_1
	elif x <= 7e+126:
		tmp = y * (x * z)
	else:
		tmp = x * (a * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (x <= -1.02e+20)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= -6.5e-214)
		tmp = t_1;
	elseif (x <= 3.6e-197)
		tmp = Float64(a * Float64(j * c));
	elseif (x <= 2.45e-147)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (x <= 1.0)
		tmp = Float64(c * Float64(j * a));
	elseif (x <= 4e+47)
		tmp = t_1;
	elseif (x <= 7e+126)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(x * Float64(a * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	tmp = 0.0;
	if (x <= -1.02e+20)
		tmp = z * (x * y);
	elseif (x <= -6.5e-214)
		tmp = t_1;
	elseif (x <= 3.6e-197)
		tmp = a * (j * c);
	elseif (x <= 2.45e-147)
		tmp = c * -(z * b);
	elseif (x <= 1.0)
		tmp = c * (j * a);
	elseif (x <= 4e+47)
		tmp = t_1;
	elseif (x <= 7e+126)
		tmp = y * (x * z);
	else
		tmp = x * (a * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+20], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-214], t$95$1, If[LessEqual[x, 3.6e-197], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e-147], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.0], N[(c * N[(j * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+47], t$95$1, If[LessEqual[x, 7e+126], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(a * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.02e20

   1. Initial program 75.6%

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

   3. Taylor expanded in z around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in y around inf 45.6%

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

   if -1.02e20 < x < -6.5000000000000004e-214 or 1 < x < 4.0000000000000002e47

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 58.0%

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

      1. associate-*r* 58.0%

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

      2. neg-mul-1 58.0%

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

      3. fma-neg 58.0%

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

      4. mul-1-neg 58.0%

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

      5. remove-double-neg 58.0%

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

      6. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in a around 0 42.0%

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

   if -6.5000000000000004e-214 < x < 3.5999999999999998e-197

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. *-commutative 41.5%

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

      5. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in j around inf 39.4%

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

   if 3.5999999999999998e-197 < x < 2.45000000000000002e-147

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. *-commutative 51.6%

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

      3. associate-*r* 51.6%

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

      4. *-commutative 51.6%

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

      5. distribute-rgt-neg-out 51.6%

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

      6. distribute-rgt-neg-in 51.6%

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

   8. Simplified 51.6%

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

   if 2.45000000000000002e-147 < x < 1

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 30.6%

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

      1. +-commutative 30.6%

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

      2. mul-1-neg 30.6%

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

      3. unsub-neg 30.6%

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

      4. *-commutative 30.6%

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

      5. *-commutative 30.6%

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

   5. Simplified 30.6%

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

   6. Taylor expanded in j around inf 18.8%

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

      1. associate-*r* 26.9%

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

      2. *-commutative 26.9%

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

      3. associate-*r* 34.8%

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

   8. Simplified 34.8%

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

   if 4.0000000000000002e47 < x < 7.0000000000000005e126

   1. Initial program 74.9%

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

      1. +-commutative 74.9%

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

      2. fma-define 74.9%

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

      3. *-commutative 74.9%

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

      4. *-commutative 74.9%

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

      5. *-commutative 74.9%

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

      6. *-commutative 74.9%

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

      7. *-commutative 74.9%

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

      8. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in z around 0 68.8%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in y around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   11. Taylor expanded in z around inf 39.2%

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

       1. *-commutative 39.2%

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

   13. Simplified 39.2%

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

   if 7.0000000000000005e126 < x

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf 68.2%

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

      1. associate-*r* 68.2%

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

      2. neg-mul-1 68.2%

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

      3. fma-neg 71.0%

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

      4. mul-1-neg 71.0%

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

      5. remove-double-neg 71.0%

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

      6. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in a around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. distribute-rgt-neg-in 57.9%

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

      4. associate-*r* 57.0%

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

   8. Simplified 57.0%

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

   9. Taylor expanded in t around 0 57.9%

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

       1. mul-1-neg 57.9%

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

       2. associate-*r* 57.1%

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

   11. Simplified 57.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ t_2 := x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+161}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* a c)) (* b (- (* i t) (* c z)))))
        (t_2 (* x (- (* y z) (* a t)))))
   (if (<= x -3.7e+161)
     t_2
     (if (<= x -4.2e+107)
       t_1
       (if (<= x -2.8e+26)
         t_2
         (if (<= x -6e-299)
           t_1
           (if (<= x 1.75e+116)
             (- (* i (- (* b t) (* j y))) (* z (* c b)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((i * t) - (c * z)));
	double t_2 = x * ((y * z) - (a * t));
	double tmp;
	if (x <= -3.7e+161) {
		tmp = t_2;
	} else if (x <= -4.2e+107) {
		tmp = t_1;
	} else if (x <= -2.8e+26) {
		tmp = t_2;
	} else if (x <= -6e-299) {
		tmp = t_1;
	} else if (x <= 1.75e+116) {
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (a * c)) + (b * ((i * t) - (c * z)))
    t_2 = x * ((y * z) - (a * t))
    if (x <= (-3.7d+161)) then
        tmp = t_2
    else if (x <= (-4.2d+107)) then
        tmp = t_1
    else if (x <= (-2.8d+26)) then
        tmp = t_2
    else if (x <= (-6d-299)) then
        tmp = t_1
    else if (x <= 1.75d+116) then
        tmp = (i * ((b * t) - (j * y))) - (z * (c * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * (a * c)) + (b * ((i * t) - (c * z)));
	double t_2 = x * ((y * z) - (a * t));
	double tmp;
	if (x <= -3.7e+161) {
		tmp = t_2;
	} else if (x <= -4.2e+107) {
		tmp = t_1;
	} else if (x <= -2.8e+26) {
		tmp = t_2;
	} else if (x <= -6e-299) {
		tmp = t_1;
	} else if (x <= 1.75e+116) {
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (a * c)) + (b * ((i * t) - (c * z)))
	t_2 = x * ((y * z) - (a * t))
	tmp = 0
	if x <= -3.7e+161:
		tmp = t_2
	elif x <= -4.2e+107:
		tmp = t_1
	elif x <= -2.8e+26:
		tmp = t_2
	elif x <= -6e-299:
		tmp = t_1
	elif x <= 1.75e+116:
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(a * c)) + Float64(b * Float64(Float64(i * t) - Float64(c * z))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	tmp = 0.0
	if (x <= -3.7e+161)
		tmp = t_2;
	elseif (x <= -4.2e+107)
		tmp = t_1;
	elseif (x <= -2.8e+26)
		tmp = t_2;
	elseif (x <= -6e-299)
		tmp = t_1;
	elseif (x <= 1.75e+116)
		tmp = Float64(Float64(i * Float64(Float64(b * t) - Float64(j * y))) - Float64(z * Float64(c * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * (a * c)) + (b * ((i * t) - (c * z)));
	t_2 = x * ((y * z) - (a * t));
	tmp = 0.0;
	if (x <= -3.7e+161)
		tmp = t_2;
	elseif (x <= -4.2e+107)
		tmp = t_1;
	elseif (x <= -2.8e+26)
		tmp = t_2;
	elseif (x <= -6e-299)
		tmp = t_1;
	elseif (x <= 1.75e+116)
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+161], t$95$2, If[LessEqual[x, -4.2e+107], t$95$1, If[LessEqual[x, -2.8e+26], t$95$2, If[LessEqual[x, -6e-299], t$95$1, If[LessEqual[x, 1.75e+116], N[(N[(i * N[(N[(b * t), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.69999999999999979e161 or -4.1999999999999999e107 < x < -2.8e26 or 1.74999999999999998e116 < x

   1. Initial program 79.7%

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

      1. +-commutative 79.7%

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

      2. fma-define 83.0%

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

      3. *-commutative 83.0%

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

      4. *-commutative 83.0%

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

      5. *-commutative 83.0%

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

      6. *-commutative 83.0%

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

      7. *-commutative 83.0%

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

      8. *-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in z around 0 66.7%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in x around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

   10. Simplified 71.9%

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

   if -3.69999999999999979e161 < x < -4.1999999999999999e107 or -2.8e26 < x < -5.99999999999999969e-299

   1. Initial program 72.1%

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

   3. Taylor expanded in x around 0 69.9%

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

   4. Taylor expanded in a around inf 70.1%

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

      1. *-commutative 70.1%

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

   6. Simplified 70.1%

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

   if -5.99999999999999969e-299 < x < 1.74999999999999998e116

   1. Initial program 73.8%

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

   3. Taylor expanded in x around 0 62.8%

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

   4. Taylor expanded in c around -inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. mul-1-neg 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

      4. associate-*r* 64.7%

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

      5. neg-mul-1 64.7%

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

      6. cancel-sign-sub 64.7%

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

      7. +-commutative 64.7%

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

      8. mul-1-neg 64.7%

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

      9. unsub-neg 64.7%

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

      10. *-commutative 64.7%

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

      11. associate-*r* 64.7%

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

      12. neg-mul-1 64.7%

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

      13. cancel-sign-sub 64.7%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in a around 0 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

      5. *-commutative 60.1%

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

      6. associate-*l* 64.5%

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

   9. Simplified 64.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_2 := t\_1 + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{-79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-154}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right) - i \cdot \left(j \cdot y - b \cdot t\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(t\_1 - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* a t))))
        (t_2 (+ t_1 (* b (- (* i t) (* c z))))))
   (if (<= x -2.15e-79)
     t_2
     (if (<= x 7.8e-154)
       (- (* c (- (* j a) (* z b))) (* i (- (* j y) (* b t))))
       (if (<= x 5.8e+122)
         (+ (* j (- (* a c) (* y i))) (- t_1 (* c (* z b))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double t_2 = t_1 + (b * ((i * t) - (c * z)));
	double tmp;
	if (x <= -2.15e-79) {
		tmp = t_2;
	} else if (x <= 7.8e-154) {
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)));
	} else if (x <= 5.8e+122) {
		tmp = (j * ((a * c) - (y * i))) + (t_1 - (c * (z * b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (a * t))
    t_2 = t_1 + (b * ((i * t) - (c * z)))
    if (x <= (-2.15d-79)) then
        tmp = t_2
    else if (x <= 7.8d-154) then
        tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)))
    else if (x <= 5.8d+122) then
        tmp = (j * ((a * c) - (y * i))) + (t_1 - (c * (z * b)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double t_2 = t_1 + (b * ((i * t) - (c * z)));
	double tmp;
	if (x <= -2.15e-79) {
		tmp = t_2;
	} else if (x <= 7.8e-154) {
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)));
	} else if (x <= 5.8e+122) {
		tmp = (j * ((a * c) - (y * i))) + (t_1 - (c * (z * b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (a * t))
	t_2 = t_1 + (b * ((i * t) - (c * z)))
	tmp = 0
	if x <= -2.15e-79:
		tmp = t_2
	elif x <= 7.8e-154:
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)))
	elif x <= 5.8e+122:
		tmp = (j * ((a * c) - (y * i))) + (t_1 - (c * (z * b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(i * t) - Float64(c * z))))
	tmp = 0.0
	if (x <= -2.15e-79)
		tmp = t_2;
	elseif (x <= 7.8e-154)
		tmp = Float64(Float64(c * Float64(Float64(j * a) - Float64(z * b))) - Float64(i * Float64(Float64(j * y) - Float64(b * t))));
	elseif (x <= 5.8e+122)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(t_1 - Float64(c * Float64(z * b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (a * t));
	t_2 = t_1 + (b * ((i * t) - (c * z)));
	tmp = 0.0;
	if (x <= -2.15e-79)
		tmp = t_2;
	elseif (x <= 7.8e-154)
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)));
	elseif (x <= 5.8e+122)
		tmp = (j * ((a * c) - (y * i))) + (t_1 - (c * (z * b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e-79], t$95$2, If[LessEqual[x, 7.8e-154], N[(N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(j * y), $MachinePrecision] - N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+122], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.14999999999999991e-79 or 5.8000000000000002e122 < x

