Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.7% → 81.6%

Time: 37.7s

Alternatives: 24

Speedup: 0.5×

• 58.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double t_2 = (t * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = c * ((t * j) - (z * 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(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(Float64(t * 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(c * Float64(Float64(t * j) - Float64(z * 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[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * 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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * 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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 92.2%

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

      1. +-commutative 92.2%

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

      2. fma-def 92.2%

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

      3. *-commutative 92.2%

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

      4. *-commutative 92.2%

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

      5. cancel-sign-sub-inv 92.2%

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

      6. cancel-sign-sub 92.2%

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

      7. remove-double-neg 92.2%

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

      8. *-commutative 92.2%

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

      9. *-commutative 92.2%

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

   3. Simplified 92.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 54.1%

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

      1. *-commutative 54.1%

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

   4. Simplified 54.1%

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

4. Final simplification 83.9%

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

Alternative 2: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * ((t * j) - (z * 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(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

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

   1. Initial program 92.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 54.1%

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

      1. *-commutative 54.1%

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

   4. Simplified 54.1%

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

4. Final simplification 83.9%

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

Alternative 3: 55.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right) + t_2\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+208}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -510000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;t_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j)))
        (t_2 (* i (* a b)))
        (t_3 (+ (* y (- (* x z) (* i j))) t_2))
        (t_4 (* c (- (* t j) (* z b)))))
   (if (<= c -3e+208)
     t_4
     (if (<= c -1.25e+178)
       (* x (- (* y z) (* t a)))
       (if (<= c -3.6e+132)
         t_4
         (if (<= c -1.65e+57)
           t_3
           (if (<= c -6.5e+37)
             (* t (- (* c j) (* x a)))
             (if (<= c -510000000.0)
               (* z (- (* x y) (* b c)))
               (if (<= c 9.5e-213)
                 t_3
                 (if (<= c 4.6e-83)
                   (* a (- (* b i) (* x t)))
                   (if (<= c 5.6e+43)
                     (- t_1 (* i (* y j)))
                     (if (<= c 1.7e+110) (+ t_1 t_2) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double t_3 = (y * ((x * z) - (i * j))) + t_2;
	double t_4 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+208) {
		tmp = t_4;
	} else if (c <= -1.25e+178) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -3.6e+132) {
		tmp = t_4;
	} else if (c <= -1.65e+57) {
		tmp = t_3;
	} else if (c <= -6.5e+37) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -510000000.0) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= 9.5e-213) {
		tmp = t_3;
	} else if (c <= 4.6e-83) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 5.6e+43) {
		tmp = t_1 - (i * (y * j));
	} else if (c <= 1.7e+110) {
		tmp = t_1 + t_2;
	} 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 = c * (t * j)
    t_2 = i * (a * b)
    t_3 = (y * ((x * z) - (i * j))) + t_2
    t_4 = c * ((t * j) - (z * b))
    if (c <= (-3d+208)) then
        tmp = t_4
    else if (c <= (-1.25d+178)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-3.6d+132)) then
        tmp = t_4
    else if (c <= (-1.65d+57)) then
        tmp = t_3
    else if (c <= (-6.5d+37)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-510000000.0d0)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= 9.5d-213) then
        tmp = t_3
    else if (c <= 4.6d-83) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 5.6d+43) then
        tmp = t_1 - (i * (y * j))
    else if (c <= 1.7d+110) then
        tmp = t_1 + t_2
    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 = c * (t * j);
	double t_2 = i * (a * b);
	double t_3 = (y * ((x * z) - (i * j))) + t_2;
	double t_4 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+208) {
		tmp = t_4;
	} else if (c <= -1.25e+178) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -3.6e+132) {
		tmp = t_4;
	} else if (c <= -1.65e+57) {
		tmp = t_3;
	} else if (c <= -6.5e+37) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -510000000.0) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= 9.5e-213) {
		tmp = t_3;
	} else if (c <= 4.6e-83) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 5.6e+43) {
		tmp = t_1 - (i * (y * j));
	} else if (c <= 1.7e+110) {
		tmp = t_1 + t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = i * (a * b)
	t_3 = (y * ((x * z) - (i * j))) + t_2
	t_4 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3e+208:
		tmp = t_4
	elif c <= -1.25e+178:
		tmp = x * ((y * z) - (t * a))
	elif c <= -3.6e+132:
		tmp = t_4
	elif c <= -1.65e+57:
		tmp = t_3
	elif c <= -6.5e+37:
		tmp = t * ((c * j) - (x * a))
	elif c <= -510000000.0:
		tmp = z * ((x * y) - (b * c))
	elif c <= 9.5e-213:
		tmp = t_3
	elif c <= 4.6e-83:
		tmp = a * ((b * i) - (x * t))
	elif c <= 5.6e+43:
		tmp = t_1 - (i * (y * j))
	elif c <= 1.7e+110:
		tmp = t_1 + t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(i * Float64(a * b))
	t_3 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_2)
	t_4 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3e+208)
		tmp = t_4;
	elseif (c <= -1.25e+178)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -3.6e+132)
		tmp = t_4;
	elseif (c <= -1.65e+57)
		tmp = t_3;
	elseif (c <= -6.5e+37)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -510000000.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= 9.5e-213)
		tmp = t_3;
	elseif (c <= 4.6e-83)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 5.6e+43)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (c <= 1.7e+110)
		tmp = Float64(t_1 + t_2);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = i * (a * b);
	t_3 = (y * ((x * z) - (i * j))) + t_2;
	t_4 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3e+208)
		tmp = t_4;
	elseif (c <= -1.25e+178)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -3.6e+132)
		tmp = t_4;
	elseif (c <= -1.65e+57)
		tmp = t_3;
	elseif (c <= -6.5e+37)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -510000000.0)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= 9.5e-213)
		tmp = t_3;
	elseif (c <= 4.6e-83)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 5.6e+43)
		tmp = t_1 - (i * (y * j));
	elseif (c <= 1.7e+110)
		tmp = t_1 + t_2;
	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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+208], t$95$4, If[LessEqual[c, -1.25e+178], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e+132], t$95$4, If[LessEqual[c, -1.65e+57], t$95$3, If[LessEqual[c, -6.5e+37], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -510000000.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-213], t$95$3, If[LessEqual[c, 4.6e-83], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e+43], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+110], N[(t$95$1 + t$95$2), $MachinePrecision], t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -2.99999999999999995e208 or -1.24999999999999998e178 < c < -3.60000000000000016e132 or 1.7000000000000001e110 < c

   1. Initial program 68.5%

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

   2. Taylor expanded in c around inf 84.8%

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

      1. *-commutative 84.8%

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

   4. Simplified 84.8%

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

   if -2.99999999999999995e208 < c < -1.24999999999999998e178

   1. Initial program 16.5%

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

   2. Taylor expanded in t around -inf 30.6%

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

   4. Simplified 30.6%

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

   5. Taylor expanded in x around inf 86.3%

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

   if -3.60000000000000016e132 < c < -1.6500000000000001e57 or -5.1e8 < c < 9.50000000000000055e-213

   1. Initial program 72.4%

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

   2. Taylor expanded in t around 0 63.3%

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

      1. sub-neg 63.3%

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

      2. associate-*r* 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*r* 65.2%

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

      5. mul-1-neg 65.2%

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

      6. distribute-rgt-neg-in 65.2%

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

      7. mul-1-neg 65.2%

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

      8. distribute-lft-in 66.3%

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

      9. +-commutative 66.3%

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

      10. mul-1-neg 66.3%

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

      11. unsub-neg 66.3%

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

      12. mul-1-neg 66.3%

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

      13. associate-*r* 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in c around 0 68.4%

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

   if -1.6500000000000001e57 < c < -6.4999999999999998e37

   1. Initial program 60.0%

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

   2. Taylor expanded in t around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

   4. Simplified 80.9%

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

   if -6.4999999999999998e37 < c < -5.1e8

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 83.1%

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

   if 9.50000000000000055e-213 < c < 4.59999999999999979e-83

   1. Initial program 76.1%

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

   2. Taylor expanded in t around -inf 64.8%

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

   4. Simplified 64.7%

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

   5. Taylor expanded in a around inf 64.5%

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

   if 4.59999999999999979e-83 < c < 5.60000000000000038e43

   1. Initial program 86.0%

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

   2. Taylor expanded in t around -inf 90.7%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in x around -inf 86.1%

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

      1. fma-def 95.2%

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

      2. *-commutative 95.2%

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

      3. *-commutative 95.2%

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

      4. distribute-lft-out 95.2%

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

      5. associate-*r* 95.2%

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

      6. *-commutative 95.2%

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

      7. associate-*r* 86.7%

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

      8. *-commutative 86.7%

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

      9. distribute-lft-out-- 86.7%

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

      10. associate-*r* 86.7%

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

      11. neg-mul-1 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in j around inf 55.9%

