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

Percentage Accurate: 74.2% → 82.2%

Time: 19.2s

Alternatives: 20

Speedup: 0.7×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 0 28.0%

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

   5. Simplified 28.0%

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

   6. Taylor expanded in t around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

      4. *-commutative 52.6%

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

      5. *-commutative 52.6%

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

   8. Simplified 52.6%

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

4. Final simplification 84.5%

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

Alternative 2: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.1 \cdot 10^{+81} \lor \neg \left(j \leq 8.8 \cdot 10^{+154}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.1e+81) (not (<= j 8.8e+154)))
   (* j (- (* a c) (* y i)))
   (+
    (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i j))))
    (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.1e+81) || !(j <= 8.8e+154)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-6.1d+81)) .or. (.not. (j <= 8.8d+154))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.1e+81) || !(j <= 8.8e+154)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.1e+81) or not (j <= 8.8e+154):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.1e+81) || !(j <= 8.8e+154))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j)))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6.1e+81) || ~((j <= 8.8e+154)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = ((a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.1e+81], N[Not[LessEqual[j, 8.8e+154]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.10000000000000038e81 or 8.8000000000000004e154 < j

   1. Initial program 68.6%

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

   3. Taylor expanded in i around inf 66.0%

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

      1. associate-/l* 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in j around inf 79.3%

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

      1. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   if -6.10000000000000038e81 < j < 8.8000000000000004e154

   1. Initial program 76.6%

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

   3. Taylor expanded in y around 0 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.1 \cdot 10^{+81} \lor \neg \left(j \leq 8.8 \cdot 10^{+154}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - b \cdot \left(c \cdot \frac{z}{j}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -1.85e-38)
     t_1
     (if (<= z -7e-167)
       (* t (- (* b i) (* x a)))
       (if (<= z 2e-111)
         (* j (- (* a c) (* y i)))
         (if (<= z 1.7e+23) (* j (- (* a c) (* b (* c (/ z 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.85e-38) {
		tmp = t_1;
	} else if (z <= -7e-167) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 2e-111) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.7e+23) {
		tmp = j * ((a * c) - (b * (c * (z / 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 = z * ((x * y) - (b * c))
    if (z <= (-1.85d-38)) then
        tmp = t_1
    else if (z <= (-7d-167)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 2d-111) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 1.7d+23) then
        tmp = j * ((a * c) - (b * (c * (z / 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.85e-38) {
		tmp = t_1;
	} else if (z <= -7e-167) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 2e-111) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.7e+23) {
		tmp = j * ((a * c) - (b * (c * (z / j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.85e-38:
		tmp = t_1
	elif z <= -7e-167:
		tmp = t * ((b * i) - (x * a))
	elif z <= 2e-111:
		tmp = j * ((a * c) - (y * i))
	elif z <= 1.7e+23:
		tmp = j * ((a * c) - (b * (c * (z / j))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.85e-38)
		tmp = t_1;
	elseif (z <= -7e-167)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 2e-111)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 1.7e+23)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(b * Float64(c * Float64(z / 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 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.85e-38)
		tmp = t_1;
	elseif (z <= -7e-167)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 2e-111)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 1.7e+23)
		tmp = j * ((a * c) - (b * (c * (z / 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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-38], t$95$1, If[LessEqual[z, -7e-167], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-111], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+23], N[(j * N[(N[(a * c), $MachinePrecision] - N[(b * N[(c * N[(z / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.85e-38 or 1.69999999999999996e23 < z

   1. Initial program 66.4%

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

   3. Taylor expanded in z around inf 60.2%

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

      1. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if -1.85e-38 < z < -6.9999999999999998e-167