   1. Initial program 78.7%

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

   3. Taylor expanded in j around 0 77.4%

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

   if -2.14999999999999991e-79 < x < 7.80000000000000065e-154

   1. Initial program 66.9%

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

   3. Taylor expanded in x around 0 73.2%

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

   4. Taylor expanded in c around -inf 76.8%

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

      1. associate--l+ 76.8%

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

      2. mul-1-neg 76.8%

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

      3. distribute-rgt-neg-in 76.8%

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

      4. associate-*r* 76.8%

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

      5. neg-mul-1 76.8%

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

      6. cancel-sign-sub 76.8%

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

      7. +-commutative 76.8%

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

      8. mul-1-neg 76.8%

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

      9. unsub-neg 76.8%

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

      10. *-commutative 76.8%

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

      11. associate-*r* 76.8%

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

      12. neg-mul-1 76.8%

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

      13. cancel-sign-sub 76.8%

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

   6. Simplified 79.3%

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

   if 7.80000000000000065e-154 < x < 5.8000000000000002e122

   1. Initial program 81.2%

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

   3. Taylor expanded in c around inf 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*l* 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-154}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right) - i \cdot \left(j \cdot y - b \cdot t\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - a \cdot t\right) - c \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(i \cdot t - c \cdot z\right)\\ t_3 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_4 := t\_3 + t\_2\\ \mathbf{if}\;x \leq -1.66 \cdot 10^{-77}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-155}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-22}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* b (- (* i t) (* c z))))
        (t_3 (* x (- (* y z) (* a t))))
        (t_4 (+ t_3 t_2)))
   (if (<= x -1.66e-77)
     t_4
     (if (<= x -2e-299)
       (+ t_1 t_2)
       (if (<= x 6.5e-155)
         (- (* i (- (* b t) (* j y))) (* z (* c b)))
         (if (<= x 3.2e-22) (+ t_3 t_1) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((i * t) - (c * z));
	double t_3 = x * ((y * z) - (a * t));
	double t_4 = t_3 + t_2;
	double tmp;
	if (x <= -1.66e-77) {
		tmp = t_4;
	} else if (x <= -2e-299) {
		tmp = t_1 + t_2;
	} else if (x <= 6.5e-155) {
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	} else if (x <= 3.2e-22) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = b * ((i * t) - (c * z))
    t_3 = x * ((y * z) - (a * t))
    t_4 = t_3 + t_2
    if (x <= (-1.66d-77)) then
        tmp = t_4
    else if (x <= (-2d-299)) then
        tmp = t_1 + t_2
    else if (x <= 6.5d-155) then
        tmp = (i * ((b * t) - (j * y))) - (z * (c * b))
    else if (x <= 3.2d-22) then
        tmp = t_3 + t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * ((i * t) - (c * z));
	double t_3 = x * ((y * z) - (a * t));
	double t_4 = t_3 + t_2;
	double tmp;
	if (x <= -1.66e-77) {
		tmp = t_4;
	} else if (x <= -2e-299) {
		tmp = t_1 + t_2;
	} else if (x <= 6.5e-155) {
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	} else if (x <= 3.2e-22) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((i * t) - (c * z))
	t_3 = x * ((y * z) - (a * t))
	t_4 = t_3 + t_2
	tmp = 0
	if x <= -1.66e-77:
		tmp = t_4
	elif x <= -2e-299:
		tmp = t_1 + t_2
	elif x <= 6.5e-155:
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b))
	elif x <= 3.2e-22:
		tmp = t_3 + t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(i * t) - Float64(c * z)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_4 = Float64(t_3 + t_2)
	tmp = 0.0
	if (x <= -1.66e-77)
		tmp = t_4;
	elseif (x <= -2e-299)
		tmp = Float64(t_1 + t_2);
	elseif (x <= 6.5e-155)
		tmp = Float64(Float64(i * Float64(Float64(b * t) - Float64(j * y))) - Float64(z * Float64(c * b)));
	elseif (x <= 3.2e-22)
		tmp = Float64(t_3 + t_1);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = b * ((i * t) - (c * z));
	t_3 = x * ((y * z) - (a * t));
	t_4 = t_3 + t_2;
	tmp = 0.0;
	if (x <= -1.66e-77)
		tmp = t_4;
	elseif (x <= -2e-299)
		tmp = t_1 + t_2;
	elseif (x <= 6.5e-155)
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	elseif (x <= 3.2e-22)
		tmp = t_3 + t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$2), $MachinePrecision]}, If[LessEqual[x, -1.66e-77], t$95$4, If[LessEqual[x, -2e-299], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[x, 6.5e-155], N[(N[(i * N[(N[(b * t), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-22], N[(t$95$3 + t$95$1), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.66e-77 or 3.19999999999999987e-22 < x

   1. Initial program 79.4%

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

   3. Taylor expanded in j around 0 75.5%

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

   if -1.66e-77 < x < -1.99999999999999998e-299

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 77.7%

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

   if -1.99999999999999998e-299 < x < 6.5e-155

   1. Initial program 64.1%

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

   3. Taylor expanded in x around 0 67.3%

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

   4. Taylor expanded in c around -inf 78.3%

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

      1. associate--l+ 78.3%

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

      2. mul-1-neg 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. associate-*r* 78.3%

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

      5. neg-mul-1 78.3%

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

      6. cancel-sign-sub 78.3%

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

      7. +-commutative 78.3%

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

      8. mul-1-neg 78.3%

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

      9. unsub-neg 78.3%

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

      10. *-commutative 78.3%

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

      11. associate-*r* 78.3%

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

      12. neg-mul-1 78.3%

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

      13. cancel-sign-sub 78.3%

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

   6. Simplified 86.5%

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

   7. Taylor expanded in a around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

      5. *-commutative 73.0%

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

      6. associate-*l* 81.1%

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

   9. Simplified 81.1%

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

   if 6.5e-155 < x < 3.19999999999999987e-22

   1. Initial program 79.5%

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

   3. Taylor expanded in b around 0 68.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.66 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-155}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.05:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= x -1e+20)
     (* z (* x y))
     (if (<= x -6.5e-214)
       t_1
       (if (<= x 1.35e-177)
         (* a (* j c))
         (if (<= x 2.5e-105)
           t_1
           (if (<= x 0.05)
             (* c (* j a))
             (if (<= x 8.8e+48) t_1 (* x (* a (- t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (x <= -1e+20) {
		tmp = z * (x * y);
	} else if (x <= -6.5e-214) {
		tmp = t_1;
	} else if (x <= 1.35e-177) {
		tmp = a * (j * c);
	} else if (x <= 2.5e-105) {
		tmp = t_1;
	} else if (x <= 0.05) {
		tmp = c * (j * a);
	} else if (x <= 8.8e+48) {
		tmp = t_1;
	} else {
		tmp = x * (a * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (i * b)
    if (x <= (-1d+20)) then
        tmp = z * (x * y)
    else if (x <= (-6.5d-214)) then
        tmp = t_1
    else if (x <= 1.35d-177) then
        tmp = a * (j * c)
    else if (x <= 2.5d-105) then
        tmp = t_1
    else if (x <= 0.05d0) then
        tmp = c * (j * a)
    else if (x <= 8.8d+48) then
        tmp = t_1
    else
        tmp = x * (a * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double tmp;
	if (x <= -1e+20) {
		tmp = z * (x * y);
	} else if (x <= -6.5e-214) {
		tmp = t_1;
	} else if (x <= 1.35e-177) {
		tmp = a * (j * c);
	} else if (x <= 2.5e-105) {
		tmp = t_1;
	} else if (x <= 0.05) {
		tmp = c * (j * a);
	} else if (x <= 8.8e+48) {
		tmp = t_1;
	} else {
		tmp = x * (a * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if x <= -1e+20:
		tmp = z * (x * y)
	elif x <= -6.5e-214:
		tmp = t_1
	elif x <= 1.35e-177:
		tmp = a * (j * c)
	elif x <= 2.5e-105:
		tmp = t_1
	elif x <= 0.05:
		tmp = c * (j * a)
	elif x <= 8.8e+48:
		tmp = t_1
	else:
		tmp = x * (a * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (x <= -1e+20)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= -6.5e-214)
		tmp = t_1;
	elseif (x <= 1.35e-177)
		tmp = Float64(a * Float64(j * c));
	elseif (x <= 2.5e-105)
		tmp = t_1;
	elseif (x <= 0.05)
		tmp = Float64(c * Float64(j * a));
	elseif (x <= 8.8e+48)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(a * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	tmp = 0.0;
	if (x <= -1e+20)
		tmp = z * (x * y);
	elseif (x <= -6.5e-214)
		tmp = t_1;
	elseif (x <= 1.35e-177)
		tmp = a * (j * c);
	elseif (x <= 2.5e-105)
		tmp = t_1;
	elseif (x <= 0.05)
		tmp = c * (j * a);
	elseif (x <= 8.8e+48)
		tmp = t_1;
	else
		tmp = x * (a * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+20], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-214], t$95$1, If[LessEqual[x, 1.35e-177], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-105], t$95$1, If[LessEqual[x, 0.05], N[(c * N[(j * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e+48], t$95$1, N[(x * N[(a * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1e20

   1. Initial program 75.6%

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

   3. Taylor expanded in z around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in y around inf 45.6%

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

   if -1e20 < x < -6.5000000000000004e-214 or 1.3500000000000001e-177 < x < 2.49999999999999982e-105 or 0.050000000000000003 < x < 8.7999999999999997e48

