Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 95.6% → 98.4%

Time: 8.1s

Alternatives: 12

Speedup: 0.8×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \lor \neg \left(z \leq 1.55 \cdot 10^{+17}\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.06) (not (<= z 1.55e+17)))
   (* (+ y -1.0) (* z x))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.06) || !(z <= 1.55e+17)) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.06d0)) .or. (.not. (z <= 1.55d+17))) then
        tmp = (y + (-1.0d0)) * (z * x)
    else
        tmp = x * (1.0d0 + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.06) || !(z <= 1.55e+17)) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.06) or not (z <= 1.55e+17):
		tmp = (y + -1.0) * (z * x)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.06) || !(z <= 1.55e+17))
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.06) || ~((z <= 1.55e+17)))
		tmp = (y + -1.0) * (z * x);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.06], N[Not[LessEqual[z, 1.55e+17]], $MachinePrecision]], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0600000000000001 or 1.55e17 < z

   1. Initial program 89.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. distribute-rgt-in 89.6%

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

      4. *-un-lft-identity 89.6%

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

   3. Applied egg-rr 89.6%

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

   4. Taylor expanded in x around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. *-commutative 89.6%

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

      3. sub-neg 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in z around inf 89.5%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

   9. Simplified 99.8%

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

   if -1.0600000000000001 < z < 1.55e17

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in y around inf 98.5%

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

      1. *-commutative 98.5%

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

   5. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. distribute-rgt1-in 98.5%

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

   7. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{\left(z \cdot y + 1\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \lor \neg \left(z \leq 1.55 \cdot 10^{+17}\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 2: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -3.2e+185)
     t_0
     (if (<= z -1.1e+153)
       t_1
       (if (<= z -5.1e+95)
         t_0
         (if (<= z -6.8e-69)
           t_1
           (if (<= z 6.8e-13) x (if (<= z 5.5e+88) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -3.2e+185) {
		tmp = t_0;
	} else if (z <= -1.1e+153) {
		tmp = t_1;
	} else if (z <= -5.1e+95) {
		tmp = t_0;
	} else if (z <= -6.8e-69) {
		tmp = t_1;
	} else if (z <= 6.8e-13) {
		tmp = x;
	} else if (z <= 5.5e+88) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * -x
    t_1 = x * (y * z)
    if (z <= (-3.2d+185)) then
        tmp = t_0
    else if (z <= (-1.1d+153)) then
        tmp = t_1
    else if (z <= (-5.1d+95)) then
        tmp = t_0
    else if (z <= (-6.8d-69)) then
        tmp = t_1
    else if (z <= 6.8d-13) then
        tmp = x
    else if (z <= 5.5d+88) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -3.2e+185) {
		tmp = t_0;
	} else if (z <= -1.1e+153) {
		tmp = t_1;
	} else if (z <= -5.1e+95) {
		tmp = t_0;
	} else if (z <= -6.8e-69) {
		tmp = t_1;
	} else if (z <= 6.8e-13) {
		tmp = x;
	} else if (z <= 5.5e+88) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -3.2e+185:
		tmp = t_0
	elif z <= -1.1e+153:
		tmp = t_1
	elif z <= -5.1e+95:
		tmp = t_0
	elif z <= -6.8e-69:
		tmp = t_1
	elif z <= 6.8e-13:
		tmp = x
	elif z <= 5.5e+88:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -3.2e+185)
		tmp = t_0;
	elseif (z <= -1.1e+153)
		tmp = t_1;
	elseif (z <= -5.1e+95)
		tmp = t_0;
	elseif (z <= -6.8e-69)
		tmp = t_1;
	elseif (z <= 6.8e-13)
		tmp = x;
	elseif (z <= 5.5e+88)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -3.2e+185)
		tmp = t_0;
	elseif (z <= -1.1e+153)
		tmp = t_1;
	elseif (z <= -5.1e+95)
		tmp = t_0;
	elseif (z <= -6.8e-69)
		tmp = t_1;
	elseif (z <= 6.8e-13)
		tmp = x;
	elseif (z <= 5.5e+88)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+185], t$95$0, If[LessEqual[z, -1.1e+153], t$95$1, If[LessEqual[z, -5.1e+95], t$95$0, If[LessEqual[z, -6.8e-69], t$95$1, If[LessEqual[z, 6.8e-13], x, If[LessEqual[z, 5.5e+88], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000006e185 or -1.1e153 < z < -5.10000000000000003e95 or 5.5e88 < z