   1. Initial program 76.3%

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

   3. Taylor expanded in y around 0 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

   8. Simplified 78.5%

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

   if -6.9999999999999998e-167 < z < 2.00000000000000018e-111

   1. Initial program 87.1%

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

   3. Taylor expanded in i around inf 87.1%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in j around inf 59.9%

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

      1. *-commutative 59.9%

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

   8. Simplified 59.9%

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

   if 2.00000000000000018e-111 < z < 1.69999999999999996e23

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in c around inf 66.6%

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

      1. +-commutative 66.6%

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

      2. mul-1-neg 66.6%

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

      3. sub-neg 66.6%

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

      4. *-commutative 66.6%

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

      5. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in b around inf 49.9%

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

       1. +-commutative 49.9%

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

       2. mul-1-neg 49.9%

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

       3. unsub-neg 49.9%

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

       4. associate-/l* 49.9%

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

       5. *-commutative 49.9%

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

   11. Simplified 49.9%

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

   12. Taylor expanded in j around inf 65.9%

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

       1. +-commutative 65.9%

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

       2. mul-1-neg 65.9%

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

       3. unsub-neg 65.9%

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

       4. *-commutative 65.9%

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

       5. associate-/l* 65.8%

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

       6. associate-/l* 70.3%

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

   14. Simplified 70.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - b \cdot \left(c \cdot \frac{z}{j}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -1.7e-38)
     t_1
     (if (<= z -3.7e-168)
       (* t (- (* b i) (* x a)))
       (if (<= z 1.02e-112)
         (* j (- (* a c) (* y i)))
         (if (<= z 8.2e+82) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.7e-38) {
		tmp = t_1;
	} else if (z <= -3.7e-168) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 1.02e-112) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 8.2e+82) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-1.7d-38)) then
        tmp = t_1
    else if (z <= (-3.7d-168)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 1.02d-112) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 8.2d+82) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.7e-38) {
		tmp = t_1;
	} else if (z <= -3.7e-168) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 1.02e-112) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 8.2e+82) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.7e-38:
		tmp = t_1
	elif z <= -3.7e-168:
		tmp = t * ((b * i) - (x * a))
	elif z <= 1.02e-112:
		tmp = j * ((a * c) - (y * i))
	elif z <= 8.2e+82:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.7e-38)
		tmp = t_1;
	elseif (z <= -3.7e-168)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 1.02e-112)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 8.2e+82)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.7e-38)
		tmp = t_1;
	elseif (z <= -3.7e-168)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 1.02e-112)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 8.2e+82)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e-38], t$95$1, If[LessEqual[z, -3.7e-168], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-112], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+82], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7000000000000001e-38 or 8.1999999999999999e82 < z

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if -1.7000000000000001e-38 < z < -3.69999999999999997e-168

   1. Initial program 76.3%

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

   3. Taylor expanded in y around 0 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. *-commutative 78.5%

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

      5. *-commutative 78.5%

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

   8. Simplified 78.5%

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

   if -3.69999999999999997e-168 < z < 1.01999999999999996e-112

   1. Initial program 87.1%

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

   3. Taylor expanded in i around inf 87.1%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in j around inf 59.9%

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

      1. *-commutative 59.9%

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

   8. Simplified 59.9%

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

   if 1.01999999999999996e-112 < z < 8.1999999999999999e82

   1. Initial program 79.3%

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

   3. Taylor expanded in c around inf 65.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{-17} \lor \neg \left(b \leq 1.52 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -9.6e-17) (not (<= b 1.52e+28)))
   (- (* y (- (* x z) (* i j))) (* b (- (* z c) (* t i))))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -9.6e-17) || !(b <= 1.52e+28)) {
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (t * i)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-9.6d-17)) .or. (.not. (b <= 1.52d+28))) then
        tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (t * i)))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -9.6e-17) || !(b <= 1.52e+28)) {
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (t * i)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -9.6e-17) or not (b <= 1.52e+28):
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (t * i)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -9.6e-17) || !(b <= 1.52e+28))
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -9.6e-17) || ~((b <= 1.52e+28)))
		tmp = (y * ((x * z) - (i * j))) - (b * ((z * c) - (t * i)));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -9.6e-17], N[Not[LessEqual[b, 1.52e+28]], $MachinePrecision]], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.59999999999999945e-17 or 1.52000000000000009e28 < b