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

      1. neg-mul-1 55.9%

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

      2. *-commutative 55.9%

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

      3. distribute-rgt-neg-in 55.9%

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

   10. Simplified 55.9%

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

   if 5.60000000000000038e43 < c < 1.7000000000000001e110

   1. Initial program 88.9%

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

   2. Taylor expanded in t around -inf 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in x around -inf 77.6%

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

      1. fma-def 77.6%

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

      2. *-commutative 77.6%

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

      3. *-commutative 77.6%

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

      4. distribute-lft-out 77.6%

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

      5. associate-*r* 77.6%

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

      6. *-commutative 77.6%

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

      7. associate-*r* 77.6%

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

      8. *-commutative 77.6%

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

      9. distribute-lft-out-- 77.6%

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

      10. associate-*r* 77.6%

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

      11. neg-mul-1 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in y around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-rgt-neg-in 77.6%

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

      3. distribute-rgt-neg-in 77.6%

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

   10. Simplified 77.6%

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

   11. Taylor expanded in a around inf 77.7%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} - \left(-c\right) \cdot \left(t \cdot j\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+208}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -510000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 4: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -5.2e+77)
     t_2
     (if (<= y -3e+46)
       (* c (- (* t j) (* z b)))
       (if (<= y -4.5e-17)
         (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
         (if (<= y -1.35e-88)
           (+ (* i (* a b)) t_1)
           (if (<= y 5.5e+122)
             (- t_1 (* b (- (* z c) (* a i))))
             (+ 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.2e+77) {
		tmp = t_2;
	} else if (y <= -3e+46) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= -4.5e-17) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (y <= -1.35e-88) {
		tmp = (i * (a * b)) + t_1;
	} else if (y <= 5.5e+122) {
		tmp = t_1 - (b * ((z * c) - (a * i)));
	} 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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-5.2d+77)) then
        tmp = t_2
    else if (y <= (-3d+46)) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= (-4.5d-17)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (y <= (-1.35d-88)) then
        tmp = (i * (a * b)) + t_1
    else if (y <= 5.5d+122) then
        tmp = t_1 - (b * ((z * c) - (a * i)))
    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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.2e+77) {
		tmp = t_2;
	} else if (y <= -3e+46) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= -4.5e-17) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (y <= -1.35e-88) {
		tmp = (i * (a * b)) + t_1;
	} else if (y <= 5.5e+122) {
		tmp = t_1 - (b * ((z * c) - (a * i)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5.2e+77:
		tmp = t_2
	elif y <= -3e+46:
		tmp = c * ((t * j) - (z * b))
	elif y <= -4.5e-17:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif y <= -1.35e-88:
		tmp = (i * (a * b)) + t_1
	elif y <= 5.5e+122:
		tmp = t_1 - (b * ((z * c) - (a * i)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.2e+77)
		tmp = t_2;
	elseif (y <= -3e+46)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= -4.5e-17)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (y <= -1.35e-88)
		tmp = Float64(Float64(i * Float64(a * b)) + t_1);
	elseif (y <= 5.5e+122)
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5.2e+77)
		tmp = t_2;
	elseif (y <= -3e+46)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= -4.5e-17)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (y <= -1.35e-88)
		tmp = (i * (a * b)) + t_1;
	elseif (y <= 5.5e+122)
		tmp = t_1 - (b * ((z * c) - (a * i)));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+77], t$95$2, If[LessEqual[y, -3e+46], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-17], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-88], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 5.5e+122], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.2000000000000004e77

   1. Initial program 58.9%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

   4. Simplified 71.4%

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

   if -5.2000000000000004e77 < y < -3.00000000000000023e46

   1. Initial program 33.3%

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

   2. Taylor expanded in c around inf 89.2%

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

      1. *-commutative 89.2%

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

   4. Simplified 89.2%

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

   if -3.00000000000000023e46 < y < -4.49999999999999978e-17

   1. Initial program 99.7%

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

   2. Taylor expanded in j around 0 99.7%

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

   if -4.49999999999999978e-17 < y < -1.34999999999999997e-88

   1. Initial program 74.1%

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

   2. Taylor expanded in t around -inf 73.5%

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

   4. Simplified 66.8%

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

   5. Taylor expanded in z around 0 73.3%

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

   6. Taylor expanded in y around 0 80.0%

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

      1. *-commutative 80.0%

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

   8. Simplified 80.0%

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

   if -1.34999999999999997e-88 < y < 5.4999999999999998e122

   1. Initial program 79.6%

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

   2. Taylor expanded in y around 0 75.1%

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

   4. Simplified 74.4%

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

   if 5.4999999999999998e122 < y

   1. Initial program 66.7%

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

   2. Taylor expanded in t around -inf 67.1%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in b around 0 72.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 5: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3e+131)
     t_2
     (if (<= c -2.6e+74)
       t_1
       (if (<= c -4.6e-15)
         (* z (- (* x y) (* b c)))
         (if (<= c -2.2e-62)
           t_1
           (if (<= c -1e-176)
             (* y (- (* x z) (* i j)))
             (if (<= c 9.8e-82)
               (* a (- (* b i) (* x t)))
               (if (<= c 3e+98)
                 (* t (- (* c j) (* x a)))
                 (if (<= c 1.65e+107) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+131) {
		tmp = t_2;
	} else if (c <= -2.6e+74) {
		tmp = t_1;
	} else if (c <= -4.6e-15) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.2e-62) {
		tmp = t_1;
	} else if (c <= -1e-176) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 9.8e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3e+98) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 1.65e+107) {
		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 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3d+131)) then
        tmp = t_2
    else if (c <= (-2.6d+74)) then
        tmp = t_1
    else if (c <= (-4.6d-15)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-2.2d-62)) then
        tmp = t_1
    else if (c <= (-1d-176)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 9.8d-82) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 3d+98) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 1.65d+107) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+131) {
		tmp = t_2;
	} else if (c <= -2.6e+74) {
		tmp = t_1;
	} else if (c <= -4.6e-15) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.2e-62) {
		tmp = t_1;
	} else if (c <= -1e-176) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 9.8e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3e+98) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 1.65e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3e+131:
		tmp = t_2
	elif c <= -2.6e+74:
		tmp = t_1
	elif c <= -4.6e-15:
		tmp = z * ((x * y) - (b * c))
	elif c <= -2.2e-62:
		tmp = t_1
	elif c <= -1e-176:
		tmp = y * ((x * z) - (i * j))
	elif c <= 9.8e-82:
		tmp = a * ((b * i) - (x * t))
	elif c <= 3e+98:
		tmp = t * ((c * j) - (x * a))
	elif c <= 1.65e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3e+131)
		tmp = t_2;
	elseif (c <= -2.6e+74)
		tmp = t_1;
	elseif (c <= -4.6e-15)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -2.2e-62)
		tmp = t_1;
	elseif (c <= -1e-176)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 9.8e-82)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 3e+98)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 1.65e+107)
		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 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3e+131)
		tmp = t_2;
	elseif (c <= -2.6e+74)
		tmp = t_1;
	elseif (c <= -4.6e-15)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -2.2e-62)
		tmp = t_1;
	elseif (c <= -1e-176)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 9.8e-82)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 3e+98)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 1.65e+107)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+131], t$95$2, If[LessEqual[c, -2.6e+74], t$95$1, If[LessEqual[c, -4.6e-15], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.2e-62], t$95$1, If[LessEqual[c, -1e-176], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.8e-82], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+98], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e+107], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -3.0000000000000001e131 or 1.65000000000000016e107 < c

   1. Initial program 64.7%

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

   2. Taylor expanded in c around inf 79.7%

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

      1. *-commutative 79.7%

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

   4. Simplified 79.7%

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

   if -3.0000000000000001e131 < c < -2.6000000000000001e74 or -4.59999999999999981e-15 < c < -2.20000000000000017e-62 or 3.0000000000000001e98 < c < 1.65000000000000016e107