   1. Initial program 88.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 69.8%

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

      1. neg-mul-1 69.8%

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

   7. Simplified 69.8%

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

   if -3.20000000000000006e185 < z < -1.1e153 or -5.10000000000000003e95 < z < -6.80000000000000016e-69 or 6.80000000000000031e-13 < z < 5.5e88

   1. Initial program 94.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 67.5%

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

      1. *-commutative 67.5%

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

   4. Simplified 67.5%

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

   if -6.80000000000000016e-69 < z < 6.80000000000000031e-13

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 77.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -2 \cdot 10^{+197}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot z - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -2e+197)
   (* (+ y -1.0) (* z x))
   (* x (+ 1.0 (- (* y z) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -2e+197) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + ((y * z) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= (-2d+197)) then
        tmp = (y + (-1.0d0)) * (z * x)
    else
        tmp = x * (1.0d0 + ((y * z) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -2e+197) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + ((y * z) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -2e+197:
		tmp = (y + -1.0) * (z * x)
	else:
		tmp = x * (1.0 + ((y * z) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -2e+197)
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y * z) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -2e+197)
		tmp = (y + -1.0) * (z * x);
	else
		tmp = x * (1.0 + ((y * z) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -2e+197], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -1.9999999999999999e197

   1. Initial program 79.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.7%

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

      2. sub-neg 79.7%

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

      3. distribute-rgt-in 79.8%

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

      4. *-un-lft-identity 79.8%

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

   3. Applied egg-rr 79.8%

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

   4. Taylor expanded in x around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. *-commutative 79.8%

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

      3. sub-neg 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in z around inf 79.7%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   9. Simplified 100.0%

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

   if -1.9999999999999999e197 < (*.f64 (-.f64 1 y) z)

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 98.6%

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

      2. sub-neg 98.6%

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

      3. distribute-rgt-in 98.6%

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

      4. *-un-lft-identity 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in x around 0 98.6%

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

      1. mul-1-neg 98.6%

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

      2. *-commutative 98.6%

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

      3. sub-neg 98.6%

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

   6. Simplified 98.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \left(z - z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -2 \cdot 10^{+197}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot z - z\right)\right)\\ \end{array} \]

Alternative 4: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+67)
   (* (+ y -1.0) (* z x))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+67) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= (-1d+67)) then
        tmp = (y + (-1.0d0)) * (z * x)
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+67) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+67:
		tmp = (y + -1.0) * (z * x)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -1e+67)
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -1e+67)
		tmp = (y + -1.0) * (z * x);
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -1e+67], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -9.99999999999999983e66

   1. Initial program 85.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 85.3%

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

      2. sub-neg 85.3%

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

      3. distribute-rgt-in 85.3%

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

      4. *-un-lft-identity 85.3%

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

   3. Applied egg-rr 85.3%

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

   4. Taylor expanded in x around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. *-commutative 85.3%

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

      3. sub-neg 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in z around inf 85.3%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   9. Simplified 99.9%

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

   if -9.99999999999999983e66 < (*.f64 (-.f64 1 y) z)