   1. Initial program 73.8%

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

   3. Taylor expanded in a around 0 66.3%

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

   5. Simplified 69.7%

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

   if -9.59999999999999945e-17 < b < 1.52000000000000009e28

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0 74.2%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{-17} \lor \neg \left(b \leq 1.52 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-15} \lor \neg \left(b \leq 2 \cdot 10^{+94}\right):\\ \;\;\;\;b \cdot \left(i \cdot \left(t - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.02e-15) (not (<= b 2e+94)))
   (* b (* i (- t (* c (/ z i)))))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.02e-15) || !(b <= 2e+94)) {
		tmp = b * (i * (t - (c * (z / i))));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.02d-15)) .or. (.not. (b <= 2d+94))) then
        tmp = b * (i * (t - (c * (z / i))))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.02e-15) || !(b <= 2e+94)) {
		tmp = b * (i * (t - (c * (z / i))));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.02e-15) or not (b <= 2e+94):
		tmp = b * (i * (t - (c * (z / i))))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.02e-15) || !(b <= 2e+94))
		tmp = Float64(b * Float64(i * Float64(t - Float64(c * Float64(z / i)))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.02e-15) || ~((b <= 2e+94)))
		tmp = b * (i * (t - (c * (z / i))));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.02e-15], N[Not[LessEqual[b, 2e+94]], $MachinePrecision]], N[(b * N[(i * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.02e-15 or 2e94 < b

   1. Initial program 73.0%

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

   3. Taylor expanded in i around inf 72.9%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in b around inf 69.4%

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

      1. associate-*r* 69.4%

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

      2. neg-mul-1 69.4%

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

      3. associate-/l* 69.4%

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

   8. Simplified 69.4%

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

   if -1.02e-15 < b < 2e94

   1. Initial program 75.0%

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

   3. Taylor expanded in b around 0 72.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-15} \lor \neg \left(b \leq 2 \cdot 10^{+94}\right):\\ \;\;\;\;b \cdot \left(i \cdot \left(t - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+140} \lor \neg \left(t \leq 4.5 \cdot 10^{+70}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -5.4e+140) (not (<= t 4.5e+70)))
   (* t (- (* b i) (* x a)))
   (+ (* a (- (* c j) (* x t))) (* y (- (* x z) (* i 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 ((t <= -5.4e+140) || !(t <= 4.5e+70)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * 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 ((t <= (-5.4d+140)) .or. (.not. (t <= 4.5d+70))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * 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 ((t <= -5.4e+140) || !(t <= 4.5e+70)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -5.4e+140) or not (t <= 4.5e+70):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -5.4e+140) || !(t <= 4.5e+70))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -5.4e+140) || ~((t <= 4.5e+70)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (a * ((c * j) - (x * t))) + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -5.4e+140], N[Not[LessEqual[t, 4.5e+70]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.40000000000000036e140 or 4.4999999999999999e70 < t

   1. Initial program 56.0%

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

   3. Taylor expanded in y around 0 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in t around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. *-commutative 72.5%

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

   8. Simplified 72.5%

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

   if -5.40000000000000036e140 < t < 4.4999999999999999e70

   1. Initial program 81.3%

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

   3. Taylor expanded in y around 0 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in b around 0 67.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+140} \lor \neg \left(t \leq 4.5 \cdot 10^{+70}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3e-38)
   (* y (* x z))
   (if (<= z -1.15e-134)
     (* t (* b i))
     (if (<= z 5.4e+25)
       (* a (* c j))
       (if (<= z 6.6e+59) (* c (* z (- b))) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3e-38) {
		tmp = y * (x * z);
	} else if (z <= -1.15e-134) {
		tmp = t * (b * i);
	} else if (z <= 5.4e+25) {
		tmp = a * (c * j);
	} else if (z <= 6.6e+59) {
		tmp = c * (z * -b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3d-38)) then
        tmp = y * (x * z)
    else if (z <= (-1.15d-134)) then
        tmp = t * (b * i)
    else if (z <= 5.4d+25) then
        tmp = a * (c * j)
    else if (z <= 6.6d+59) then
        tmp = c * (z * -b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3e-38) {
		tmp = y * (x * z);
	} else if (z <= -1.15e-134) {
		tmp = t * (b * i);
	} else if (z <= 5.4e+25) {
		tmp = a * (c * j);
	} else if (z <= 6.6e+59) {
		tmp = c * (z * -b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3e-38:
		tmp = y * (x * z)
	elif z <= -1.15e-134:
		tmp = t * (b * i)
	elif z <= 5.4e+25:
		tmp = a * (c * j)
	elif z <= 6.6e+59:
		tmp = c * (z * -b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3e-38)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -1.15e-134)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 5.4e+25)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 6.6e+59)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3e-38)
		tmp = y * (x * z);
	elseif (z <= -1.15e-134)
		tmp = t * (b * i);
	elseif (z <= 5.4e+25)
		tmp = a * (c * j);
	elseif (z <= 6.6e+59)
		tmp = c * (z * -b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3e-38], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-134], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+25], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+59], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.99999999999999989e-38