   1. Initial program 75.6%

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

   3. Taylor expanded in t around inf 54.9%

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

      1. associate-*r* 54.9%

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

      2. neg-mul-1 54.9%

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

      3. fma-neg 54.9%

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

      4. mul-1-neg 54.9%

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

      5. remove-double-neg 54.9%

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

      6. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in a around 0 40.9%

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

   if -6.5000000000000004e-214 < x < 1.3500000000000001e-177

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 39.1%

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

      1. +-commutative 39.1%

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

      2. mul-1-neg 39.1%

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

      3. unsub-neg 39.1%

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

      4. *-commutative 39.1%

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

      5. *-commutative 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in j around inf 37.1%

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

   if 2.49999999999999982e-105 < x < 0.050000000000000003

   1. Initial program 77.2%

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

   3. Taylor expanded in a around inf 34.6%

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

      1. +-commutative 34.6%

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

      2. mul-1-neg 34.6%

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

      3. unsub-neg 34.6%

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

      4. *-commutative 34.6%

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

      5. *-commutative 34.6%

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

   5. Simplified 34.6%

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

   6. Taylor expanded in j around inf 23.9%

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

      1. associate-*r* 29.3%

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

      2. *-commutative 29.3%

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

      3. associate-*r* 40.0%

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

   8. Simplified 40.0%

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

   if 8.7999999999999997e48 < x

   1. Initial program 81.6%

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

   3. Taylor expanded in t around inf 56.8%

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

      1. associate-*r* 56.8%

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

      2. neg-mul-1 56.8%

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

      3. fma-neg 58.7%

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

      4. mul-1-neg 58.7%

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

      5. remove-double-neg 58.7%

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

      6. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in a around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. *-commutative 49.3%

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

      3. distribute-rgt-neg-in 49.3%

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

      4. associate-*r* 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in t around 0 49.3%

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

       1. mul-1-neg 49.3%

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

       2. associate-*r* 48.7%

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

   11. Simplified 48.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 0.05:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ t_2 := a \cdot \left(j \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))) (t_2 (* a (* j c))) (t_3 (* x (* y z))))
   (if (<= z -1.22e+35)
     t_3
     (if (<= z -3.8e-253)
       (* i (* b t))
       (if (<= z -6.5e-298)
         t_2
         (if (<= z 7.8e-230)
           t_1
           (if (<= z 9e-189) t_2 (if (<= z 3.1e-90) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double t_2 = a * (j * c);
	double t_3 = x * (y * z);
	double tmp;
	if (z <= -1.22e+35) {
		tmp = t_3;
	} else if (z <= -3.8e-253) {
		tmp = i * (b * t);
	} else if (z <= -6.5e-298) {
		tmp = t_2;
	} else if (z <= 7.8e-230) {
		tmp = t_1;
	} else if (z <= 9e-189) {
		tmp = t_2;
	} else if (z <= 3.1e-90) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (i * b)
    t_2 = a * (j * c)
    t_3 = x * (y * z)
    if (z <= (-1.22d+35)) then
        tmp = t_3
    else if (z <= (-3.8d-253)) then
        tmp = i * (b * t)
    else if (z <= (-6.5d-298)) then
        tmp = t_2
    else if (z <= 7.8d-230) then
        tmp = t_1
    else if (z <= 9d-189) then
        tmp = t_2
    else if (z <= 3.1d-90) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double t_2 = a * (j * c);
	double t_3 = x * (y * z);
	double tmp;
	if (z <= -1.22e+35) {
		tmp = t_3;
	} else if (z <= -3.8e-253) {
		tmp = i * (b * t);
	} else if (z <= -6.5e-298) {
		tmp = t_2;
	} else if (z <= 7.8e-230) {
		tmp = t_1;
	} else if (z <= 9e-189) {
		tmp = t_2;
	} else if (z <= 3.1e-90) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	t_2 = a * (j * c)
	t_3 = x * (y * z)
	tmp = 0
	if z <= -1.22e+35:
		tmp = t_3
	elif z <= -3.8e-253:
		tmp = i * (b * t)
	elif z <= -6.5e-298:
		tmp = t_2
	elif z <= 7.8e-230:
		tmp = t_1
	elif z <= 9e-189:
		tmp = t_2
	elif z <= 3.1e-90:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	t_2 = Float64(a * Float64(j * c))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.22e+35)
		tmp = t_3;
	elseif (z <= -3.8e-253)
		tmp = Float64(i * Float64(b * t));
	elseif (z <= -6.5e-298)
		tmp = t_2;
	elseif (z <= 7.8e-230)
		tmp = t_1;
	elseif (z <= 9e-189)
		tmp = t_2;
	elseif (z <= 3.1e-90)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	t_2 = a * (j * c);
	t_3 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.22e+35)
		tmp = t_3;
	elseif (z <= -3.8e-253)
		tmp = i * (b * t);
	elseif (z <= -6.5e-298)
		tmp = t_2;
	elseif (z <= 7.8e-230)
		tmp = t_1;
	elseif (z <= 9e-189)
		tmp = t_2;
	elseif (z <= 3.1e-90)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e+35], t$95$3, If[LessEqual[z, -3.8e-253], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-298], t$95$2, If[LessEqual[z, 7.8e-230], t$95$1, If[LessEqual[z, 9e-189], t$95$2, If[LessEqual[z, 3.1e-90], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.21999999999999999e35 or 3.1000000000000001e-90 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in y around inf 39.6%

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

      1. *-commutative 39.6%

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

   8. Simplified 39.6%

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

   if -1.21999999999999999e35 < z < -3.80000000000000012e-253

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 63.2%

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

      1. associate-*r* 63.2%

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

      2. neg-mul-1 63.2%

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

      3. fma-neg 63.2%

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

      4. mul-1-neg 63.2%

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

      5. remove-double-neg 63.2%

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

      6. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in a around 0 40.2%

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

      1. associate-*r* 42.1%

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

      2. *-commutative 42.1%

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

      3. associate-*r* 43.8%

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

   8. Simplified 43.8%

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

   if -3.80000000000000012e-253 < z < -6.5000000000000002e-298 or 7.8000000000000004e-230 < z < 8.9999999999999992e-189

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

      4. *-commutative 71.7%

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

      5. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in j around inf 51.8%

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

   if -6.5000000000000002e-298 < z < 7.8000000000000004e-230 or 8.9999999999999992e-189 < z < 3.1000000000000001e-90

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 59.5%

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

      1. associate-*r* 59.5%

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

      2. neg-mul-1 59.5%

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

      3. fma-neg 59.5%

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

      4. mul-1-neg 59.5%

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

      5. remove-double-neg 59.5%

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

      6. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in a around 0 37.1%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-253}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-189}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ t_2 := a \cdot \left(j \cdot c\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))) (t_2 (* a (* j c))))
   (if (<= z -2.55e+34)
     (* y (* x z))
     (if (<= z -3.3e-251)
       (* i (* b t))
       (if (<= z -1.2e-295)
         t_2
         (if (<= z 1.65e-231)
           t_1
           (if (<= z 5.4e-188) t_2 (if (<= z 5.6e-90) t_1 (* x (* y 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 = t * (i * b);
	double t_2 = a * (j * c);
	double tmp;
	if (z <= -2.55e+34) {
		tmp = y * (x * z);
	} else if (z <= -3.3e-251) {
		tmp = i * (b * t);
	} else if (z <= -1.2e-295) {
		tmp = t_2;
	} else if (z <= 1.65e-231) {
		tmp = t_1;
	} else if (z <= 5.4e-188) {
		tmp = t_2;
	} else if (z <= 5.6e-90) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (i * b)
    t_2 = a * (j * c)
    if (z <= (-2.55d+34)) then
        tmp = y * (x * z)
    else if (z <= (-3.3d-251)) then
        tmp = i * (b * t)
    else if (z <= (-1.2d-295)) then
        tmp = t_2
    else if (z <= 1.65d-231) then
        tmp = t_1
    else if (z <= 5.4d-188) then
        tmp = t_2
    else if (z <= 5.6d-90) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (i * b);
	double t_2 = a * (j * c);
	double tmp;
	if (z <= -2.55e+34) {
		tmp = y * (x * z);
	} else if (z <= -3.3e-251) {
		tmp = i * (b * t);
	} else if (z <= -1.2e-295) {
		tmp = t_2;
	} else if (z <= 1.65e-231) {
		tmp = t_1;
	} else if (z <= 5.4e-188) {
		tmp = t_2;
	} else if (z <= 5.6e-90) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	t_2 = a * (j * c)
	tmp = 0
	if z <= -2.55e+34:
		tmp = y * (x * z)
	elif z <= -3.3e-251:
		tmp = i * (b * t)
	elif z <= -1.2e-295:
		tmp = t_2
	elif z <= 1.65e-231:
		tmp = t_1
	elif z <= 5.4e-188:
		tmp = t_2
	elif z <= 5.6e-90:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(i * b))
	t_2 = Float64(a * Float64(j * c))
	tmp = 0.0
	if (z <= -2.55e+34)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -3.3e-251)
		tmp = Float64(i * Float64(b * t));
	elseif (z <= -1.2e-295)
		tmp = t_2;
	elseif (z <= 1.65e-231)
		tmp = t_1;
	elseif (z <= 5.4e-188)
		tmp = t_2;
	elseif (z <= 5.6e-90)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (i * b);
	t_2 = a * (j * c);
	tmp = 0.0;
	if (z <= -2.55e+34)
		tmp = y * (x * z);
	elseif (z <= -3.3e-251)
		tmp = i * (b * t);
	elseif (z <= -1.2e-295)
		tmp = t_2;
	elseif (z <= 1.65e-231)
		tmp = t_1;
	elseif (z <= 5.4e-188)
		tmp = t_2;
	elseif (z <= 5.6e-90)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+34], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-251], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-295], t$95$2, If[LessEqual[z, 1.65e-231], t$95$1, If[LessEqual[z, 5.4e-188], t$95$2, If[LessEqual[z, 5.6e-90], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.55000000000000018e34

   1. Initial program 56.0%

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

      1. +-commutative 56.0%

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

      2. fma-define 61.5%

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

      3. *-commutative 61.5%

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

      4. *-commutative 61.5%

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

      5. *-commutative 61.5%

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

      6. *-commutative 61.5%

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

      7. *-commutative 61.5%

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

      8. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around 0 70.5%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in y around inf 57.5%

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

      1. +-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

      4. *-commutative 57.5%

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

   10. Simplified 57.5%

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

   11. Taylor expanded in z around inf 47.3%

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

       1. *-commutative 47.3%

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

   13. Simplified 47.3%

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

   if -2.55000000000000018e34 < z < -3.3e-251

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 63.2%

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

      1. associate-*r* 63.2%

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

      2. neg-mul-1 63.2%

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

      3. fma-neg 63.2%

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

      4. mul-1-neg 63.2%

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

      5. remove-double-neg 63.2%

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

      6. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in a around 0 40.2%

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

      1. associate-*r* 42.1%

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

      2. *-commutative 42.1%

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

      3. associate-*r* 43.8%

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

   8. Simplified 43.8%

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

   if -3.3e-251 < z < -1.1999999999999999e-295 or 1.65000000000000014e-231 < z < 5.4000000000000002e-188