   1. Initial program 98.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+67}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 5: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-67} \lor \neg \left(z \leq 4.8 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.2e-67) (not (<= z 4.8e-13)))
   (* z (* (+ y -1.0) x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.2e-67) || !(z <= 4.8e-13)) {
		tmp = z * ((y + -1.0) * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.2d-67)) .or. (.not. (z <= 4.8d-13))) then
        tmp = z * ((y + (-1.0d0)) * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.2e-67) || !(z <= 4.8e-13)) {
		tmp = z * ((y + -1.0) * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.2e-67) or not (z <= 4.8e-13):
		tmp = z * ((y + -1.0) * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.2e-67) || !(z <= 4.8e-13))
		tmp = Float64(z * Float64(Float64(y + -1.0) * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.2e-67) || ~((z <= 4.8e-13)))
		tmp = z * ((y + -1.0) * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.2e-67], N[Not[LessEqual[z, 4.8e-13]], $MachinePrecision]], N[(z * N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999998e-67 or 4.7999999999999997e-13 < z

   1. Initial program 91.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*r* 94.6%

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

      3. *-commutative 94.6%

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

      4. sub-neg 94.6%

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

      5. metadata-eval 94.6%

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

   4. Simplified 94.6%

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

   if -7.19999999999999998e-67 < z < 4.7999999999999997e-13

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 77.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-67} \lor \neg \left(z \leq 4.8 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 6: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{-65} \lor \neg \left(z \leq 2.1 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.9e-65) (not (<= z 2.1e-11)))
   (* z (- (* y x) x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.9e-65) || !(z <= 2.1e-11)) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-6.9d-65)) .or. (.not. (z <= 2.1d-11))) then
        tmp = z * ((y * x) - x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.9e-65) || !(z <= 2.1e-11)) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.9e-65) or not (z <= 2.1e-11):
		tmp = z * ((y * x) - x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.9e-65) || !(z <= 2.1e-11))
		tmp = Float64(z * Float64(Float64(y * x) - x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.9e-65) || ~((z <= 2.1e-11)))
		tmp = z * ((y * x) - x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.9e-65], N[Not[LessEqual[z, 2.1e-11]], $MachinePrecision]], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.89999999999999991e-65 or 2.0999999999999999e-11 < z

   1. Initial program 91.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*r* 94.6%

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

      3. *-commutative 94.6%

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

      4. sub-neg 94.6%

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

      5. metadata-eval 94.6%

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

   4. Simplified 94.6%

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

      1. distribute-lft-in 94.6%

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

      2. *-commutative 94.6%

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

      3. mul-1-neg 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in z around 0 94.6%

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

   if -6.89999999999999991e-65 < z < 2.0999999999999999e-11

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 77.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{-65} \lor \neg \left(z \leq 2.1 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e-66)
   (* z (- (* y x) x))
   (if (<= z 1.6e-11) (* x (- 1.0 z)) (* (+ y -1.0) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e-66) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1.6e-11) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.5d-66)) then
        tmp = z * ((y * x) - x)
    else if (z <= 1.6d-11) then
        tmp = x * (1.0d0 - z)
    else
        tmp = (y + (-1.0d0)) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e-66) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1.6e-11) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e-66:
		tmp = z * ((y * x) - x)
	elif z <= 1.6e-11:
		tmp = x * (1.0 - z)
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e-66)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 1.6e-11)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e-66)
		tmp = z * ((y * x) - x);
	elseif (z <= 1.6e-11)
		tmp = x * (1.0 - z);
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e-66], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-11], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999981e-66

   1. Initial program 89.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*r* 91.9%

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

      3. *-commutative 91.9%

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

      4. sub-neg 91.9%

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

      5. metadata-eval 91.9%

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

   4. Simplified 91.9%

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

      1. distribute-lft-in 91.9%

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

      2. *-commutative 91.9%

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

      3. mul-1-neg 91.9%

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

   6. Applied egg-rr 91.9%

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

   7. Taylor expanded in z around 0 91.9%

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

   if -2.49999999999999981e-66 < z < 1.59999999999999997e-11

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 77.6%

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

   if 1.59999999999999997e-11 < z

   1. Initial program 93.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. distribute-rgt-in 93.6%

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

      4. *-un-lft-identity 93.6%

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

   3. Applied egg-rr 93.6%

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

   4. Taylor expanded in x around 0 93.6%

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

      1. mul-1-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. sub-neg 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in z around inf 91.9%