   1. Initial program 67.6%

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

   3. Taylor expanded in y around 0 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in z around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. sub-neg 57.8%

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

      4. *-commutative 57.8%

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

      5. *-commutative 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in y around inf 42.0%

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

       1. *-commutative 42.0%

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

       2. associate-*r* 45.7%

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

   11. Simplified 45.7%

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

   if -2.99999999999999989e-38 < z < -1.15e-134

   1. Initial program 72.6%

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

   3. Taylor expanded in i around inf 51.7%

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

      1. distribute-lft-out-- 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in j around 0 47.1%

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

      1. associate-*r* 51.0%

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

      2. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   if -1.15e-134 < z < 5.4e25

   1. Initial program 85.1%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   if 5.4e25 < z < 6.5999999999999999e59

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in c around inf 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. sub-neg 85.9%

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

      4. *-commutative 85.9%

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

      5. *-commutative 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in j around 0 85.9%

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

       1. mul-1-neg 85.9%

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

       2. *-commutative 85.9%

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

       3. distribute-rgt-neg-in 85.9%

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

   11. Simplified 85.9%

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

   if 6.5999999999999999e59 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in i around 0 62.2%

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

   4. Taylor expanded in a around 0 62.2%

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

   5. Taylor expanded in y around inf 49.2%

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

      1. *-commutative 49.2%

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

   7. Simplified 49.2%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-15} \lor \neg \left(b \leq 3 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot \left(i \cdot \left(t - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.02e-15) (not (<= b 3e+50)))
   (* b (* i (- t (* c (/ z i)))))
   (+ (* x (- (* y z) (* t a))) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.02e-15) || !(b <= 3e+50)) {
		tmp = b * (i * (t - (c * (z / i))));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.02d-15)) .or. (.not. (b <= 3d+50))) then
        tmp = b * (i * (t - (c * (z / i))))
    else
        tmp = (x * ((y * z) - (t * a))) + (a * (c * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.02e-15) || !(b <= 3e+50)) {
		tmp = b * (i * (t - (c * (z / i))));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.02e-15) or not (b <= 3e+50):
		tmp = b * (i * (t - (c * (z / i))))
	else:
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.02e-15) || !(b <= 3e+50))
		tmp = Float64(b * Float64(i * Float64(t - Float64(c * Float64(z / i)))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(a * Float64(c * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.02e-15) || ~((b <= 3e+50)))
		tmp = b * (i * (t - (c * (z / i))));
	else
		tmp = (x * ((y * z) - (t * a))) + (a * (c * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.02e-15], N[Not[LessEqual[b, 3e+50]], $MachinePrecision]], N[(b * N[(i * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.02e-15 or 2.9999999999999998e50 < b

   1. Initial program 73.8%

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

   3. Taylor expanded in i around inf 72.8%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in b around inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. neg-mul-1 67.8%

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

      3. associate-/l* 67.8%

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

   8. Simplified 67.8%

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

   if -1.02e-15 < b < 2.9999999999999998e50

   1. Initial program 74.5%

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

   3. Taylor expanded in i around 0 65.7%

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

   4. Taylor expanded in b around 0 65.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-15} \lor \neg \left(b \leq 3 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot \left(i \cdot \left(t - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-90}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -3.8e+87)
     t_1
     (if (<= j -6e-90)
       (* c (- (* a j) (* z b)))
       (if (<= j 2.8e+21) (* x (- (* y z) (* t a))) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8e+87) {
		tmp = t_1;
	} else if (j <= -6e-90) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 2.8e+21) {
		tmp = x * ((y * z) - (t * a));
	} 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 = j * ((a * c) - (y * i))
    if (j <= (-3.8d+87)) then
        tmp = t_1
    else if (j <= (-6d-90)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 2.8d+21) then
        tmp = x * ((y * z) - (t * a))
    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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8e+87) {
		tmp = t_1;
	} else if (j <= -6e-90) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 2.8e+21) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.8e+87:
		tmp = t_1
	elif j <= -6e-90:
		tmp = c * ((a * j) - (z * b))
	elif j <= 2.8e+21:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.8e+87)
		tmp = t_1;
	elseif (j <= -6e-90)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 2.8e+21)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.8e+87)
		tmp = t_1;
	elseif (j <= -6e-90)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 2.8e+21)
		tmp = x * ((y * z) - (t * a));
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e+87], t$95$1, If[LessEqual[j, -6e-90], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e+21], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.80000000000000011e87 or 2.8e21 < j