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

      4. *-commutative 71.7%

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

      5. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in j around inf 51.8%

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

   if -1.1999999999999999e-295 < z < 1.65000000000000014e-231 or 5.4000000000000002e-188 < z < 5.5999999999999998e-90

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 59.5%

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

      1. associate-*r* 59.5%

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

      2. neg-mul-1 59.5%

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

      3. fma-neg 59.5%

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

      4. mul-1-neg 59.5%

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

      5. remove-double-neg 59.5%

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

      6. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in a around 0 37.1%

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

   if 5.5999999999999998e-90 < z

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in y around inf 37.9%

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

      1. *-commutative 37.9%

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

   8. Simplified 37.9%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-188}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+18} \lor \neg \left(x \leq 3.6 \cdot 10^{+113}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* a t)))))
   (if (<= x -6e+122)
     t_1
     (if (<= x -2.8e+107)
       (* b (- (* i t) (* c z)))
       (if (or (<= x -6.8e+18) (not (<= x 3.6e+113)))
         t_1
         (- (* i (- (* b t) (* j y))) (* z (* c b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double tmp;
	if (x <= -6e+122) {
		tmp = t_1;
	} else if (x <= -2.8e+107) {
		tmp = b * ((i * t) - (c * z));
	} else if ((x <= -6.8e+18) || !(x <= 3.6e+113)) {
		tmp = t_1;
	} else {
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (a * t))
    if (x <= (-6d+122)) then
        tmp = t_1
    else if (x <= (-2.8d+107)) then
        tmp = b * ((i * t) - (c * z))
    else if ((x <= (-6.8d+18)) .or. (.not. (x <= 3.6d+113))) then
        tmp = t_1
    else
        tmp = (i * ((b * t) - (j * y))) - (z * (c * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double tmp;
	if (x <= -6e+122) {
		tmp = t_1;
	} else if (x <= -2.8e+107) {
		tmp = b * ((i * t) - (c * z));
	} else if ((x <= -6.8e+18) || !(x <= 3.6e+113)) {
		tmp = t_1;
	} else {
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (a * t))
	tmp = 0
	if x <= -6e+122:
		tmp = t_1
	elif x <= -2.8e+107:
		tmp = b * ((i * t) - (c * z))
	elif (x <= -6.8e+18) or not (x <= 3.6e+113):
		tmp = t_1
	else:
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	tmp = 0.0
	if (x <= -6e+122)
		tmp = t_1;
	elseif (x <= -2.8e+107)
		tmp = Float64(b * Float64(Float64(i * t) - Float64(c * z)));
	elseif ((x <= -6.8e+18) || !(x <= 3.6e+113))
		tmp = t_1;
	else
		tmp = Float64(Float64(i * Float64(Float64(b * t) - Float64(j * y))) - Float64(z * Float64(c * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (a * t));
	tmp = 0.0;
	if (x <= -6e+122)
		tmp = t_1;
	elseif (x <= -2.8e+107)
		tmp = b * ((i * t) - (c * z));
	elseif ((x <= -6.8e+18) || ~((x <= 3.6e+113)))
		tmp = t_1;
	else
		tmp = (i * ((b * t) - (j * y))) - (z * (c * b));
	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[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+122], t$95$1, If[LessEqual[x, -2.8e+107], N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -6.8e+18], N[Not[LessEqual[x, 3.6e+113]], $MachinePrecision]], t$95$1, N[(N[(i * N[(N[(b * t), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.99999999999999972e122 or -2.79999999999999985e107 < x < -6.8e18 or 3.59999999999999992e113 < x

   1. Initial program 80.6%

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

      1. +-commutative 80.6%

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

      2. fma-define 83.6%

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

      3. *-commutative 83.6%

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

      4. *-commutative 83.6%

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

      5. *-commutative 83.6%

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

      6. *-commutative 83.6%

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

      7. *-commutative 83.6%

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

      8. *-commutative 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in z around 0 68.7%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in x around inf 68.7%

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

      1. +-commutative 68.7%

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

      2. mul-1-neg 68.7%

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

      3. unsub-neg 68.7%

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

      4. *-commutative 68.7%

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

      5. *-commutative 68.7%

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

   10. Simplified 68.7%

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

   if -5.99999999999999972e122 < x < -2.79999999999999985e107

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 84.1%

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

   if -6.8e18 < x < 3.59999999999999992e113

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 66.6%

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

   4. Taylor expanded in c around -inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. mul-1-neg 69.0%

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

      3. distribute-rgt-neg-in 69.0%

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

      4. associate-*r* 69.0%

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

      5. neg-mul-1 69.0%

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

      6. cancel-sign-sub 69.0%

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

      7. +-commutative 69.0%

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

      8. mul-1-neg 69.0%

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

      9. unsub-neg 69.0%

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

      10. *-commutative 69.0%

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

      11. associate-*r* 69.0%

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

      12. neg-mul-1 69.0%

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

      13. cancel-sign-sub 69.0%

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

   6. Simplified 69.0%

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

   7. Taylor expanded in a around 0 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

      4. *-commutative 56.7%

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

      5. *-commutative 56.7%

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

      6. associate-*l* 59.6%

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

   9. Simplified 59.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+18} \lor \neg \left(x \leq 3.6 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{if}\;c \leq -9.2 \cdot 10^{+124}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+271}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* j c) (* x t)))))
   (if (<= c -9.2e+124)
     (* c (- (* j a) (* z b)))
     (if (<= c -8.6e+21)
       (* y (* x z))
       (if (<= c -1.05e-173)
         t_1
         (if (<= c 8.5e-34)
           (* i (- (* b t) (* j y)))
           (if (<= c 4.2e+271) t_1 (* c (- (* z b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((j * c) - (x * t));
	double tmp;
	if (c <= -9.2e+124) {
		tmp = c * ((j * a) - (z * b));
	} else if (c <= -8.6e+21) {
		tmp = y * (x * z);
	} else if (c <= -1.05e-173) {
		tmp = t_1;
	} else if (c <= 8.5e-34) {
		tmp = i * ((b * t) - (j * y));
	} else if (c <= 4.2e+271) {
		tmp = t_1;
	} else {
		tmp = c * -(z * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((j * c) - (x * t))
    if (c <= (-9.2d+124)) then
        tmp = c * ((j * a) - (z * b))
    else if (c <= (-8.6d+21)) then
        tmp = y * (x * z)
    else if (c <= (-1.05d-173)) then
        tmp = t_1
    else if (c <= 8.5d-34) then
        tmp = i * ((b * t) - (j * y))
    else if (c <= 4.2d+271) then
        tmp = t_1
    else
        tmp = c * -(z * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((j * c) - (x * t));
	double tmp;
	if (c <= -9.2e+124) {
		tmp = c * ((j * a) - (z * b));
	} else if (c <= -8.6e+21) {
		tmp = y * (x * z);
	} else if (c <= -1.05e-173) {
		tmp = t_1;
	} else if (c <= 8.5e-34) {
		tmp = i * ((b * t) - (j * y));
	} else if (c <= 4.2e+271) {
		tmp = t_1;
	} else {
		tmp = c * -(z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((j * c) - (x * t))
	tmp = 0
	if c <= -9.2e+124:
		tmp = c * ((j * a) - (z * b))
	elif c <= -8.6e+21:
		tmp = y * (x * z)
	elif c <= -1.05e-173:
		tmp = t_1
	elif c <= 8.5e-34:
		tmp = i * ((b * t) - (j * y))
	elif c <= 4.2e+271:
		tmp = t_1
	else:
		tmp = c * -(z * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(j * c) - Float64(x * t)))
	tmp = 0.0
	if (c <= -9.2e+124)
		tmp = Float64(c * Float64(Float64(j * a) - Float64(z * b)));
	elseif (c <= -8.6e+21)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= -1.05e-173)
		tmp = t_1;
	elseif (c <= 8.5e-34)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(j * y)));
	elseif (c <= 4.2e+271)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(-Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((j * c) - (x * t));
	tmp = 0.0;
	if (c <= -9.2e+124)
		tmp = c * ((j * a) - (z * b));
	elseif (c <= -8.6e+21)
		tmp = y * (x * z);
	elseif (c <= -1.05e-173)
		tmp = t_1;
	elseif (c <= 8.5e-34)
		tmp = i * ((b * t) - (j * y));
	elseif (c <= 4.2e+271)
		tmp = t_1;
	else
		tmp = c * -(z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.2e+124], N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.6e+21], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e-173], t$95$1, If[LessEqual[c, 8.5e-34], N[(i * N[(N[(b * t), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e+271], t$95$1, N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -9.19999999999999938e124

   1. Initial program 68.5%

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

   3. Taylor expanded in c around inf 78.7%

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

   if -9.19999999999999938e124 < c < -8.6e21

   1. Initial program 73.4%

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

      1. +-commutative 73.4%

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

      2. fma-define 73.4%

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

      3. *-commutative 73.4%

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

      4. *-commutative 73.4%

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

      5. *-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. *-commutative 73.4%

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

      8. *-commutative 73.4%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in z around 0 64.1%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in y around inf 58.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   9. 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. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   10. Simplified 58.5%

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

   11. Taylor expanded in z around inf 49.6%

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

       1. *-commutative 49.6%

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

   13. Simplified 49.6%

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

   if -8.6e21 < c < -1.05000000000000001e-173 or 8.5000000000000001e-34 < c < 4.1999999999999999e271

   1. Initial program 76.1%

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

   3. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

      4. *-commutative 54.0%

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

      5. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   if -1.05000000000000001e-173 < c < 8.5000000000000001e-34

   1. Initial program 80.7%

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

      1. +-commutative 80.7%

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

      2. fma-define 82.9%

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

      3. *-commutative 82.9%

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

      4. *-commutative 82.9%

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

      5. *-commutative 82.9%

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

      6. *-commutative 82.9%

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

      7. *-commutative 82.9%

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

      8. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in z around 0 78.4%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in i around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. *-commutative 53.4%