   1. Initial program 59.1%

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

   2. Taylor expanded in i around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. cancel-sign-sub-inv 64.6%

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

      3. metadata-eval 64.6%

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

      4. *-lft-identity 64.6%

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

      5. +-commutative 64.6%

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

      6. mul-1-neg 64.6%

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

      7. unsub-neg 64.6%

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

   4. Simplified 64.6%

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

   if -2.6000000000000001e74 < c < -4.59999999999999981e-15

   1. Initial program 83.3%

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

   2. Taylor expanded in z around inf 66.7%

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

   if -2.20000000000000017e-62 < c < -1e-176

   1. Initial program 69.5%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

   4. Simplified 69.2%

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

   if -1e-176 < c < 9.8000000000000006e-82

   1. Initial program 79.1%

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

   2. Taylor expanded in t around -inf 79.3%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in a around inf 59.0%

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

   if 9.8000000000000006e-82 < c < 3.0000000000000001e98

   1. Initial program 89.0%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

   4. Simplified 56.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+131}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-62}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+107}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 57.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* i (* a b)) (* t (- (* c j) (* x a)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -5.2e+80)
     t_2
     (if (<= y -2e+31)
       (* z (- (* x y) (* b c)))
       (if (<= y 9.5e-236)
         t_1
         (if (<= y 1.8e-175)
           (* c (- (* t j) (* z b)))
           (if (<= y 8e+117) 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 = (i * (a * b)) + (t * ((c * j) - (x * a)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.2e+80) {
		tmp = t_2;
	} else if (y <= -2e+31) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 9.5e-236) {
		tmp = t_1;
	} else if (y <= 1.8e-175) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 8e+117) {
		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 = (i * (a * b)) + (t * ((c * j) - (x * a)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-5.2d+80)) then
        tmp = t_2
    else if (y <= (-2d+31)) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= 9.5d-236) then
        tmp = t_1
    else if (y <= 1.8d-175) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 8d+117) 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 = (i * (a * b)) + (t * ((c * j) - (x * a)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.2e+80) {
		tmp = t_2;
	} else if (y <= -2e+31) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 9.5e-236) {
		tmp = t_1;
	} else if (y <= 1.8e-175) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 8e+117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * (a * b)) + (t * ((c * j) - (x * a)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5.2e+80:
		tmp = t_2
	elif y <= -2e+31:
		tmp = z * ((x * y) - (b * c))
	elif y <= 9.5e-236:
		tmp = t_1
	elif y <= 1.8e-175:
		tmp = c * ((t * j) - (z * b))
	elif y <= 8e+117:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(a * b)) + Float64(t * Float64(Float64(c * j) - Float64(x * a))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.2e+80)
		tmp = t_2;
	elseif (y <= -2e+31)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= 9.5e-236)
		tmp = t_1;
	elseif (y <= 1.8e-175)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 8e+117)
		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 = (i * (a * b)) + (t * ((c * j) - (x * a)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5.2e+80)
		tmp = t_2;
	elseif (y <= -2e+31)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= 9.5e-236)
		tmp = t_1;
	elseif (y <= 1.8e-175)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 8e+117)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+80], t$95$2, If[LessEqual[y, -2e+31], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-236], t$95$1, If[LessEqual[y, 1.8e-175], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+117], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.19999999999999963e80 or 8.0000000000000004e117 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in y around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

   4. Simplified 70.5%

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

   if -5.19999999999999963e80 < y < -1.9999999999999999e31

   1. Initial program 50.0%

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

   2. Taylor expanded in z around inf 83.0%

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

   if -1.9999999999999999e31 < y < 9.50000000000000065e-236 or 1.8e-175 < y < 8.0000000000000004e117

   1. Initial program 79.1%

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

   2. Taylor expanded in t around -inf 76.0%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in z around 0 67.4%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. *-commutative 66.3%

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

   8. Simplified 66.3%

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

   if 9.50000000000000065e-236 < y < 1.8e-175

   1. Initial program 84.9%

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

   2. Taylor expanded in c around inf 74.9%

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

      1. *-commutative 74.9%

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

   4. Simplified 74.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-236}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 7: 67.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+28} \lor \neg \left(y \leq 2.6 \cdot 10^{+108}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right) - \left(c \cdot \left(z \cdot b\right) + y \cdot \left(i \cdot j - x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -3.6e+28) (not (<= y 2.6e+108)))
   (- (* c (* t j)) (+ (* c (* z b)) (* y (- (* i j) (* x z)))))
   (- (* t (- (* c j) (* x a))) (* b (- (* z c) (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -3.6e+28) || !(y <= 2.6e+108)) {
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))));
	} else {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-3.6d+28)) .or. (.not. (y <= 2.6d+108))) then
        tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))))
    else
        tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -3.6e+28) || !(y <= 2.6e+108)) {
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))));
	} else {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -3.6e+28) or not (y <= 2.6e+108):
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))))
	else:
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -3.6e+28) || !(y <= 2.6e+108))
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(Float64(c * Float64(z * b)) + Float64(y * Float64(Float64(i * j) - Float64(x * z)))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -3.6e+28) || ~((y <= 2.6e+108)))
		tmp = (c * (t * j)) - ((c * (z * b)) + (y * ((i * j) - (x * z))));
	else
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -3.6e+28], N[Not[LessEqual[y, 2.6e+108]], $MachinePrecision]], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e28 or 2.6000000000000002e108 < y

   1. Initial program 61.4%

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

   2. Taylor expanded in t around -inf 65.3%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in a around 0 73.8%

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

   if -3.5999999999999999e28 < y < 2.6000000000000002e108

   1. Initial program 79.6%

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

   2. Taylor expanded in y around 0 74.3%

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

   4. Simplified 74.8%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+28} \lor \neg \left(y \leq 2.6 \cdot 10^{+108}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right) - \left(c \cdot \left(z \cdot b\right) + y \cdot \left(i \cdot j - x \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \]

Alternative 8: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{+210} \lor \neg \left(x \leq 1.6 \cdot 10^{+251}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.2e+116)
     t_2
     (if (<= x 4e-262)
       (* c (- (* t j) (* z b)))
       (if (<= x 1.9e-111)
         t_1
         (if (<= x 8.5e-25)
           (- (* i (* a b)) (* z (* b c)))
           (if (<= x 1.5e+33)
             t_1
             (if (or (<= x 1e+210) (not (<= x 1.6e+251)))
               t_2
               (* z (- (* x y) (* b c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.2e+116) {
		tmp = t_2;
	} else if (x <= 4e-262) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.9e-111) {
		tmp = t_1;
	} else if (x <= 8.5e-25) {
		tmp = (i * (a * b)) - (z * (b * c));
	} else if (x <= 1.5e+33) {
		tmp = t_1;
	} else if ((x <= 1e+210) || !(x <= 1.6e+251)) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.2d+116)) then
        tmp = t_2
    else if (x <= 4d-262) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.9d-111) then
        tmp = t_1
    else if (x <= 8.5d-25) then
        tmp = (i * (a * b)) - (z * (b * c))
    else if (x <= 1.5d+33) then
        tmp = t_1
    else if ((x <= 1d+210) .or. (.not. (x <= 1.6d+251))) then
        tmp = t_2
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.2e+116) {
		tmp = t_2;
	} else if (x <= 4e-262) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.9e-111) {
		tmp = t_1;
	} else if (x <= 8.5e-25) {
		tmp = (i * (a * b)) - (z * (b * c));
	} else if (x <= 1.5e+33) {
		tmp = t_1;
	} else if ((x <= 1e+210) || !(x <= 1.6e+251)) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.2e+116:
		tmp = t_2
	elif x <= 4e-262:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.9e-111:
		tmp = t_1
	elif x <= 8.5e-25:
		tmp = (i * (a * b)) - (z * (b * c))
	elif x <= 1.5e+33:
		tmp = t_1
	elif (x <= 1e+210) or not (x <= 1.6e+251):
		tmp = t_2
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.2e+116)
		tmp = t_2;
	elseif (x <= 4e-262)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.9e-111)
		tmp = t_1;
	elseif (x <= 8.5e-25)
		tmp = Float64(Float64(i * Float64(a * b)) - Float64(z * Float64(b * c)));
	elseif (x <= 1.5e+33)
		tmp = t_1;
	elseif ((x <= 1e+210) || !(x <= 1.6e+251))
		tmp = t_2;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.2e+116)
		tmp = t_2;
	elseif (x <= 4e-262)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.9e-111)
		tmp = t_1;
	elseif (x <= 8.5e-25)
		tmp = (i * (a * b)) - (z * (b * c));
	elseif (x <= 1.5e+33)
		tmp = t_1;
	elseif ((x <= 1e+210) || ~((x <= 1.6e+251)))
		tmp = t_2;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+116], t$95$2, If[LessEqual[x, 4e-262], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-111], t$95$1, If[LessEqual[x, 8.5e-25], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+33], t$95$1, If[Or[LessEqual[x, 1e+210], N[Not[LessEqual[x, 1.6e+251]], $MachinePrecision]], t$95$2, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.2e116 or 1.49999999999999992e33 < x < 9.99999999999999927e209 or 1.5999999999999999e251 < x