   1. Initial program 73.9%

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

   3. Taylor expanded in i around inf 71.1%

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

      1. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in j around inf 71.4%

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

      1. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   if -3.80000000000000011e87 < j < -6.00000000000000041e-90

   1. Initial program 73.4%

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

   3. Taylor expanded in c around inf 51.0%

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

   if -6.00000000000000041e-90 < j < 2.8e21

   1. Initial program 74.7%

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

   3. Taylor expanded in y around 0 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. sub-neg 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-90}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.4 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -4.4e+90)
     t_1
     (if (<= i -2.8e-86)
       (* x (* y z))
       (if (<= i 6e+40) (* c (- (* a j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.4e+90) {
		tmp = t_1;
	} else if (i <= -2.8e-86) {
		tmp = x * (y * z);
	} else if (i <= 6e+40) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-4.4d+90)) then
        tmp = t_1
    else if (i <= (-2.8d-86)) then
        tmp = x * (y * z)
    else if (i <= 6d+40) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.4e+90) {
		tmp = t_1;
	} else if (i <= -2.8e-86) {
		tmp = x * (y * z);
	} else if (i <= 6e+40) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.4e+90:
		tmp = t_1
	elif i <= -2.8e-86:
		tmp = x * (y * z)
	elif i <= 6e+40:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.4e+90)
		tmp = t_1;
	elseif (i <= -2.8e-86)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 6e+40)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.4e+90)
		tmp = t_1;
	elseif (i <= -2.8e-86)
		tmp = x * (y * z);
	elseif (i <= 6e+40)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.4e+90], t$95$1, If[LessEqual[i, -2.8e-86], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e+40], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.39999999999999981e90 or 6.0000000000000004e40 < i

   1. Initial program 61.9%

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

   3. Taylor expanded in y around 0 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in i around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. *-commutative 66.0%

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

      3. mul-1-neg 66.0%

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

      4. unsub-neg 66.0%

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

      5. *-commutative 66.0%

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

   8. Simplified 66.0%

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

   if -4.39999999999999981e90 < i < -2.80000000000000009e-86

   1. Initial program 80.3%

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

   3. Taylor expanded in i around 0 65.0%

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

   4. Taylor expanded in a around 0 61.7%

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

   5. Taylor expanded in y around inf 52.2%

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

      1. *-commutative 52.2%

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

   7. Simplified 52.2%

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

   if -2.80000000000000009e-86 < i < 6.0000000000000004e40

   1. Initial program 83.0%

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

   3. Taylor expanded in c around inf 52.9%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+90}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2e-39)
   (* y (* x z))
   (if (<= z -6e-135)
     (* t (* b i))
     (if (<= z 6.8e+43) (* a (* c j)) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2e-39) {
		tmp = y * (x * z);
	} else if (z <= -6e-135) {
		tmp = t * (b * i);
	} else if (z <= 6.8e+43) {
		tmp = a * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2d-39)) then
        tmp = y * (x * z)
    else if (z <= (-6d-135)) then
        tmp = t * (b * i)
    else if (z <= 6.8d+43) then
        tmp = a * (c * j)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2e-39) {
		tmp = y * (x * z);
	} else if (z <= -6e-135) {
		tmp = t * (b * i);
	} else if (z <= 6.8e+43) {
		tmp = a * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2e-39:
		tmp = y * (x * z)
	elif z <= -6e-135:
		tmp = t * (b * i)
	elif z <= 6.8e+43:
		tmp = a * (c * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2e-39)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -6e-135)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 6.8e+43)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2e-39)
		tmp = y * (x * z);
	elseif (z <= -6e-135)
		tmp = t * (b * i);
	elseif (z <= 6.8e+43)
		tmp = a * (c * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2e-39], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-135], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+43], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999986e-39