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

   10. Simplified 53.4%

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

   if 4.1999999999999999e271 < c

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+124}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-34}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+271}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;t \leq -650:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* i b) (* x a)))))
   (if (<= t -1.55e+122)
     t_1
     (if (<= t -4.4e+28)
       (* c (- (* j a) (* z b)))
       (if (<= t -650.0)
         t_1
         (if (<= t 5.3e-140)
           (* j (- (* a c) (* y i)))
           (if (<= t 1.8e-28) (* b (- (* i t) (* c 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 = t * ((i * b) - (x * a));
	double tmp;
	if (t <= -1.55e+122) {
		tmp = t_1;
	} else if (t <= -4.4e+28) {
		tmp = c * ((j * a) - (z * b));
	} else if (t <= -650.0) {
		tmp = t_1;
	} else if (t <= 5.3e-140) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 1.8e-28) {
		tmp = b * ((i * t) - (c * 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 = t * ((i * b) - (x * a))
    if (t <= (-1.55d+122)) then
        tmp = t_1
    else if (t <= (-4.4d+28)) then
        tmp = c * ((j * a) - (z * b))
    else if (t <= (-650.0d0)) then
        tmp = t_1
    else if (t <= 5.3d-140) then
        tmp = j * ((a * c) - (y * i))
    else if (t <= 1.8d-28) then
        tmp = b * ((i * t) - (c * 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 = t * ((i * b) - (x * a));
	double tmp;
	if (t <= -1.55e+122) {
		tmp = t_1;
	} else if (t <= -4.4e+28) {
		tmp = c * ((j * a) - (z * b));
	} else if (t <= -650.0) {
		tmp = t_1;
	} else if (t <= 5.3e-140) {
		tmp = j * ((a * c) - (y * i));
	} else if (t <= 1.8e-28) {
		tmp = b * ((i * t) - (c * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((i * b) - (x * a))
	tmp = 0
	if t <= -1.55e+122:
		tmp = t_1
	elif t <= -4.4e+28:
		tmp = c * ((j * a) - (z * b))
	elif t <= -650.0:
		tmp = t_1
	elif t <= 5.3e-140:
		tmp = j * ((a * c) - (y * i))
	elif t <= 1.8e-28:
		tmp = b * ((i * t) - (c * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(i * b) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.55e+122)
		tmp = t_1;
	elseif (t <= -4.4e+28)
		tmp = Float64(c * Float64(Float64(j * a) - Float64(z * b)));
	elseif (t <= -650.0)
		tmp = t_1;
	elseif (t <= 5.3e-140)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (t <= 1.8e-28)
		tmp = Float64(b * Float64(Float64(i * t) - Float64(c * 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 = t * ((i * b) - (x * a));
	tmp = 0.0;
	if (t <= -1.55e+122)
		tmp = t_1;
	elseif (t <= -4.4e+28)
		tmp = c * ((j * a) - (z * b));
	elseif (t <= -650.0)
		tmp = t_1;
	elseif (t <= 5.3e-140)
		tmp = j * ((a * c) - (y * i));
	elseif (t <= 1.8e-28)
		tmp = b * ((i * t) - (c * 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[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+122], t$95$1, If[LessEqual[t, -4.4e+28], N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -650.0], t$95$1, If[LessEqual[t, 5.3e-140], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-28], N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.54999999999999999e122 or -4.39999999999999973e28 < t < -650 or 1.7999999999999999e-28 < t

   1. Initial program 71.2%

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

      1. +-commutative 71.2%

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

      2. fma-define 75.2%

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

      3. *-commutative 75.2%

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

      4. *-commutative 75.2%

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

      5. *-commutative 75.2%

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

      6. *-commutative 75.2%

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

      7. *-commutative 75.2%

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

      8. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in z around 0 72.5%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in t around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. distribute-lft-neg-out 65.7%

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

      3. +-commutative 65.7%

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

      4. distribute-lft-neg-out 65.7%

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

      5. unsub-neg 65.7%

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

      6. *-commutative 65.7%

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

   10. Simplified 65.7%

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

   if -1.54999999999999999e122 < t < -4.39999999999999973e28

   1. Initial program 78.0%

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

   3. Taylor expanded in c around inf 63.4%

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

   if -650 < t < 5.29999999999999984e-140

   1. Initial program 79.6%

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

      1. +-commutative 79.6%

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

      2. fma-define 81.9%

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

      3. *-commutative 81.9%

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

      4. *-commutative 81.9%

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

      5. *-commutative 81.9%

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

      6. *-commutative 81.9%

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

      7. *-commutative 81.9%

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

      8. *-commutative 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around 0 80.7%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in j around inf 53.2%

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

      1. *-commutative 53.2%

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

      2. *-commutative 53.2%

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

   10. Simplified 53.2%

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

   if 5.29999999999999984e-140 < t < 1.7999999999999999e-28

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+122}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;t \leq -650:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_2 := c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* a t)))) (t_2 (* c (- (* j a) (* z b)))))
   (if (<= c -1.5e+125)
     t_2
     (if (<= c -1.36e-18)
       t_1
       (if (<= c -4.2e-291)
         (* t (- (* i b) (* x a)))
         (if (<= c 9.2e-178)
           (* i (- (* b t) (* j y)))
           (if (<= c 3.2e+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 = x * ((y * z) - (a * t));
	double t_2 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -1.5e+125) {
		tmp = t_2;
	} else if (c <= -1.36e-18) {
		tmp = t_1;
	} else if (c <= -4.2e-291) {
		tmp = t * ((i * b) - (x * a));
	} else if (c <= 9.2e-178) {
		tmp = i * ((b * t) - (j * y));
	} else if (c <= 3.2e+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 = x * ((y * z) - (a * t))
    t_2 = c * ((j * a) - (z * b))
    if (c <= (-1.5d+125)) then
        tmp = t_2
    else if (c <= (-1.36d-18)) then
        tmp = t_1
    else if (c <= (-4.2d-291)) then
        tmp = t * ((i * b) - (x * a))
    else if (c <= 9.2d-178) then
        tmp = i * ((b * t) - (j * y))
    else if (c <= 3.2d+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 = x * ((y * z) - (a * t));
	double t_2 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -1.5e+125) {
		tmp = t_2;
	} else if (c <= -1.36e-18) {
		tmp = t_1;
	} else if (c <= -4.2e-291) {
		tmp = t * ((i * b) - (x * a));
	} else if (c <= 9.2e-178) {
		tmp = i * ((b * t) - (j * y));
	} else if (c <= 3.2e+45) {
		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) - (a * t))
	t_2 = c * ((j * a) - (z * b))
	tmp = 0
	if c <= -1.5e+125:
		tmp = t_2
	elif c <= -1.36e-18:
		tmp = t_1
	elif c <= -4.2e-291:
		tmp = t * ((i * b) - (x * a))
	elif c <= 9.2e-178:
		tmp = i * ((b * t) - (j * y))
	elif c <= 3.2e+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(x * Float64(Float64(y * z) - Float64(a * t)))
	t_2 = Float64(c * Float64(Float64(j * a) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.5e+125)
		tmp = t_2;
	elseif (c <= -1.36e-18)
		tmp = t_1;
	elseif (c <= -4.2e-291)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(x * a)));
	elseif (c <= 9.2e-178)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(j * y)));
	elseif (c <= 3.2e+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 = x * ((y * z) - (a * t));
	t_2 = c * ((j * a) - (z * b));
	tmp = 0.0;
	if (c <= -1.5e+125)
		tmp = t_2;
	elseif (c <= -1.36e-18)
		tmp = t_1;
	elseif (c <= -4.2e-291)
		tmp = t * ((i * b) - (x * a));
	elseif (c <= 9.2e-178)
		tmp = i * ((b * t) - (j * y));
	elseif (c <= 3.2e+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[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.5e+125], t$95$2, If[LessEqual[c, -1.36e-18], t$95$1, If[LessEqual[c, -4.2e-291], N[(t * N[(N[(i * b), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e-178], N[(i * N[(N[(b * t), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+45], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.50000000000000008e125 or 3.2000000000000003e45 < c

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 69.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -1.50000000000000008e125 < c < -1.3600000000000001e-18 or 9.19999999999999978e-178 < c < 3.2000000000000003e45

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 82.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(c \cdot z - t \cdot i\right) \cdot b}\right) \]

      5. *-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(c \cdot z - \color{blue}{i \cdot t}\right) \cdot b\right) \]

      6. *-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right) \]

      7. *-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right) \]

      8. *-commutative 82.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(z \cdot c - t \cdot i\right)}\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 77.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) \]

   7. Simplified 76.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right) + t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)}\right) \]

   8. Taylor expanded in x around inf 56.5%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   9. Step-by-step derivation

      1. +-commutative 56.5%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 56.5%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 56.5%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 56.5%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      5. *-commutative 56.5%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   10. Simplified 56.5%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   if -1.3600000000000001e-18 < c < -4.1999999999999999e-291

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(c \cdot z - t \cdot i\right) \cdot b}\right) \]

      5. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(c \cdot z - \color{blue}{i \cdot t}\right) \cdot b\right) \]

      6. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right) \]

      7. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right) \]

      8. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(z \cdot c - t \cdot i\right)}\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 74.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) \]

   7. Simplified 84.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right) + t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)}\right) \]

   8. Taylor expanded in t around inf 62.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 62.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a \cdot x\right)} + b \cdot i\right) \]

      2. distribute-lft-neg-out 62.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right) \cdot x} + b \cdot i\right) \]

      3. +-commutative 62.8%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i + \left(-a\right) \cdot x\right)} \]

      4. distribute-lft-neg-out 62.8%

         \[\leadsto t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right) \]

      5. unsub-neg 62.8%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)} \]

      6. *-commutative 62.8%

         \[\leadsto t \cdot \left(b \cdot i - \color{blue}{x \cdot a}\right) \]

   10. Simplified 62.8%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]

   if -4.1999999999999999e-291 < c < 9.19999999999999978e-178

   1. Initial program 84.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 84.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(c \cdot z - t \cdot i\right) \cdot b}\right) \]

      5. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(c \cdot z - \color{blue}{i \cdot t}\right) \cdot b\right) \]

      6. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right) \]

      7. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right) \]

      8. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(z \cdot c - t \cdot i\right)}\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 84.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) \]

   7. Simplified 87.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right) + t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)}\right) \]

   8. Taylor expanded in i around inf 56.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 56.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 56.7%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 56.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(i \cdot b - x \cdot a\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-178}:\\ \;\;\;\;i \cdot \left(b \cdot t - j \cdot y\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - a \cdot t\right)\\ t_2 := t\_1 + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right) - i \cdot \left(j \cdot y - b \cdot t\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+124}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* a t))))
        (t_2 (+ t_1 (* b (- (* i t) (* c z))))))
   (if (<= x -1.9e-77)
     t_2
     (if (<= x 2.4e-153)
       (- (* c (- (* j a) (* z b))) (* i (- (* j y) (* b t))))
       (if (<= x 4.9e+124) (+ t_1 (* j (- (* a c) (* y i)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double t_2 = t_1 + (b * ((i * t) - (c * z)));
	double tmp;
	if (x <= -1.9e-77) {
		tmp = t_2;
	} else if (x <= 2.4e-153) {
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)));
	} else if (x <= 4.9e+124) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (a * t))
    t_2 = t_1 + (b * ((i * t) - (c * z)))
    if (x <= (-1.9d-77)) then
        tmp = t_2
    else if (x <= 2.4d-153) then
        tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)))
    else if (x <= 4.9d+124) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (a * t));
	double t_2 = t_1 + (b * ((i * t) - (c * z)));
	double tmp;
	if (x <= -1.9e-77) {
		tmp = t_2;
	} else if (x <= 2.4e-153) {
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)));
	} else if (x <= 4.9e+124) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (a * t))
	t_2 = t_1 + (b * ((i * t) - (c * z)))
	tmp = 0
	if x <= -1.9e-77:
		tmp = t_2
	elif x <= 2.4e-153:
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)))
	elif x <= 4.9e+124:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(a * t)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(i * t) - Float64(c * z))))
	tmp = 0.0
	if (x <= -1.9e-77)
		tmp = t_2;
	elseif (x <= 2.4e-153)
		tmp = Float64(Float64(c * Float64(Float64(j * a) - Float64(z * b))) - Float64(i * Float64(Float64(j * y) - Float64(b * t))));
	elseif (x <= 4.9e+124)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (a * t));
	t_2 = t_1 + (b * ((i * t) - (c * z)));
	tmp = 0.0;
	if (x <= -1.9e-77)
		tmp = t_2;
	elseif (x <= 2.4e-153)
		tmp = (c * ((j * a) - (z * b))) - (i * ((j * y) - (b * t)));
	elseif (x <= 4.9e+124)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e-77], t$95$2, If[LessEqual[x, 2.4e-153], N[(N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(j * y), $MachinePrecision] - N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+124], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8999999999999999e-77 or 4.90000000000000035e124 < x