   1. Initial program 82.0%

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

   2. Taylor expanded in t around -inf 57.1%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in x around inf 73.8%

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

   if -1.2e116 < x < 4.00000000000000005e-262

   1. Initial program 70.8%

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

   2. Taylor expanded in c around inf 63.7%

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

      1. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if 4.00000000000000005e-262 < x < 1.90000000000000011e-111 or 8.49999999999999981e-25 < x < 1.49999999999999992e33

   1. Initial program 63.1%

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

   2. Taylor expanded in i around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. cancel-sign-sub-inv 58.7%

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

      3. metadata-eval 58.7%

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

      4. *-lft-identity 58.7%

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

      5. +-commutative 58.7%

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

      6. mul-1-neg 58.7%

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

      7. unsub-neg 58.7%

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

   4. Simplified 58.7%

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

   if 1.90000000000000011e-111 < x < 8.49999999999999981e-25

   1. Initial program 79.2%

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

   2. Taylor expanded in t around 0 74.5%

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

      1. sub-neg 74.5%

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

      2. associate-*r* 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-*r* 74.5%

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

      5. mul-1-neg 74.5%

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

      6. distribute-rgt-neg-in 74.5%

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

      7. mul-1-neg 74.5%

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

      8. distribute-lft-in 74.5%

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

      9. +-commutative 74.5%

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

      10. mul-1-neg 74.5%

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

      11. unsub-neg 74.5%

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

      12. mul-1-neg 74.5%

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

      13. associate-*r* 74.5%

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

   4. Simplified 74.5%

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

   5. Taylor expanded in x around 0 69.5%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in a around inf 84.6%

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

   if 9.99999999999999927e209 < x < 1.5999999999999999e251

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 74.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-262}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-111}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 10^{+210} \lor \neg \left(x \leq 1.6 \cdot 10^{+251}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 9: 48.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.06 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 1.46 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -6e+133)
     t_2
     (if (<= c -3e+74)
       t_1
       (if (<= c -1.06e+30)
         t_2
         (if (<= c -5.5e-141)
           (* z (* x y))
           (if (<= c 1.05e-82)
             (* a (- (* b i) (* x t)))
             (if (<= c 9.6e+97)
               (* j (- (* t c) (* y i)))
               (if (<= c 1.46e+110) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6e+133) {
		tmp = t_2;
	} else if (c <= -3e+74) {
		tmp = t_1;
	} else if (c <= -1.06e+30) {
		tmp = t_2;
	} else if (c <= -5.5e-141) {
		tmp = z * (x * y);
	} else if (c <= 1.05e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 9.6e+97) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 1.46e+110) {
		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 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-6d+133)) then
        tmp = t_2
    else if (c <= (-3d+74)) then
        tmp = t_1
    else if (c <= (-1.06d+30)) then
        tmp = t_2
    else if (c <= (-5.5d-141)) then
        tmp = z * (x * y)
    else if (c <= 1.05d-82) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 9.6d+97) then
        tmp = j * ((t * c) - (y * i))
    else if (c <= 1.46d+110) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6e+133) {
		tmp = t_2;
	} else if (c <= -3e+74) {
		tmp = t_1;
	} else if (c <= -1.06e+30) {
		tmp = t_2;
	} else if (c <= -5.5e-141) {
		tmp = z * (x * y);
	} else if (c <= 1.05e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 9.6e+97) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 1.46e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -6e+133:
		tmp = t_2
	elif c <= -3e+74:
		tmp = t_1
	elif c <= -1.06e+30:
		tmp = t_2
	elif c <= -5.5e-141:
		tmp = z * (x * y)
	elif c <= 1.05e-82:
		tmp = a * ((b * i) - (x * t))
	elif c <= 9.6e+97:
		tmp = j * ((t * c) - (y * i))
	elif c <= 1.46e+110:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -6e+133)
		tmp = t_2;
	elseif (c <= -3e+74)
		tmp = t_1;
	elseif (c <= -1.06e+30)
		tmp = t_2;
	elseif (c <= -5.5e-141)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.05e-82)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 9.6e+97)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (c <= 1.46e+110)
		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 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -6e+133)
		tmp = t_2;
	elseif (c <= -3e+74)
		tmp = t_1;
	elseif (c <= -1.06e+30)
		tmp = t_2;
	elseif (c <= -5.5e-141)
		tmp = z * (x * y);
	elseif (c <= 1.05e-82)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 9.6e+97)
		tmp = j * ((t * c) - (y * i));
	elseif (c <= 1.46e+110)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6e+133], t$95$2, If[LessEqual[c, -3e+74], t$95$1, If[LessEqual[c, -1.06e+30], t$95$2, If[LessEqual[c, -5.5e-141], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e-82], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.6e+97], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.46e+110], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6.00000000000000013e133 or -3e74 < c < -1.06e30 or 1.46e110 < c

   1. Initial program 65.1%

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

   2. Taylor expanded in c around inf 79.2%

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

      1. *-commutative 79.2%

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

   4. Simplified 79.2%

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

   if -6.00000000000000013e133 < c < -3e74 or 9.6000000000000001e97 < c < 1.46e110

   1. Initial program 60.9%

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

   2. Taylor expanded in i around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. cancel-sign-sub-inv 63.6%

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

      3. metadata-eval 63.6%

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

      4. *-lft-identity 63.6%

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

      5. +-commutative 63.6%

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

      6. mul-1-neg 63.6%

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

      7. unsub-neg 63.6%

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

   4. Simplified 63.6%

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

   if -1.06e30 < c < -5.4999999999999998e-141

   1. Initial program 70.9%

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

   2. Taylor expanded in z around inf 49.7%

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

   3. Taylor expanded in y around inf 46.5%

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

   if -5.4999999999999998e-141 < c < 1.05e-82

   1. Initial program 78.1%

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

   2. Taylor expanded in t around -inf 78.3%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in a around inf 58.4%

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

   if 1.05e-82 < c < 9.6000000000000001e97

   1. Initial program 89.0%

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

   2. Taylor expanded in t around -inf 85.5%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in z around 0 73.0%

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

   6. Taylor expanded in j around inf 54.7%

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

      1. *-commutative 54.7%

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

      2. sub-neg 54.7%

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

      3. neg-mul-1 54.7%

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

      4. remove-double-neg 54.7%

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

      5. +-commutative 54.7%

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

      6. mul-1-neg 54.7%

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

      7. *-commutative 54.7%

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

      8. sub-neg 54.7%

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

      9. *-commutative 54.7%

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

      10. *-commutative 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+133}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.06 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 1.46 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 10: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3e+131)
     t_2
     (if (<= c -1.12e+70)
       t_1
       (if (<= c -4.4e+29)
         t_2
         (if (<= c -5.6e-141)
           (* z (* x y))
           (if (<= c 1.02e-81)
             (* a (- (* b i) (* x t)))
             (if (<= c 3.4e+97)
               (* t (- (* c j) (* x a)))
               (if (<= c 2.5e+110) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+131) {
		tmp = t_2;
	} else if (c <= -1.12e+70) {
		tmp = t_1;
	} else if (c <= -4.4e+29) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 1.02e-81) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.4e+97) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 2.5e+110) {
		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 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3d+131)) then
        tmp = t_2
    else if (c <= (-1.12d+70)) then
        tmp = t_1
    else if (c <= (-4.4d+29)) then
        tmp = t_2
    else if (c <= (-5.6d-141)) then
        tmp = z * (x * y)
    else if (c <= 1.02d-81) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 3.4d+97) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 2.5d+110) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+131) {
		tmp = t_2;
	} else if (c <= -1.12e+70) {
		tmp = t_1;
	} else if (c <= -4.4e+29) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 1.02e-81) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.4e+97) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 2.5e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3e+131:
		tmp = t_2
	elif c <= -1.12e+70:
		tmp = t_1
	elif c <= -4.4e+29:
		tmp = t_2
	elif c <= -5.6e-141:
		tmp = z * (x * y)
	elif c <= 1.02e-81:
		tmp = a * ((b * i) - (x * t))
	elif c <= 3.4e+97:
		tmp = t * ((c * j) - (x * a))
	elif c <= 2.5e+110:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3e+131)
		tmp = t_2;
	elseif (c <= -1.12e+70)
		tmp = t_1;
	elseif (c <= -4.4e+29)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.02e-81)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 3.4e+97)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 2.5e+110)
		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 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3e+131)
		tmp = t_2;
	elseif (c <= -1.12e+70)
		tmp = t_1;
	elseif (c <= -4.4e+29)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = z * (x * y);
	elseif (c <= 1.02e-81)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 3.4e+97)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 2.5e+110)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+131], t$95$2, If[LessEqual[c, -1.12e+70], t$95$1, If[LessEqual[c, -4.4e+29], t$95$2, If[LessEqual[c, -5.6e-141], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e-81], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+97], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+110], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.0000000000000001e131 or -1.11999999999999993e70 < c < -4.4000000000000003e29 or 2.49999999999999989e110 < c