   1. Initial program 67.6%

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

   3. Taylor expanded in y around 0 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in z around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. sub-neg 57.8%

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

      4. *-commutative 57.8%

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

      5. *-commutative 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in y around inf 42.0%

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

       1. *-commutative 42.0%

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

       2. associate-*r* 45.7%

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

   11. Simplified 45.7%

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

   if -1.99999999999999986e-39 < z < -6.00000000000000024e-135

   1. Initial program 72.6%

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

   3. Taylor expanded in i around inf 51.7%

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

      1. distribute-lft-out-- 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in j around 0 47.1%

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

      1. associate-*r* 51.0%

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

      2. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   if -6.00000000000000024e-135 < z < 6.80000000000000024e43

   1. Initial program 85.8%

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

   3. Taylor expanded in a around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in c around inf 35.6%

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

      1. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if 6.80000000000000024e43 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in i around 0 63.6%

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

   4. Taylor expanded in a around 0 63.6%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

   7. Simplified 48.6%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-134}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.3e-38)
   (* y (* x z))
   (if (<= z -1e-134)
     (* b (* t i))
     (if (<= z 1.12e+45) (* a (* c j)) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e-38) {
		tmp = y * (x * z);
	} else if (z <= -1e-134) {
		tmp = b * (t * i);
	} else if (z <= 1.12e+45) {
		tmp = a * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.3d-38)) then
        tmp = y * (x * z)
    else if (z <= (-1d-134)) then
        tmp = b * (t * i)
    else if (z <= 1.12d+45) then
        tmp = a * (c * j)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.3e-38) {
		tmp = y * (x * z);
	} else if (z <= -1e-134) {
		tmp = b * (t * i);
	} else if (z <= 1.12e+45) {
		tmp = a * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.3e-38:
		tmp = y * (x * z)
	elif z <= -1e-134:
		tmp = b * (t * i)
	elif z <= 1.12e+45:
		tmp = a * (c * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.3e-38)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -1e-134)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 1.12e+45)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.3e-38)
		tmp = y * (x * z);
	elseif (z <= -1e-134)
		tmp = b * (t * i);
	elseif (z <= 1.12e+45)
		tmp = a * (c * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.3e-38], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-134], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+45], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.30000000000000002e-38

   1. Initial program 67.6%

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

   3. Taylor expanded in y around 0 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in z around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. sub-neg 57.8%

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

      4. *-commutative 57.8%

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

      5. *-commutative 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in y around inf 42.0%

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

       1. *-commutative 42.0%

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

       2. associate-*r* 45.7%

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

   11. Simplified 45.7%

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

   if -2.30000000000000002e-38 < z < -1.00000000000000004e-134

   1. Initial program 72.6%

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

   3. Taylor expanded in i around inf 51.7%

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

      1. distribute-lft-out-- 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in j around 0 47.1%

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

   if -1.00000000000000004e-134 < z < 1.12e45

   1. Initial program 85.8%

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

   3. Taylor expanded in a around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in c around inf 35.6%

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

      1. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if 1.12e45 < z

   1. Initial program 61.4%

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

   3. Taylor expanded in i around 0 63.6%

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

   4. Taylor expanded in a around 0 63.6%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

   7. Simplified 48.6%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-134}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -3.5e-38)
     t_1
     (if (<= z -1.05e-134)
       (* b (* t i))
       (if (<= z 4.2e+43) (* a (* c 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 = x * (y * z);
	double tmp;
	if (z <= -3.5e-38) {
		tmp = t_1;
	} else if (z <= -1.05e-134) {
		tmp = b * (t * i);
	} else if (z <= 4.2e+43) {
		tmp = a * (c * 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 = x * (y * z)
    if (z <= (-3.5d-38)) then
        tmp = t_1
    else if (z <= (-1.05d-134)) then
        tmp = b * (t * i)
    else if (z <= 4.2d+43) then
        tmp = a * (c * 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 = x * (y * z);
	double tmp;
	if (z <= -3.5e-38) {
		tmp = t_1;
	} else if (z <= -1.05e-134) {
		tmp = b * (t * i);
	} else if (z <= 4.2e+43) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -3.5e-38:
		tmp = t_1
	elif z <= -1.05e-134:
		tmp = b * (t * i)
	elif z <= 4.2e+43:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -3.5e-38)
		tmp = t_1;
	elseif (z <= -1.05e-134)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 4.2e+43)
		tmp = Float64(a * Float64(c * 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 = x * (y * z);
	tmp = 0.0;
	if (z <= -3.5e-38)
		tmp = t_1;
	elseif (z <= -1.05e-134)
		tmp = b * (t * i);
	elseif (z <= 4.2e+43)
		tmp = a * (c * 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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-38], t$95$1, If[LessEqual[z, -1.05e-134], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+43], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000001e-38 or 4.20000000000000003e43 < z