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 77.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -1.8999999999999999e-77 < x < 2.4000000000000002e-153

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   4. Taylor expanded in c around -inf 76.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot \left(-1 \cdot \left(a \cdot j\right) - -1 \cdot \left(b \cdot z\right)\right)\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 76.8%

         \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(-1 \cdot \left(a \cdot j\right) - -1 \cdot \left(b \cdot z\right)\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right)} \]

      2. mul-1-neg 76.8%

         \[\leadsto \color{blue}{\left(-c \cdot \left(-1 \cdot \left(a \cdot j\right) - -1 \cdot \left(b \cdot z\right)\right)\right)} + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      3. distribute-rgt-neg-in 76.8%

         \[\leadsto \color{blue}{c \cdot \left(-\left(-1 \cdot \left(a \cdot j\right) - -1 \cdot \left(b \cdot z\right)\right)\right)} + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      4. associate-*r* 76.8%

         \[\leadsto c \cdot \left(-\left(-1 \cdot \left(a \cdot j\right) - \color{blue}{\left(-1 \cdot b\right) \cdot z}\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      5. neg-mul-1 76.8%

         \[\leadsto c \cdot \left(-\left(-1 \cdot \left(a \cdot j\right) - \color{blue}{\left(-b\right)} \cdot z\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      6. cancel-sign-sub 76.8%

         \[\leadsto c \cdot \left(-\color{blue}{\left(-1 \cdot \left(a \cdot j\right) + b \cdot z\right)}\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      7. +-commutative 76.8%

         \[\leadsto c \cdot \left(-\color{blue}{\left(b \cdot z + -1 \cdot \left(a \cdot j\right)\right)}\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      8. mul-1-neg 76.8%

         \[\leadsto c \cdot \left(-\left(b \cdot z + \color{blue}{\left(-a \cdot j\right)}\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      9. unsub-neg 76.8%

         \[\leadsto c \cdot \left(-\color{blue}{\left(b \cdot z - a \cdot j\right)}\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      10. *-commutative 76.8%

          \[\leadsto c \cdot \left(-\left(\color{blue}{z \cdot b} - a \cdot j\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)\right) \]

      11. associate-*r* 76.8%

          \[\leadsto c \cdot \left(-\left(z \cdot b - a \cdot j\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - \color{blue}{\left(-1 \cdot b\right) \cdot \left(i \cdot t\right)}\right) \]

      12. neg-mul-1 76.8%

          \[\leadsto c \cdot \left(-\left(z \cdot b - a \cdot j\right)\right) + \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) - \color{blue}{\left(-b\right)} \cdot \left(i \cdot t\right)\right) \]

      13. cancel-sign-sub 76.8%

          \[\leadsto c \cdot \left(-\left(z \cdot b - a \cdot j\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + b \cdot \left(i \cdot t\right)\right)} \]

   6. Simplified 79.3%

      \[\leadsto \color{blue}{c \cdot \left(-\left(z \cdot b - a \cdot j\right)\right) + i \cdot \left(b \cdot t - y \cdot j\right)} \]

   if 2.4000000000000002e-153 < x < 4.90000000000000035e124

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 69.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right) - i \cdot \left(j \cdot y - b \cdot t\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;i \leq -8.8 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* t (* i b))))
   (if (<= i -8.8e+163)
     t_2
     (if (<= i -2.7e-34)
       t_1
       (if (<= i -1.12e-246)
         (* t (* a (- x)))
         (if (<= i 7.4e-128)
           (* c (- (* z b)))
           (if (<= i 2.2e+156) 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 = z * (x * y);
	double t_2 = t * (i * b);
	double tmp;
	if (i <= -8.8e+163) {
		tmp = t_2;
	} else if (i <= -2.7e-34) {
		tmp = t_1;
	} else if (i <= -1.12e-246) {
		tmp = t * (a * -x);
	} else if (i <= 7.4e-128) {
		tmp = c * -(z * b);
	} else if (i <= 2.2e+156) {
		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 = z * (x * y)
    t_2 = t * (i * b)
    if (i <= (-8.8d+163)) then
        tmp = t_2
    else if (i <= (-2.7d-34)) then
        tmp = t_1
    else if (i <= (-1.12d-246)) then
        tmp = t * (a * -x)
    else if (i <= 7.4d-128) then
        tmp = c * -(z * b)
    else if (i <= 2.2d+156) 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 = z * (x * y);
	double t_2 = t * (i * b);
	double tmp;
	if (i <= -8.8e+163) {
		tmp = t_2;
	} else if (i <= -2.7e-34) {
		tmp = t_1;
	} else if (i <= -1.12e-246) {
		tmp = t * (a * -x);
	} else if (i <= 7.4e-128) {
		tmp = c * -(z * b);
	} else if (i <= 2.2e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = t * (i * b)
	tmp = 0
	if i <= -8.8e+163:
		tmp = t_2
	elif i <= -2.7e-34:
		tmp = t_1
	elif i <= -1.12e-246:
		tmp = t * (a * -x)
	elif i <= 7.4e-128:
		tmp = c * -(z * b)
	elif i <= 2.2e+156:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (i <= -8.8e+163)
		tmp = t_2;
	elseif (i <= -2.7e-34)
		tmp = t_1;
	elseif (i <= -1.12e-246)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (i <= 7.4e-128)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (i <= 2.2e+156)
		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 = z * (x * y);
	t_2 = t * (i * b);
	tmp = 0.0;
	if (i <= -8.8e+163)
		tmp = t_2;
	elseif (i <= -2.7e-34)
		tmp = t_1;
	elseif (i <= -1.12e-246)
		tmp = t * (a * -x);
	elseif (i <= 7.4e-128)
		tmp = c * -(z * b);
	elseif (i <= 2.2e+156)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.8e+163], t$95$2, If[LessEqual[i, -2.7e-34], t$95$1, If[LessEqual[i, -1.12e-246], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.4e-128], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, 2.2e+156], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.79999999999999945e163 or 2.20000000000000004e156 < i

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 64.4%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 57.1%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -8.79999999999999945e163 < i < -2.70000000000000017e-34 or 7.4e-128 < i < 2.20000000000000004e156

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 44.5%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 36.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -2.70000000000000017e-34 < i < -1.11999999999999995e-246

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 49.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 49.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 49.0%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 49.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 49.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 49.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.1%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 37.1%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. distribute-rgt-neg-in 37.1%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

      4. associate-*r* 35.4%

         \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   8. Simplified 35.4%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   if -1.11999999999999995e-246 < i < 7.4e-128

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 56.2%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.8%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 35.8%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      3. associate-*r* 39.1%

         \[\leadsto -\color{blue}{c \cdot \left(z \cdot b\right)} \]

      4. *-commutative 39.1%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      5. distribute-rgt-neg-out 39.1%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      6. distribute-rgt-neg-in 39.1%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   8. Simplified 39.1%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.8 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -0.4:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-247}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= i -3.3e+174)
     t_1
     (if (<= i -0.4)
       (* y (* j (- i)))
       (if (<= i -5e-247)
         (* t (* a (- x)))
         (if (<= i 2.3e-131)
           (* c (- (* z b)))
           (if (<= i 7.8e+155) (* 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 = t * (i * b);
	double tmp;
	if (i <= -3.3e+174) {
		tmp = t_1;
	} else if (i <= -0.4) {
		tmp = y * (j * -i);
	} else if (i <= -5e-247) {
		tmp = t * (a * -x);
	} else if (i <= 2.3e-131) {
		tmp = c * -(z * b);
	} else if (i <= 7.8e+155) {
		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 = t * (i * b)
    if (i <= (-3.3d+174)) then
        tmp = t_1
    else if (i <= (-0.4d0)) then
        tmp = y * (j * -i)
    else if (i <= (-5d-247)) then
        tmp = t * (a * -x)
    else if (i <= 2.3d-131) then
        tmp = c * -(z * b)
    else if (i <= 7.8d+155) 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 = t * (i * b);
	double tmp;
	if (i <= -3.3e+174) {
		tmp = t_1;
	} else if (i <= -0.4) {
		tmp = y * (j * -i);
	} else if (i <= -5e-247) {
		tmp = t * (a * -x);
	} else if (i <= 2.3e-131) {
		tmp = c * -(z * b);
	} else if (i <= 7.8e+155) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if i <= -3.3e+174:
		tmp = t_1
	elif i <= -0.4:
		tmp = y * (j * -i)
	elif i <= -5e-247:
		tmp = t * (a * -x)
	elif i <= 2.3e-131:
		tmp = c * -(z * b)
	elif i <= 7.8e+155:
		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(t * Float64(i * b))
	tmp = 0.0
	if (i <= -3.3e+174)
		tmp = t_1;
	elseif (i <= -0.4)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (i <= -5e-247)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (i <= 2.3e-131)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (i <= 7.8e+155)
		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 = t * (i * b);
	tmp = 0.0;
	if (i <= -3.3e+174)
		tmp = t_1;
	elseif (i <= -0.4)
		tmp = y * (j * -i);
	elseif (i <= -5e-247)
		tmp = t * (a * -x);
	elseif (i <= 2.3e-131)
		tmp = c * -(z * b);
	elseif (i <= 7.8e+155)
		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[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.3e+174], t$95$1, If[LessEqual[i, -0.4], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5e-247], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e-131], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, 7.8e+155], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.3000000000000001e174 or 7.7999999999999996e155 < i

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 64.4%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 57.1%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -3.3000000000000001e174 < i < -0.40000000000000002

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 74.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(c \cdot z\right) \cdot b}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*l* 77.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 77.3%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(y \cdot j\right)} \cdot i \]

      4. associate-*r* 47.2%

         \[\leadsto -\color{blue}{y \cdot \left(j \cdot i\right)} \]