   1. Initial program 65.1%

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

   2. Taylor expanded in c around inf 79.2%

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

      1. *-commutative 79.2%

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

   4. Simplified 79.2%

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

   if -3.0000000000000001e131 < c < -1.11999999999999993e70 or 3.4000000000000001e97 < c < 2.49999999999999989e110

   1. Initial program 60.9%

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

   2. Taylor expanded in i around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. cancel-sign-sub-inv 63.6%

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

      3. metadata-eval 63.6%

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

      4. *-lft-identity 63.6%

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

      5. +-commutative 63.6%

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

      6. mul-1-neg 63.6%

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

      7. unsub-neg 63.6%

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

   4. Simplified 63.6%

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

   if -4.4000000000000003e29 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

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

   2. Taylor expanded in z around inf 49.7%

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

   3. Taylor expanded in y around inf 46.5%

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

   if -5.60000000000000023e-141 < c < 1.01999999999999998e-81

   1. Initial program 78.1%

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

   2. Taylor expanded in t around -inf 78.3%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in a around inf 58.4%

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

   if 1.01999999999999998e-81 < c < 3.4000000000000001e97

   1. Initial program 89.0%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

   4. Simplified 56.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+131}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 11: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+81} \lor \neg \left(y \leq 5.7 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.75e+81) (not (<= y 5.7e+119)))
   (* y (- (* x z) (* i j)))
   (- (* t (- (* c j) (* x a))) (* b (- (* z c) (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.75e+81) || !(y <= 5.7e+119)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-1.75d+81)) .or. (.not. (y <= 5.7d+119))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.75e+81) || !(y <= 5.7e+119)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -1.75e+81) or not (y <= 5.7e+119):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.75e+81) || !(y <= 5.7e+119))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -1.75e+81) || ~((y <= 5.7e+119)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.75e+81], N[Not[LessEqual[y, 5.7e+119]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e81 or 5.7000000000000002e119 < y

   1. Initial program 61.6%

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

   2. Taylor expanded in y around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   4. Simplified 71.1%

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

   if -1.75e81 < y < 5.7000000000000002e119

   1. Initial program 77.8%

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

   2. Taylor expanded in y around 0 72.5%

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

   4. Simplified 74.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+81} \lor \neg \left(y \leq 5.7 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \]

Alternative 12: 67.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+123}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -4.9e+88)
     t_2
     (if (<= y 2.9e+123) (- t_1 (* b (- (* z c) (* a i)))) (+ 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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.9e+88) {
		tmp = t_2;
	} else if (y <= 2.9e+123) {
		tmp = t_1 - (b * ((z * c) - (a * i)));
	} 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 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-4.9d+88)) then
        tmp = t_2
    else if (y <= 2.9d+123) then
        tmp = t_1 - (b * ((z * c) - (a * i)))
    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 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.9e+88) {
		tmp = t_2;
	} else if (y <= 2.9e+123) {
		tmp = t_1 - (b * ((z * c) - (a * i)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.9e+88:
		tmp = t_2
	elif y <= 2.9e+123:
		tmp = t_1 - (b * ((z * c) - (a * i)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.9e+88)
		tmp = t_2;
	elseif (y <= 2.9e+123)
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	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 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.9e+88)
		tmp = t_2;
	elseif (y <= 2.9e+123)
		tmp = t_1 - (b * ((z * c) - (a * i)));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.9e+88], t$95$2, If[LessEqual[y, 2.9e+123], N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9000000000000002e88

   1. Initial program 58.9%

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

   2. Taylor expanded in y around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

   4. Simplified 71.4%

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

   if -4.9000000000000002e88 < y < 2.9000000000000001e123

   1. Initial program 77.3%

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

   2. Taylor expanded in y around 0 72.0%

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

   4. Simplified 73.7%

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

   if 2.9000000000000001e123 < y

   1. Initial program 66.7%

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

   2. Taylor expanded in t around -inf 67.1%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in b around 0 72.5%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 13: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+207} \lor \neg \left(x \leq 1.6 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -6.5e+115)
     t_1
     (if (<= x 3.3e-263)
       (* c (- (* t j) (* z b)))
       (if (<= x 3.6e+34)
         (* i (- (* a b) (* y j)))
         (if (or (<= x 2.3e+207) (not (<= x 1.6e+251)))
           t_1
           (* z (- (* x y) (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.5e+115) {
		tmp = t_1;
	} else if (x <= 3.3e-263) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 3.6e+34) {
		tmp = i * ((a * b) - (y * j));
	} else if ((x <= 2.3e+207) || !(x <= 1.6e+251)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-6.5d+115)) then
        tmp = t_1
    else if (x <= 3.3d-263) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 3.6d+34) then
        tmp = i * ((a * b) - (y * j))
    else if ((x <= 2.3d+207) .or. (.not. (x <= 1.6d+251))) then
        tmp = t_1
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.5e+115) {
		tmp = t_1;
	} else if (x <= 3.3e-263) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 3.6e+34) {
		tmp = i * ((a * b) - (y * j));
	} else if ((x <= 2.3e+207) || !(x <= 1.6e+251)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6.5e+115:
		tmp = t_1
	elif x <= 3.3e-263:
		tmp = c * ((t * j) - (z * b))
	elif x <= 3.6e+34:
		tmp = i * ((a * b) - (y * j))
	elif (x <= 2.3e+207) or not (x <= 1.6e+251):
		tmp = t_1
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6.5e+115)
		tmp = t_1;
	elseif (x <= 3.3e-263)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 3.6e+34)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif ((x <= 2.3e+207) || !(x <= 1.6e+251))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -6.5e+115)
		tmp = t_1;
	elseif (x <= 3.3e-263)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 3.6e+34)
		tmp = i * ((a * b) - (y * j));
	elseif ((x <= 2.3e+207) || ~((x <= 1.6e+251)))
		tmp = t_1;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e+115], t$95$1, If[LessEqual[x, 3.3e-263], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+34], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.3e+207], N[Not[LessEqual[x, 1.6e+251]], $MachinePrecision]], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.49999999999999966e115 or 3.6e34 < x < 2.29999999999999995e207 or 1.5999999999999999e251 < x

   1. Initial program 82.0%

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

   2. Taylor expanded in t around -inf 57.1%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in x around inf 73.8%

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

   if -6.49999999999999966e115 < x < 3.2999999999999997e-263

   1. Initial program 70.8%

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

   2. Taylor expanded in c around inf 63.7%

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

      1. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if 3.2999999999999997e-263 < x < 3.6e34

   1. Initial program 68.1%

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

   2. Taylor expanded in i around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. cancel-sign-sub-inv 58.7%

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

      3. metadata-eval 58.7%

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

      4. *-lft-identity 58.7%

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

      5. +-commutative 58.7%

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

      6. mul-1-neg 58.7%

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

      7. unsub-neg 58.7%

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

   4. Simplified 58.7%

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

   if 2.29999999999999995e207 < x < 1.5999999999999999e251

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 74.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+207} \lor \neg \left(x \leq 1.6 \cdot 10^{+251}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 14: 49.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 17200000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.15e+132)
     t_1
     (if (<= c -1.8e+68)
       (* i (- (* a b) (* y j)))
       (if (<= c -4.4e+29)
         t_1
         (if (<= c -5.6e-141)
           (* z (* x y))
           (if (<= c 17200000000000.0) (* a (- (* b i) (* x t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.15e+132) {
		tmp = t_1;
	} else if (c <= -1.8e+68) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -4.4e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 17200000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-1.15d+132)) then
        tmp = t_1
    else if (c <= (-1.8d+68)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= (-4.4d+29)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = z * (x * y)
    else if (c <= 17200000000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.15e+132) {
		tmp = t_1;
	} else if (c <= -1.8e+68) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -4.4e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 17200000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.15e+132:
		tmp = t_1
	elif c <= -1.8e+68:
		tmp = i * ((a * b) - (y * j))
	elif c <= -4.4e+29:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = z * (x * y)
	elif c <= 17200000000000.0:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.15e+132)
		tmp = t_1;
	elseif (c <= -1.8e+68)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= -4.4e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 17200000000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.15e+132)
		tmp = t_1;
	elseif (c <= -1.8e+68)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= -4.4e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = z * (x * y);
	elseif (c <= 17200000000000.0)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+132], t$95$1, If[LessEqual[c, -1.8e+68], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.4e+29], t$95$1, If[LessEqual[c, -5.6e-141], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 17200000000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.1500000000000001e132 or -1.7999999999999999e68 < c < -4.4000000000000003e29 or 1.72e13 < c