   1. Initial program 65.1%

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

   3. Taylor expanded in i around 0 63.9%

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

   4. Taylor expanded in a around 0 60.7%

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

   5. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

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

   7. Simplified 44.7%

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

   if -3.5000000000000001e-38 < z < -1.05e-134

   1. Initial program 72.6%

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

   3. Taylor expanded in i around inf 51.7%

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

      1. distribute-lft-out-- 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in j around 0 47.1%

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

   if -1.05e-134 < z < 4.20000000000000003e43

   1. Initial program 85.8%

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

   3. Taylor expanded in a around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in c around inf 35.6%

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

      1. *-commutative 35.6%

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

   8. Simplified 35.6%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-134}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+80} \lor \neg \left(b \leq 3 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.6e+80) (not (<= b 3e+50)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.6e+80) || !(b <= 3e+50)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.6d+80)) .or. (.not. (b <= 3d+50))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.6e+80) || !(b <= 3e+50)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.6e+80) or not (b <= 3e+50):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.6e+80) || !(b <= 3e+50))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.6e+80) || ~((b <= 3e+50)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.6e+80], N[Not[LessEqual[b, 3e+50]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.59999999999999995e80 or 2.9999999999999998e50 < b

   1. Initial program 73.0%

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

   3. Taylor expanded in b around inf 67.2%

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

      1. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -3.59999999999999995e80 < b < 2.9999999999999998e50

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

   5. Simplified 43.6%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+80} \lor \neg \left(b \leq 3 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.2e-40)
   (* y (* x z))
   (if (<= z 2.8e+89) (* a (- (* c j) (* x t))) (* x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.2e-40) {
		tmp = y * (x * z);
	} else if (z <= 2.8e+89) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.2d-40)) then
        tmp = y * (x * z)
    else if (z <= 2.8d+89) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.2e-40) {
		tmp = y * (x * z);
	} else if (z <= 2.8e+89) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.2e-40:
		tmp = y * (x * z)
	elif z <= 2.8e+89:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.2e-40)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 2.8e+89)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.2e-40)
		tmp = y * (x * z);
	elseif (z <= 2.8e+89)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.2e-40], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+89], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000009e-40

   1. Initial program 68.0%

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

   3. Taylor expanded in y around 0 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in z around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

      3. sub-neg 57.1%

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

      4. *-commutative 57.1%

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

      5. *-commutative 57.1%

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

   8. Simplified 57.1%

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

   9. Taylor expanded in y around inf 41.5%

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

       1. *-commutative 41.5%

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

       2. associate-*r* 45.1%

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

   11. Simplified 45.1%

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

   if -2.20000000000000009e-40 < z < 2.7999999999999998e89

   1. Initial program 82.6%

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

   3. Taylor expanded in a around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. mul-1-neg 47.4%

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

      3. unsub-neg 47.4%

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

   5. Simplified 47.4%

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

   if 2.7999999999999998e89 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in i around 0 64.6%