      5. *-commutative 47.2%

         \[\leadsto -y \cdot \color{blue}{\left(i \cdot j\right)} \]

      6. distribute-rgt-neg-out 47.2%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      7. *-commutative 47.2%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      8. distribute-rgt-neg-in 47.2%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 47.2%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   if -0.40000000000000002 < i < -4.99999999999999978e-247

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 47.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 47.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 47.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 48.0%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 48.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 48.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 48.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around inf 33.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 33.3%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 33.3%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. distribute-rgt-neg-in 33.3%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

      4. associate-*r* 32.8%

         \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   if -4.99999999999999978e-247 < i < 2.30000000000000022e-131

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 56.2%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.8%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 35.8%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      3. associate-*r* 39.1%

         \[\leadsto -\color{blue}{c \cdot \left(z \cdot b\right)} \]

      4. *-commutative 39.1%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      5. distribute-rgt-neg-out 39.1%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      6. distribute-rgt-neg-in 39.1%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   8. Simplified 39.1%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(-z\right)\right)} \]

   if 2.30000000000000022e-131 < i < 7.7999999999999996e155

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 39.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 39.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 39.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 32.2%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;i \leq -0.4:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-247}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-131}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -0.0034:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 10^{+156}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* i b))))
   (if (<= i -1.2e+171)
     t_1
     (if (<= i -0.0034)
       (* y (* j (- i)))
       (if (<= i -3.7e-246)
         (* t (* a (- x)))
         (if (<= i 1.3e-125)
           (* z (* c (- b)))
           (if (<= i 1e+156) (* 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 = t * (i * b);
	double tmp;
	if (i <= -1.2e+171) {
		tmp = t_1;
	} else if (i <= -0.0034) {
		tmp = y * (j * -i);
	} else if (i <= -3.7e-246) {
		tmp = t * (a * -x);
	} else if (i <= 1.3e-125) {
		tmp = z * (c * -b);
	} else if (i <= 1e+156) {
		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 = t * (i * b)
    if (i <= (-1.2d+171)) then
        tmp = t_1
    else if (i <= (-0.0034d0)) then
        tmp = y * (j * -i)
    else if (i <= (-3.7d-246)) then
        tmp = t * (a * -x)
    else if (i <= 1.3d-125) then
        tmp = z * (c * -b)
    else if (i <= 1d+156) 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 = t * (i * b);
	double tmp;
	if (i <= -1.2e+171) {
		tmp = t_1;
	} else if (i <= -0.0034) {
		tmp = y * (j * -i);
	} else if (i <= -3.7e-246) {
		tmp = t * (a * -x);
	} else if (i <= 1.3e-125) {
		tmp = z * (c * -b);
	} else if (i <= 1e+156) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (i * b)
	tmp = 0
	if i <= -1.2e+171:
		tmp = t_1
	elif i <= -0.0034:
		tmp = y * (j * -i)
	elif i <= -3.7e-246:
		tmp = t * (a * -x)
	elif i <= 1.3e-125:
		tmp = z * (c * -b)
	elif i <= 1e+156:
		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(t * Float64(i * b))
	tmp = 0.0
	if (i <= -1.2e+171)
		tmp = t_1;
	elseif (i <= -0.0034)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (i <= -3.7e-246)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (i <= 1.3e-125)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 1e+156)
		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 = t * (i * b);
	tmp = 0.0;
	if (i <= -1.2e+171)
		tmp = t_1;
	elseif (i <= -0.0034)
		tmp = y * (j * -i);
	elseif (i <= -3.7e-246)
		tmp = t * (a * -x);
	elseif (i <= 1.3e-125)
		tmp = z * (c * -b);
	elseif (i <= 1e+156)
		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[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.2e+171], t$95$1, If[LessEqual[i, -0.0034], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.7e-246], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-125], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1e+156], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.19999999999999999e171 or 9.9999999999999998e155 < i

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 64.4%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 57.1%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -1.19999999999999999e171 < i < -0.00339999999999999981

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 74.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(c \cdot z\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(c \cdot z\right) \cdot b}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*l* 77.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 77.3%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. *-commutative 42.1%

         \[\leadsto -\color{blue}{\left(y \cdot j\right)} \cdot i \]

      4. associate-*r* 47.2%

         \[\leadsto -\color{blue}{y \cdot \left(j \cdot i\right)} \]

      5. *-commutative 47.2%

         \[\leadsto -y \cdot \color{blue}{\left(i \cdot j\right)} \]

      6. distribute-rgt-neg-out 47.2%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      7. *-commutative 47.2%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      8. distribute-rgt-neg-in 47.2%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 47.2%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   if -0.00339999999999999981 < i < -3.7e-246

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 47.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 47.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 47.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 48.0%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 48.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 48.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 48.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around inf 33.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 33.3%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 33.3%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. distribute-rgt-neg-in 33.3%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

      4. associate-*r* 32.8%

         \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   8. Simplified 32.8%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   if -3.7e-246 < i < 1.30000000000000003e-125

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 56.2%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 40.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.8%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 40.8%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 40.8%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   if 1.30000000000000003e-125 < i < 9.9999999999999998e155

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 39.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 39.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 39.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 32.2%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;i \leq -0.0034:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-246}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 10^{+156}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;i \leq -8.8 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* t (* i b))))
   (if (<= i -8.8e+163)
     t_2
     (if (<= i -3.2e-38)
       t_1
       (if (<= i -1.6e-246)
         (* a (* t (- x)))
         (if (<= i 3.9e-129)
           (* z (* c (- b)))
           (if (<= i 7.8e+155) 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 = z * (x * y);
	double t_2 = t * (i * b);
	double tmp;
	if (i <= -8.8e+163) {
		tmp = t_2;
	} else if (i <= -3.2e-38) {
		tmp = t_1;
	} else if (i <= -1.6e-246) {
		tmp = a * (t * -x);
	} else if (i <= 3.9e-129) {
		tmp = z * (c * -b);
	} else if (i <= 7.8e+155) {
		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 = z * (x * y)
    t_2 = t * (i * b)
    if (i <= (-8.8d+163)) then
        tmp = t_2
    else if (i <= (-3.2d-38)) then
        tmp = t_1
    else if (i <= (-1.6d-246)) then
        tmp = a * (t * -x)
    else if (i <= 3.9d-129) then
        tmp = z * (c * -b)
    else if (i <= 7.8d+155) 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 = z * (x * y);
	double t_2 = t * (i * b);
	double tmp;
	if (i <= -8.8e+163) {
		tmp = t_2;
	} else if (i <= -3.2e-38) {
		tmp = t_1;
	} else if (i <= -1.6e-246) {
		tmp = a * (t * -x);
	} else if (i <= 3.9e-129) {
		tmp = z * (c * -b);
	} else if (i <= 7.8e+155) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = t * (i * b)
	tmp = 0
	if i <= -8.8e+163:
		tmp = t_2
	elif i <= -3.2e-38:
		tmp = t_1
	elif i <= -1.6e-246:
		tmp = a * (t * -x)
	elif i <= 3.9e-129:
		tmp = z * (c * -b)
	elif i <= 7.8e+155:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(t * Float64(i * b))
	tmp = 0.0
	if (i <= -8.8e+163)
		tmp = t_2;
	elseif (i <= -3.2e-38)
		tmp = t_1;
	elseif (i <= -1.6e-246)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (i <= 3.9e-129)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 7.8e+155)
		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 = z * (x * y);
	t_2 = t * (i * b);
	tmp = 0.0;
	if (i <= -8.8e+163)
		tmp = t_2;
	elseif (i <= -3.2e-38)
		tmp = t_1;
	elseif (i <= -1.6e-246)
		tmp = a * (t * -x);
	elseif (i <= 3.9e-129)
		tmp = z * (c * -b);
	elseif (i <= 7.8e+155)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.8e+163], t$95$2, If[LessEqual[i, -3.2e-38], t$95$1, If[LessEqual[i, -1.6e-246], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.9e-129], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.8e+155], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.79999999999999945e163 or 7.7999999999999996e155 < i

   1. Initial program 53.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 62.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 64.4%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 64.4%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 57.1%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -8.79999999999999945e163 < i < -3.19999999999999977e-38 or 3.9000000000000001e-129 < i < 7.7999999999999996e155

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 44.5%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 36.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -3.19999999999999977e-38 < i < -1.6e-246

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 49.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 49.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 49.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 49.0%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 49.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 49.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 49.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 37.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 37.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 37.1%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 37.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if -1.6e-246 < i < 3.9000000000000001e-129

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 56.2%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 40.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.8%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 40.8%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 40.8%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.8 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + t\_1\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* i t) (* c z)))))
   (if (<= b -4.7e-48)
     (+ (* j (* a c)) t_1)
     (if (<= b 2.45e+95)
       (+ (* x (- (* y z) (* a t))) (* j (- (* a c) (* y i))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (c * z));
	double tmp;
	if (b <= -4.7e-48) {
		tmp = (j * (a * c)) + t_1;
	} else if (b <= 2.45e+95) {
		tmp = (x * ((y * z) - (a * t))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((i * t) - (c * z))
    if (b <= (-4.7d-48)) then
        tmp = (j * (a * c)) + t_1
    else if (b <= 2.45d+95) then
        tmp = (x * ((y * z) - (a * t))) + (j * ((a * c) - (y * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (c * z));
	double tmp;
	if (b <= -4.7e-48) {
		tmp = (j * (a * c)) + t_1;
	} else if (b <= 2.45e+95) {
		tmp = (x * ((y * z) - (a * t))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((i * t) - (c * z))
	tmp = 0
	if b <= -4.7e-48:
		tmp = (j * (a * c)) + t_1
	elif b <= 2.45e+95:
		tmp = (x * ((y * z) - (a * t))) + (j * ((a * c) - (y * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(i * t) - Float64(c * z)))
	tmp = 0.0
	if (b <= -4.7e-48)
		tmp = Float64(Float64(j * Float64(a * c)) + t_1);
	elseif (b <= 2.45e+95)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(a * t))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((i * t) - (c * z));
	tmp = 0.0;
	if (b <= -4.7e-48)
		tmp = (j * (a * c)) + t_1;
	elseif (b <= 2.45e+95)
		tmp = (x * ((y * z) - (a * t))) + (j * ((a * c) - (y * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e-48], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 2.45e+95], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.6999999999999998e-48

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   4. Taylor expanded in a around inf 67.0%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]
   5. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   6. Simplified 67.0%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   if -4.6999999999999998e-48 < b < 2.4499999999999999e95

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 73.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 2.4499999999999999e95 < b