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

      1. associate-*r* 98.3%

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

      2. *-commutative 98.3%

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

      3. sub-neg 98.3%

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

      4. metadata-eval 98.3%

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

   9. Simplified 98.3%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 8: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+115} \lor \neg \left(y \leq 2.15 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+115) (not (<= y 2.15e+15)))
   (* x (* y z))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+115) || !(y <= 2.15e+15)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.7d+115)) .or. (.not. (y <= 2.15d+15))) then
        tmp = x * (y * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+115) || !(y <= 2.15e+15)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+115) or not (y <= 2.15e+15):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+115) || !(y <= 2.15e+15))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e+115) || ~((y <= 2.15e+15)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+115], N[Not[LessEqual[y, 2.15e+15]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000004e115 or 2.15e15 < y

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 71.5%

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

      1. *-commutative 71.5%

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

   4. Simplified 71.5%

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

   if -2.70000000000000004e115 < y < 2.15e15

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 93.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+115} \lor \neg \left(y \leq 2.15 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+116} \lor \neg \left(y \leq 1.9 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.8e+116) (not (<= y 1.9e+14))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e+116) || !(y <= 1.9e+14)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.8d+116)) .or. (.not. (y <= 1.9d+14))) then
        tmp = z * (y * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e+116) || !(y <= 1.9e+14)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.8e+116) or not (y <= 1.9e+14):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.8e+116) || !(y <= 1.9e+14))
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.8e+116) || ~((y <= 1.9e+14)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.8e+116], N[Not[LessEqual[y, 1.9e+14]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.80000000000000065e116 or 1.9e14 < y

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 71.5%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

   4. Simplified 74.0%

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

   if -7.80000000000000065e116 < y < 1.9e14

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 93.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+116} \lor \neg \left(y \leq 1.9 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 10: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+113} \lor \neg \left(y \leq 1.8 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+113) (not (<= y 1.8e+15))) (* z (* y x)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+113) || !(y <= 1.8e+15)) {
		tmp = z * (y * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.7d+113)) .or. (.not. (y <= 1.8d+15))) then
        tmp = z * (y * x)
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+113) || !(y <= 1.8e+15)) {
		tmp = z * (y * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+113) or not (y <= 1.8e+15):
		tmp = z * (y * x)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+113) || !(y <= 1.8e+15))
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e+113) || ~((y <= 1.8e+15)))
		tmp = z * (y * x);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+113], N[Not[LessEqual[y, 1.8e+15]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000011e113 or 1.8e15 < y

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 71.5%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

   4. Simplified 74.0%

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

   if -2.70000000000000011e113 < y < 1.8e15

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-*r* 99.5%

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

      3. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot z, y - 1, x\right)} \]

      4. sub-neg 99.5%

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

      5. metadata-eval 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in y around 0 93.3%

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

      1. mul-1-neg 93.3%

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

      2. sub-neg 93.3%

         \[\leadsto \color{blue}{x - x \cdot z} \]

   7. Simplified 93.3%

      \[\leadsto \color{blue}{x - x \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+113} \lor \neg \left(y \leq 1.8 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 11: 63.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -29 \lor \neg \left(z \leq 80000000000000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -29.0) (not (<= z 80000000000000.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -29.0) || !(z <= 80000000000000.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-29.0d0)) .or. (.not. (z <= 80000000000000.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -29.0) || !(z <= 80000000000000.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -29.0) or not (z <= 80000000000000.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -29.0) || !(z <= 80000000000000.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -29.0) || ~((z <= 80000000000000.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -29.0], N[Not[LessEqual[z, 80000000000000.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -29 or 8e13 < z

   1. Initial program 89.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 55.2%

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

      1. neg-mul-1 55.2%

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

   7. Simplified 55.2%

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

   if -29 < z < 8e13

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 68.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29 \lor \neg \left(z \leq 80000000000000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 38.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.1%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 38.0%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 38.0%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))