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

   4. Taylor expanded in a around 0 62.4%

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

   5. Taylor expanded in y around inf 52.2%

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

      1. *-commutative 52.2%

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

   7. Simplified 52.2%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+109} \lor \neg \left(c \leq 1.85 \cdot 10^{+121}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.15e+109) (not (<= c 1.85e+121)))
   (* j (* a c))
   (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.15e+109) || !(c <= 1.85e+121)) {
		tmp = j * (a * c);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.15d+109)) .or. (.not. (c <= 1.85d+121))) then
        tmp = j * (a * c)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.15e+109) || !(c <= 1.85e+121)) {
		tmp = j * (a * c);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.15e+109) or not (c <= 1.85e+121):
		tmp = j * (a * c)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.15e+109) || !(c <= 1.85e+121))
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.15e+109) || ~((c <= 1.85e+121)))
		tmp = j * (a * c);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.15e+109], N[Not[LessEqual[c, 1.85e+121]], $MachinePrecision]], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.15000000000000005e109 or 1.85000000000000006e121 < c

   1. Initial program 66.4%

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

   3. Taylor expanded in a around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in c around inf 52.3%

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

      1. associate-*r* 54.4%

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

      2. *-commutative 54.4%

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

   8. Simplified 54.4%

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

   if -1.15000000000000005e109 < c < 1.85000000000000006e121

   1. Initial program 77.9%

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

   3. Taylor expanded in i around inf 43.7%

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

      1. distribute-lft-out-- 43.7%

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

      2. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in j around 0 25.2%

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

      1. pow1 25.2%

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

   8. Applied egg-rr 25.2%

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

      1. unpow1 25.2%

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

      2. associate-*r* 26.8%

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

      3. *-commutative 26.8%

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

      4. associate-*r* 25.8%

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

   10. Simplified 25.8%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+109} \lor \neg \left(c \leq 1.85 \cdot 10^{+121}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+108} \lor \neg \left(c \leq 2.2 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.8e+108) (not (<= c 2.2e+125))) (* a (* c j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.8e+108) || !(c <= 2.2e+125)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.8d+108)) .or. (.not. (c <= 2.2d+125))) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.8e+108) || !(c <= 2.2e+125)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.8e+108) or not (c <= 2.2e+125):
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.8e+108) || !(c <= 2.2e+125))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.8e+108) || ~((c <= 2.2e+125)))
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.8e+108], N[Not[LessEqual[c, 2.2e+125]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.80000000000000008e108 or 2.19999999999999991e125 < c

   1. Initial program 66.4%

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

   3. Taylor expanded in a around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in c around inf 52.3%

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

      1. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   if -3.80000000000000008e108 < c < 2.19999999999999991e125

   1. Initial program 77.9%

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

   3. Taylor expanded in i around inf 43.7%

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

      1. distribute-lft-out-- 43.7%

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

      2. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in j around 0 25.2%

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

      1. pow1 25.2%

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

   8. Applied egg-rr 25.2%

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

      1. unpow1 25.2%

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

      2. associate-*r* 26.8%

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

      3. *-commutative 26.8%

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

      4. associate-*r* 25.8%

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

   10. Simplified 25.8%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+108} \lor \neg \left(c \leq 2.2 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.85 \cdot 10^{+110} \lor \neg \left(c \leq 1.65 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.85e+110) (not (<= c 1.65e+125)))
   (* a (* c j))
   (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.85e+110) || !(c <= 1.65e+125)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.85d+110)) .or. (.not. (c <= 1.65d+125))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.85e+110) || !(c <= 1.65e+125)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.85e+110) or not (c <= 1.65e+125):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.85e+110) || !(c <= 1.65e+125))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.85e+110) || ~((c <= 1.65e+125)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.85e+110], N[Not[LessEqual[c, 1.65e+125]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.8500000000000001e110 or 1.65000000000000003e125 < c

   1. Initial program 66.4%

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

   3. Taylor expanded in a around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in c around inf 52.3%

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

      1. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   if -2.8500000000000001e110 < c < 1.65000000000000003e125

   1. Initial program 77.9%

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

   3. Taylor expanded in i around inf 43.7%

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

      1. distribute-lft-out-- 43.7%

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

      2. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in j around 0 25.2%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.85 \cdot 10^{+110} \lor \neg \left(c \leq 1.65 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.2%

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

3. Taylor expanded in a around inf 37.3%

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

   1. +-commutative 37.3%

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

   2. mul-1-neg 37.3%

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

   3. unsub-neg 37.3%

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

5. Simplified 37.3%

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

6. Taylor expanded in c around inf 23.8%

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

   1. *-commutative 23.8%

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

8. Simplified 23.8%

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

9. Final simplification 23.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 59.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

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