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 73.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t - c \cdot z\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + t\_1\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* i t) (* c z)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= b -5.1e-48)
     (+ (* j (* a c)) t_1)
     (if (<= b 2.35e+95) (+ (* x (- (* y z) (* a t))) t_2) (+ t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (c * z));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -5.1e-48) {
		tmp = (j * (a * c)) + t_1;
	} else if (b <= 2.35e+95) {
		tmp = (x * ((y * z) - (a * t))) + t_2;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((i * t) - (c * z))
    t_2 = j * ((a * c) - (y * i))
    if (b <= (-5.1d-48)) then
        tmp = (j * (a * c)) + t_1
    else if (b <= 2.35d+95) then
        tmp = (x * ((y * z) - (a * t))) + t_2
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((i * t) - (c * z));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -5.1e-48) {
		tmp = (j * (a * c)) + t_1;
	} else if (b <= 2.35e+95) {
		tmp = (x * ((y * z) - (a * t))) + t_2;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((i * t) - (c * z))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if b <= -5.1e-48:
		tmp = (j * (a * c)) + t_1
	elif b <= 2.35e+95:
		tmp = (x * ((y * z) - (a * t))) + t_2
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(i * t) - Float64(c * z)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -5.1e-48)
		tmp = Float64(Float64(j * Float64(a * c)) + t_1);
	elseif (b <= 2.35e+95)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(a * t))) + t_2);
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((i * t) - (c * z));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (b <= -5.1e-48)
		tmp = (j * (a * c)) + t_1;
	elseif (b <= 2.35e+95)
		tmp = (x * ((y * z) - (a * t))) + t_2;
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.1e-48], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 2.35e+95], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.10000000000000011e-48

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   4. Taylor expanded in a around inf 67.0%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]
   5. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   6. Simplified 67.0%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   if -5.10000000000000011e-48 < b < 2.34999999999999986e95

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 73.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 2.34999999999999986e95 < b

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z - a \cdot t\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 42.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+208}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.7e+51)
   (* y (* x z))
   (if (<= z 2e+119)
     (* a (- (* j c) (* x t)))
     (if (<= z 7e+208)
       (* c (- (* z b)))
       (if (<= z 6.8e+214) (* t (* a (- x))) (* x (* y 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 (z <= -1.7e+51) {
		tmp = y * (x * z);
	} else if (z <= 2e+119) {
		tmp = a * ((j * c) - (x * t));
	} else if (z <= 7e+208) {
		tmp = c * -(z * b);
	} else if (z <= 6.8e+214) {
		tmp = t * (a * -x);
	} else {
		tmp = x * (y * 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 (z <= (-1.7d+51)) then
        tmp = y * (x * z)
    else if (z <= 2d+119) then
        tmp = a * ((j * c) - (x * t))
    else if (z <= 7d+208) then
        tmp = c * -(z * b)
    else if (z <= 6.8d+214) then
        tmp = t * (a * -x)
    else
        tmp = x * (y * 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 (z <= -1.7e+51) {
		tmp = y * (x * z);
	} else if (z <= 2e+119) {
		tmp = a * ((j * c) - (x * t));
	} else if (z <= 7e+208) {
		tmp = c * -(z * b);
	} else if (z <= 6.8e+214) {
		tmp = t * (a * -x);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.7e+51:
		tmp = y * (x * z)
	elif z <= 2e+119:
		tmp = a * ((j * c) - (x * t))
	elif z <= 7e+208:
		tmp = c * -(z * b)
	elif z <= 6.8e+214:
		tmp = t * (a * -x)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.7e+51)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 2e+119)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	elseif (z <= 7e+208)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (z <= 6.8e+214)
		tmp = Float64(t * Float64(a * Float64(-x)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.7e+51)
		tmp = y * (x * z);
	elseif (z <= 2e+119)
		tmp = a * ((j * c) - (x * t));
	elseif (z <= 7e+208)
		tmp = c * -(z * b);
	elseif (z <= 6.8e+214)
		tmp = t * (a * -x);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.7e+51], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+119], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+208], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 6.8e+214], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.69999999999999992e51

   1. Initial program 53.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 53.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(c \cdot z - t \cdot i\right) \cdot b}\right) \]

      5. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(c \cdot z - \color{blue}{i \cdot t}\right) \cdot b\right) \]

      6. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right) \]

      7. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right) \]

      8. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b \cdot \left(z \cdot c - t \cdot i\right)}\right) \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 69.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) \]

   7. Simplified 77.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right) + t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)}\right) \]

   8. Taylor expanded in y around inf 59.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   9. Step-by-step derivation

      1. +-commutative 59.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 59.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   10. Simplified 59.0%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   11. Taylor expanded in z around inf 49.8%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   12. Step-by-step derivation

       1. *-commutative 49.8%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   13. Simplified 49.8%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -1.69999999999999992e51 < z < 1.99999999999999989e119

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 48.1%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   if 1.99999999999999989e119 < z < 7.00000000000000033e208

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 62.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 62.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 62.6%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 62.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 46.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 46.1%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      3. associate-*r* 51.4%

         \[\leadsto -\color{blue}{c \cdot \left(z \cdot b\right)} \]

      4. *-commutative 51.4%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      5. distribute-rgt-neg-out 51.4%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      6. distribute-rgt-neg-in 51.4%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   8. Simplified 51.4%

      \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(-z\right)\right)} \]

   if 7.00000000000000033e208 < z < 6.7999999999999996e214

   1. Initial program 54.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 100.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 100.0%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 100.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 100.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 100.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around inf 99.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 99.2%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 99.2%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. distribute-rgt-neg-in 99.2%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

      4. associate-*r* 100.0%

         \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   if 6.7999999999999996e214 < z

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 83.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 83.4%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 83.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 67.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Simplified 67.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+208}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+214}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+58} \lor \neg \left(t \leq 3.4 \cdot 10^{-105}\right):\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -9e+58) (not (<= t 3.4e-105))) (* i (* b t)) (* c (* j a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -9e+58) || !(t <= 3.4e-105)) {
		tmp = i * (b * t);
	} else {
		tmp = c * (j * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-9d+58)) .or. (.not. (t <= 3.4d-105))) then
        tmp = i * (b * t)
    else
        tmp = c * (j * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -9e+58) || !(t <= 3.4e-105)) {
		tmp = i * (b * t);
	} else {
		tmp = c * (j * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -9e+58) or not (t <= 3.4e-105):
		tmp = i * (b * t)
	else:
		tmp = c * (j * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -9e+58) || !(t <= 3.4e-105))
		tmp = Float64(i * Float64(b * t));
	else
		tmp = Float64(c * Float64(j * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -9e+58) || ~((t <= 3.4e-105)))
		tmp = i * (b * t);
	else
		tmp = c * (j * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -9e+58], N[Not[LessEqual[t, 3.4e-105]], $MachinePrecision]], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.9999999999999996e58 or 3.39999999999999992e-105 < t

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 59.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 59.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 59.5%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 60.2%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 60.2%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 60.2%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 60.2%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 60.2%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 35.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.9%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 34.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*r* 35.3%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   8. Simplified 35.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -8.9999999999999996e58 < t < 3.39999999999999992e-105

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 36.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 36.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 36.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 36.6%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 36.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 28.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 31.9%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

      3. associate-*r* 28.3%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   8. Simplified 28.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+58} \lor \neg \left(t \leq 3.4 \cdot 10^{-105}\right):\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-109}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.75e+58)
   (* t (* i b))
   (if (<= t 8.4e-109) (* c (* j a)) (* i (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.75e+58) {
		tmp = t * (i * b);
	} else if (t <= 8.4e-109) {
		tmp = c * (j * a);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.75d+58)) then
        tmp = t * (i * b)
    else if (t <= 8.4d-109) then
        tmp = c * (j * a)
    else
        tmp = i * (b * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.75e+58) {
		tmp = t * (i * b);
	} else if (t <= 8.4e-109) {
		tmp = c * (j * a);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.75e+58:
		tmp = t * (i * b)
	elif t <= 8.4e-109:
		tmp = c * (j * a)
	else:
		tmp = i * (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.75e+58)
		tmp = Float64(t * Float64(i * b));
	elseif (t <= 8.4e-109)
		tmp = Float64(c * Float64(j * a));
	else
		tmp = Float64(i * Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.75e+58)
		tmp = t * (i * b);
	elseif (t <= 8.4e-109)
		tmp = c * (j * a);
	else
		tmp = i * (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.75e+58], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e-109], N[(c * N[(j * a), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7499999999999999e58

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 61.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 61.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 61.0%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 61.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 61.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 61.0%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 61.0%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 38.8%

      \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   if -1.7499999999999999e58 < t < 8.39999999999999984e-109

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 36.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 36.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 36.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 36.6%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 36.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 28.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 31.9%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

      3. associate-*r* 28.3%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   8. Simplified 28.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 8.39999999999999984e-109 < t

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 58.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-1 \cdot a\right) \cdot x} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. neg-mul-1 58.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x - -1 \cdot \left(b \cdot i\right)\right) \]

      3. fma-neg 59.8%

         \[\leadsto t \cdot \color{blue}{\mathsf{fma}\left(-a, x, --1 \cdot \left(b \cdot i\right)\right)} \]

      4. mul-1-neg 59.8%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, -\color{blue}{\left(-b \cdot i\right)}\right) \]

      5. remove-double-neg 59.8%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{b \cdot i}\right) \]

      6. *-commutative 59.8%

         \[\leadsto t \cdot \mathsf{fma}\left(-a, x, \color{blue}{i \cdot b}\right) \]

   5. Simplified 59.8%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-a, x, i \cdot b\right)} \]

   6. Taylor expanded in a around 0 32.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 32.9%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 32.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*r* 34.4%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   8. Simplified 34.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-109}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.65 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x 1.65e-162) (* a (* j c)) (* c (* j a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= 1.65e-162) {
		tmp = a * (j * c);
	} else {
		tmp = c * (j * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= 1.65d-162) then
        tmp = a * (j * c)
    else
        tmp = c * (j * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= 1.65e-162) {
		tmp = a * (j * c);
	} else {
		tmp = c * (j * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= 1.65e-162:
		tmp = a * (j * c)
	else:
		tmp = c * (j * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= 1.65e-162)
		tmp = Float64(a * Float64(j * c));
	else
		tmp = Float64(c * Float64(j * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= 1.65e-162)
		tmp = a * (j * c);
	else
		tmp = c * (j * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, 1.65e-162], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.65000000000000007e-162

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 39.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 39.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 39.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 39.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 39.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 39.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 23.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 1.65000000000000007e-162 < x

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 43.6%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 13.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 19.9%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 19.9%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

      3. associate-*r* 18.8%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   8. Simplified 18.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 21.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.65 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(j \cdot c\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* j c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (j * c);
}

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 * (j * c)
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 * (j * c);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (j * c)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(j * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (j * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 40.9%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 40.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.9%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 40.9%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 40.9%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

5. Simplified 40.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

6. Taylor expanded in j around inf 19.9%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

7. Final simplification 19.9%

   \[\leadsto a \cdot \left(j \cdot c\right) \]
8. Add Preprocessing

Developer target: 59.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))