   1. Initial program 68.5%

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

   2. Taylor expanded in c around inf 75.8%

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

      1. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   if -1.1500000000000001e132 < c < -1.7999999999999999e68

   1. Initial program 59.8%

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

   2. Taylor expanded in i around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. cancel-sign-sub-inv 56.3%

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

      3. metadata-eval 56.3%

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

      4. *-lft-identity 56.3%

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

      5. +-commutative 56.3%

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

      6. mul-1-neg 56.3%

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

      7. unsub-neg 56.3%

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

   4. Simplified 56.3%

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

   if -4.4000000000000003e29 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

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

   2. Taylor expanded in z around inf 49.7%

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

   3. Taylor expanded in y around inf 46.5%

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

   if -5.60000000000000023e-141 < c < 1.72e13

   1. Initial program 78.8%

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

   2. Taylor expanded in t around -inf 80.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in a around inf 54.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 17200000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 15: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3.4e+131)
     t_1
     (if (<= c -6.5e-177)
       (* y (- (* x z) (* i j)))
       (if (<= c 2.25e-82)
         (* a (- (* b i) (* x t)))
         (if (<= c 4.8e+98)
           (* t (- (* c j) (* x a)))
           (if (<= c 6.3e+106) (* i (- (* a b) (* y j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.4e+131) {
		tmp = t_1;
	} else if (c <= -6.5e-177) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.25e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 4.8e+98) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 6.3e+106) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-3.4d+131)) then
        tmp = t_1
    else if (c <= (-6.5d-177)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 2.25d-82) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 4.8d+98) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 6.3d+106) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.4e+131) {
		tmp = t_1;
	} else if (c <= -6.5e-177) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.25e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 4.8e+98) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 6.3e+106) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.4e+131:
		tmp = t_1
	elif c <= -6.5e-177:
		tmp = y * ((x * z) - (i * j))
	elif c <= 2.25e-82:
		tmp = a * ((b * i) - (x * t))
	elif c <= 4.8e+98:
		tmp = t * ((c * j) - (x * a))
	elif c <= 6.3e+106:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.4e+131)
		tmp = t_1;
	elseif (c <= -6.5e-177)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 2.25e-82)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 4.8e+98)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 6.3e+106)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.4e+131)
		tmp = t_1;
	elseif (c <= -6.5e-177)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 2.25e-82)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 4.8e+98)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 6.3e+106)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.4e+131], t$95$1, If[LessEqual[c, -6.5e-177], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.25e-82], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+98], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.3e+106], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.39999999999999986e131 or 6.29999999999999974e106 < c

   1. Initial program 64.7%

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

   2. Taylor expanded in c around inf 79.7%

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

      1. *-commutative 79.7%

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

   4. Simplified 79.7%

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

   if -3.39999999999999986e131 < c < -6.4999999999999998e-177

   1. Initial program 67.7%

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

   2. Taylor expanded in y around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

   4. Simplified 58.2%

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

   if -6.4999999999999998e-177 < c < 2.2499999999999999e-82

   1. Initial program 79.1%

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

   2. Taylor expanded in t around -inf 79.3%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in a around inf 59.0%

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

   if 2.2499999999999999e-82 < c < 4.7999999999999997e98

   1. Initial program 89.0%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

   4. Simplified 56.6%

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

   if 4.7999999999999997e98 < c < 6.29999999999999974e106

   1. Initial program 66.7%

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

   2. Taylor expanded in i around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. cancel-sign-sub-inv 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-lft-identity 100.0%

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

      5. +-commutative 100.0%

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

      6. mul-1-neg 100.0%

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

      7. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.25 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 16: 41.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= c -1.65e+134)
     (* j (* t c))
     (if (<= c -2.7e-55)
       t_1
       (if (<= c -5.6e-141)
         (* z (* x y))
         (if (<= c 4.8e+129)
           t_1
           (if (<= c 2.8e+228) (* t (* c j)) (* (* 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 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -1.65e+134) {
		tmp = j * (t * c);
	} else if (c <= -2.7e-55) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 4.8e+129) {
		tmp = t_1;
	} else if (c <= 2.8e+228) {
		tmp = t * (c * j);
	} else {
		tmp = (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 = a * ((b * i) - (x * t))
    if (c <= (-1.65d+134)) then
        tmp = j * (t * c)
    else if (c <= (-2.7d-55)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = z * (x * y)
    else if (c <= 4.8d+129) then
        tmp = t_1
    else if (c <= 2.8d+228) then
        tmp = t * (c * j)
    else
        tmp = (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 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -1.65e+134) {
		tmp = j * (t * c);
	} else if (c <= -2.7e-55) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 4.8e+129) {
		tmp = t_1;
	} else if (c <= 2.8e+228) {
		tmp = t * (c * j);
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if c <= -1.65e+134:
		tmp = j * (t * c)
	elif c <= -2.7e-55:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = z * (x * y)
	elif c <= 4.8e+129:
		tmp = t_1
	elif c <= 2.8e+228:
		tmp = t * (c * j)
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (c <= -1.65e+134)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -2.7e-55)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 4.8e+129)
		tmp = t_1;
	elseif (c <= 2.8e+228)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (c <= -1.65e+134)
		tmp = j * (t * c);
	elseif (c <= -2.7e-55)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = z * (x * y);
	elseif (c <= 4.8e+129)
		tmp = t_1;
	elseif (c <= 2.8e+228)
		tmp = t * (c * j);
	else
		tmp = (z * c) * -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[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+134], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.7e-55], t$95$1, If[LessEqual[c, -5.6e-141], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+129], t$95$1, If[LessEqual[c, 2.8e+228], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.65e134

   1. Initial program 47.7%

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

   2. Taylor expanded in t around -inf 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in z around 0 53.6%

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

   6. Taylor expanded in c around inf 45.2%

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

      1. associate-*r* 50.7%

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

      2. *-commutative 50.7%

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

      3. *-commutative 50.7%

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

   8. Simplified 50.7%

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

   if -1.65e134 < c < -2.70000000000000004e-55 or -5.60000000000000023e-141 < c < 4.7999999999999997e129

   1. Initial program 77.7%

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

   2. Taylor expanded in t around -inf 73.1%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in a around inf 49.6%

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

   if -2.70000000000000004e-55 < c < -5.60000000000000023e-141

   1. Initial program 66.6%

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

   2. Taylor expanded in z around inf 57.0%

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

   3. Taylor expanded in y around inf 56.9%

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

   if 4.7999999999999997e129 < c < 2.7999999999999999e228

   1. Initial program 68.4%

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

   2. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in t around inf 46.0%

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

      1. *-commutative 46.0%

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

      2. associate-*l* 47.7%

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

   7. Simplified 47.7%

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

   if 2.7999999999999999e228 < c

   1. Initial program 80.0%

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

   2. Taylor expanded in c around inf 88.2%

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

      1. *-commutative 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in t around 0 61.7%

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

      1. associate-*r* 61.7%

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

      2. neg-mul-1 61.7%

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

      3. associate-*r* 69.3%

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

      4. *-commutative 69.3%

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

   7. Simplified 69.3%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]

Alternative 17: 28.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-142}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))) (t_2 (* j (* y (- i)))))
   (if (<= y -5.5e+267)
     t_2
     (if (<= y -7.2e+124)
       (* z (* x y))
       (if (<= y -1.15e-307)
         t_1
         (if (<= y 4e-142)
           (* c (* b (- z)))
           (if (<= y 1.86e+121) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double t_2 = j * (y * -i);
	double tmp;
	if (y <= -5.5e+267) {
		tmp = t_2;
	} else if (y <= -7.2e+124) {
		tmp = z * (x * y);
	} else if (y <= -1.15e-307) {
		tmp = t_1;
	} else if (y <= 4e-142) {
		tmp = c * (b * -z);
	} else if (y <= 1.86e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (c * j)
    t_2 = j * (y * -i)
    if (y <= (-5.5d+267)) then
        tmp = t_2
    else if (y <= (-7.2d+124)) then
        tmp = z * (x * y)
    else if (y <= (-1.15d-307)) then
        tmp = t_1
    else if (y <= 4d-142) then
        tmp = c * (b * -z)
    else if (y <= 1.86d+121) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double t_2 = j * (y * -i);
	double tmp;
	if (y <= -5.5e+267) {
		tmp = t_2;
	} else if (y <= -7.2e+124) {
		tmp = z * (x * y);
	} else if (y <= -1.15e-307) {
		tmp = t_1;
	} else if (y <= 4e-142) {
		tmp = c * (b * -z);
	} else if (y <= 1.86e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	t_2 = j * (y * -i)
	tmp = 0
	if y <= -5.5e+267:
		tmp = t_2
	elif y <= -7.2e+124:
		tmp = z * (x * y)
	elif y <= -1.15e-307:
		tmp = t_1
	elif y <= 4e-142:
		tmp = c * (b * -z)
	elif y <= 1.86e+121:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	t_2 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (y <= -5.5e+267)
		tmp = t_2;
	elseif (y <= -7.2e+124)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -1.15e-307)
		tmp = t_1;
	elseif (y <= 4e-142)
		tmp = Float64(c * Float64(b * Float64(-z)));
	elseif (y <= 1.86e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	t_2 = j * (y * -i);
	tmp = 0.0;
	if (y <= -5.5e+267)
		tmp = t_2;
	elseif (y <= -7.2e+124)
		tmp = z * (x * y);
	elseif (y <= -1.15e-307)
		tmp = t_1;
	elseif (y <= 4e-142)
		tmp = c * (b * -z);
	elseif (y <= 1.86e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+267], t$95$2, If[LessEqual[y, -7.2e+124], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-307], t$95$1, If[LessEqual[y, 4e-142], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.86e+121], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.49999999999999985e267 or 1.86e121 < y

   1. Initial program 62.6%

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

   2. Taylor expanded in t around -inf 62.8%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in j around inf 57.3%

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

      1. distribute-lft-out-- 57.3%

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

      2. associate-*r* 57.3%

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

      3. mul-1-neg 57.3%

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

      4. *-commutative 57.3%

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

      5. *-commutative 57.3%

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

      6. *-commutative 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   10. Simplified 51.1%

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

   if -5.49999999999999985e267 < y < -7.19999999999999972e124

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf 56.7%

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

   3. Taylor expanded in y around inf 49.0%

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

   if -7.19999999999999972e124 < y < -1.1499999999999999e-307 or 4.0000000000000002e-142 < y < 1.86e121

   1. Initial program 72.0%

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

   2. Taylor expanded in c around inf 50.1%

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

      1. *-commutative 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in t around inf 32.9%

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

      1. *-commutative 32.9%

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

      2. associate-*l* 34.3%

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

   7. Simplified 34.3%

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

   if -1.1499999999999999e-307 < y < 4.0000000000000002e-142

   1. Initial program 92.5%

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

   2. Taylor expanded in c around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in t around 0 45.3%

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

      1. associate-*r* 45.3%

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

      2. neg-mul-1 45.3%

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

   7. Simplified 45.3%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+267}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-142}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]

Alternative 18: 28.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-141}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))) (t_2 (* j (* y (- i)))))
   (if (<= y -5.8e+267)
     t_2
     (if (<= y -7.4e+124)
       (* z (* x y))
       (if (<= y -2.4e-307)
         t_1
         (if (<= y 1.45e-141)
           (* (* z c) (- b))
           (if (<= y 4.2e+121) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double t_2 = j * (y * -i);
	double tmp;
	if (y <= -5.8e+267) {
		tmp = t_2;
	} else if (y <= -7.4e+124) {
		tmp = z * (x * y);
	} else if (y <= -2.4e-307) {
		tmp = t_1;
	} else if (y <= 1.45e-141) {
		tmp = (z * c) * -b;
	} else if (y <= 4.2e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (c * j)
    t_2 = j * (y * -i)
    if (y <= (-5.8d+267)) then
        tmp = t_2
    else if (y <= (-7.4d+124)) then
        tmp = z * (x * y)
    else if (y <= (-2.4d-307)) then
        tmp = t_1
    else if (y <= 1.45d-141) then
        tmp = (z * c) * -b
    else if (y <= 4.2d+121) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double t_2 = j * (y * -i);
	double tmp;
	if (y <= -5.8e+267) {
		tmp = t_2;
	} else if (y <= -7.4e+124) {
		tmp = z * (x * y);
	} else if (y <= -2.4e-307) {
		tmp = t_1;
	} else if (y <= 1.45e-141) {
		tmp = (z * c) * -b;
	} else if (y <= 4.2e+121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	t_2 = j * (y * -i)
	tmp = 0
	if y <= -5.8e+267:
		tmp = t_2
	elif y <= -7.4e+124:
		tmp = z * (x * y)
	elif y <= -2.4e-307:
		tmp = t_1
	elif y <= 1.45e-141:
		tmp = (z * c) * -b
	elif y <= 4.2e+121:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	t_2 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (y <= -5.8e+267)
		tmp = t_2;
	elseif (y <= -7.4e+124)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -2.4e-307)
		tmp = t_1;
	elseif (y <= 1.45e-141)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= 4.2e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	t_2 = j * (y * -i);
	tmp = 0.0;
	if (y <= -5.8e+267)
		tmp = t_2;
	elseif (y <= -7.4e+124)
		tmp = z * (x * y);
	elseif (y <= -2.4e-307)
		tmp = t_1;
	elseif (y <= 1.45e-141)
		tmp = (z * c) * -b;
	elseif (y <= 4.2e+121)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+267], t$95$2, If[LessEqual[y, -7.4e+124], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-307], t$95$1, If[LessEqual[y, 1.45e-141], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, 4.2e+121], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999966e267 or 4.2000000000000003e121 < y

   1. Initial program 62.6%

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

   2. Taylor expanded in t around -inf 62.8%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in j around inf 57.3%

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

      1. distribute-lft-out-- 57.3%

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

      2. associate-*r* 57.3%

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

      3. mul-1-neg 57.3%

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

      4. *-commutative 57.3%

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

      5. *-commutative 57.3%

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

      6. *-commutative 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   10. Simplified 51.1%

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

   if -5.79999999999999966e267 < y < -7.40000000000000016e124

   1. Initial program 63.1%

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

   2. Taylor expanded in z around inf 56.7%

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

   3. Taylor expanded in y around inf 49.0%

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

   if -7.40000000000000016e124 < y < -2.40000000000000018e-307 or 1.45e-141 < y < 4.2000000000000003e121

   1. Initial program 72.0%

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

   2. Taylor expanded in c around inf 50.1%

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

      1. *-commutative 50.1%

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

   4. Simplified 50.1%

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

   5. Taylor expanded in t around inf 32.9%

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

      1. *-commutative 32.9%

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

      2. associate-*l* 34.3%

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

   7. Simplified 34.3%

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

   if -2.40000000000000018e-307 < y < 1.45e-141

   1. Initial program 92.5%

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

   2. Taylor expanded in c around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in t around 0 45.3%

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

      1. associate-*r* 45.3%

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

      2. neg-mul-1 45.3%

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

      3. associate-*r* 45.4%

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

      4. *-commutative 45.4%

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

   7. Simplified 45.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+267}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-141}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]

Alternative 19: 49.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.9 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 15500000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -4.9e+29)
     t_1
     (if (<= c -5.6e-141)
       (* z (* x y))
       (if (<= c 15500000000000.0) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.9e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 15500000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-4.9d+29)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = z * (x * y)
    else if (c <= 15500000000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.9e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = z * (x * y);
	} else if (c <= 15500000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.9e+29:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = z * (x * y)
	elif c <= 15500000000000.0:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.9e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 15500000000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.9e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = z * (x * y);
	elseif (c <= 15500000000000.0)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.9e+29], t$95$1, If[LessEqual[c, -5.6e-141], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 15500000000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.9000000000000001e29 or 1.55e13 < c

   1. Initial program 67.5%

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

   2. Taylor expanded in c around inf 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   if -4.9000000000000001e29 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

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

   2. Taylor expanded in z around inf 49.7%

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

   3. Taylor expanded in y around inf 46.5%

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

   if -5.60000000000000023e-141 < c < 1.55e13

   1. Initial program 78.8%

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

   2. Taylor expanded in t around -inf 80.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in a around inf 54.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.9 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 15500000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 20: 29.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.6e+90)
   (* j (* t c))
   (if (<= c -3.5e-213)
     (* z (* x y))
     (if (<= c 1.16e-85) (* b (* a i)) (* t (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.6e+90) {
		tmp = j * (t * c);
	} else if (c <= -3.5e-213) {
		tmp = z * (x * y);
	} else if (c <= 1.16e-85) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-2.6d+90)) then
        tmp = j * (t * c)
    else if (c <= (-3.5d-213)) then
        tmp = z * (x * y)
    else if (c <= 1.16d-85) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.6e+90) {
		tmp = j * (t * c);
	} else if (c <= -3.5e-213) {
		tmp = z * (x * y);
	} else if (c <= 1.16e-85) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.6e+90:
		tmp = j * (t * c)
	elif c <= -3.5e-213:
		tmp = z * (x * y)
	elif c <= 1.16e-85:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.6e+90)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -3.5e-213)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.16e-85)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.6e+90)
		tmp = j * (t * c);
	elseif (c <= -3.5e-213)
		tmp = z * (x * y);
	elseif (c <= 1.16e-85)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.6e+90], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.5e-213], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.16e-85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.5999999999999998e90

   1. Initial program 47.0%

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

   2. Taylor expanded in t around -inf 54.1%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in z around 0 51.7%

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

   6. Taylor expanded in c around inf 40.6%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   if -2.5999999999999998e90 < c < -3.50000000000000017e-213

   1. Initial program 75.3%

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

   2. Taylor expanded in z around inf 48.6%

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

   3. Taylor expanded in y around inf 36.7%

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

   if -3.50000000000000017e-213 < c < 1.16e-85

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. sub-neg 77.7%

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

      3. sub-neg 77.7%

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

      4. *-commutative 77.7%

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

      5. fma-neg 77.7%

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

      6. *-commutative 77.7%

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

      7. *-commutative 77.7%

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

      8. fma-neg 77.7%

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

      9. distribute-lft-neg-out 77.7%

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

      10. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around inf 40.4%

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

   5. Taylor expanded in a around inf 38.9%

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

   if 1.16e-85 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in c around inf 66.4%

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

      1. *-commutative 66.4%

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

   4. Simplified 66.4%

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

   5. Taylor expanded in t around inf 35.9%

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

      1. *-commutative 35.9%

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

      2. associate-*l* 39.5%

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

   7. Simplified 39.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 21: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+43} \lor \neg \left(b \leq 1.25 \cdot 10^{+77}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.25e+43) (not (<= b 1.25e+77))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.25e+43) || !(b <= 1.25e+77)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.25d+43)) .or. (.not. (b <= 1.25d+77))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.25e+43) || !(b <= 1.25e+77)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.25e+43) or not (b <= 1.25e+77):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.25e+43) || !(b <= 1.25e+77))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.25e+43) || ~((b <= 1.25e+77)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.25e+43], N[Not[LessEqual[b, 1.25e+77]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2500000000000001e43 or 1.25000000000000001e77 < b

   1. Initial program 72.1%

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

      1. associate-+l- 72.1%

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

      2. sub-neg 72.1%

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

      3. sub-neg 72.1%

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

      4. *-commutative 72.1%

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

      5. fma-neg 72.1%

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

      6. *-commutative 72.1%

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

      7. *-commutative 72.1%

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

      8. fma-neg 72.1%

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

      9. distribute-lft-neg-out 72.1%

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

      10. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in b around inf 63.5%

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

   5. Taylor expanded in a around inf 34.9%

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

      1. associate-*r* 33.0%

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

      2. *-commutative 33.0%

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

      3. associate-*r* 35.2%

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

   7. Simplified 35.2%

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

   if -1.2500000000000001e43 < b < 1.25000000000000001e77

   1. Initial program 72.1%

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

   2. Taylor expanded in c around inf 42.9%

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

      1. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in t around inf 32.9%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+43} \lor \neg \left(b \leq 1.25 \cdot 10^{+77}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 22: 29.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.3e+99)
   (* i (* a b))
   (if (<= b 1.45e+77) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.3e+99) {
		tmp = i * (a * b);
	} else if (b <= 1.45e+77) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.3d+99)) then
        tmp = i * (a * b)
    else if (b <= 1.45d+77) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.3e+99) {
		tmp = i * (a * b);
	} else if (b <= 1.45e+77) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.3e+99:
		tmp = i * (a * b)
	elif b <= 1.45e+77:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.3e+99)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= 1.45e+77)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.3e+99)
		tmp = i * (a * b);
	elseif (b <= 1.45e+77)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.3e+99], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+77], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e99

   1. Initial program 76.2%

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

      1. associate-+l- 76.2%

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

      2. sub-neg 76.2%

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

      3. sub-neg 76.2%

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

      4. *-commutative 76.2%

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

      5. fma-neg 76.2%

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

      6. *-commutative 76.2%

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

      7. *-commutative 76.2%

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

      8. fma-neg 76.2%

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

      9. distribute-lft-neg-out 76.2%

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

      10. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in b around inf 56.8%

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

   5. Taylor expanded in a around inf 39.9%

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

   if -1.3e99 < b < 1.4500000000000001e77

   1. Initial program 70.9%

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

   2. Taylor expanded in c around inf 44.4%

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

      1. *-commutative 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in t around inf 31.8%

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

   if 1.4500000000000001e77 < b

   1. Initial program 72.8%

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

      1. associate-+l- 72.8%

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

      2. sub-neg 72.8%

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

      3. sub-neg 72.8%

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

      4. *-commutative 72.8%

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

      5. fma-neg 72.8%

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

      6. *-commutative 72.8%

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

      7. *-commutative 72.8%

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

      8. fma-neg 72.8%

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

      9. distribute-lft-neg-out 72.8%

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

      10. *-commutative 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in b around inf 73.3%

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

   5. Taylor expanded in a around inf 36.9%

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

      1. associate-*r* 38.7%

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

      2. *-commutative 38.7%

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

      3. associate-*r* 40.6%

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

   7. Simplified 40.6%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 23: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -5.6e+131)
   (* j (* t c))
   (if (<= c 5.7e-86) (* b (* a i)) (* t (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.6e+131) {
		tmp = j * (t * c);
	} else if (c <= 5.7e-86) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-5.6d+131)) then
        tmp = j * (t * c)
    else if (c <= 5.7d-86) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -5.6e+131) {
		tmp = j * (t * c);
	} else if (c <= 5.7e-86) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -5.6e+131:
		tmp = j * (t * c)
	elif c <= 5.7e-86:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -5.6e+131)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= 5.7e-86)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -5.6e+131)
		tmp = j * (t * c);
	elseif (c <= 5.7e-86)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -5.6e+131], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.7e-86], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.6000000000000001e131

   1. Initial program 47.7%

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

   2. Taylor expanded in t around -inf 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in z around 0 53.6%

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

   6. Taylor expanded in c around inf 45.2%

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

      1. associate-*r* 50.7%

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

      2. *-commutative 50.7%

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

      3. *-commutative 50.7%

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

   8. Simplified 50.7%

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

   if -5.6000000000000001e131 < c < 5.7000000000000004e-86

   1. Initial program 74.3%

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

      1. associate-+l- 74.3%

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

      2. sub-neg 74.3%

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

      3. sub-neg 74.3%

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

      4. *-commutative 74.3%

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

      5. fma-neg 74.3%

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

      6. *-commutative 74.3%

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

      7. *-commutative 74.3%

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

      8. fma-neg 75.1%

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

      9. distribute-lft-neg-out 75.1%

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

      10. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in b around inf 33.7%

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

   5. Taylor expanded in a around inf 27.5%

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

   if 5.7000000000000004e-86 < c

   1. Initial program 77.8%

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

   2. Taylor expanded in c around inf 66.4%

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

      1. *-commutative 66.4%

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

   4. Simplified 66.4%

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

   5. Taylor expanded in t around inf 35.9%

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

      1. *-commutative 35.9%

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

      2. associate-*l* 39.5%

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

   7. Simplified 39.5%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 24: 21.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.1%

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

   1. associate-+l- 72.1%

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

   2. sub-neg 72.1%

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

   3. sub-neg 72.1%

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

   4. *-commutative 72.1%

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

   5. fma-neg 72.1%

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

   6. *-commutative 72.1%

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

   7. *-commutative 72.1%

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

   8. fma-neg 72.8%

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

   9. distribute-lft-neg-out 72.8%

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

   10. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in b around inf 38.5%

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

5. Taylor expanded in a around inf 20.2%

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

   1. associate-*r* 20.5%

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

   2. *-commutative 20.5%

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

   3. associate-*r* 20.3%

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

7. Simplified 20.3%

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

8. Final simplification 20.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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