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

Percentage Accurate: 96.0% → 97.8%

Time: 6.0s

Alternatives: 9

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: 96.0% 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: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.5e+57) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* x (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.5e+57) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (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 (z <= 2.5d+57) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.5e+57) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.5e+57:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.5e+57)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.5e+57)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.5e+57], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.49999999999999986e57

   1. Initial program 99.0%

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

   if 2.49999999999999986e57 < z

   1. Initial program 90.9%

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

   2. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 2: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.0058:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* y (* z x))))
   (if (<= z -2.4e+73)
     t_0
     (if (<= z -1.05e+51)
       t_1
       (if (<= z -0.0058)
         t_0
         (if (<= z 2.2e-65) x (if (<= z 4.5e+84) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = y * (z * x);
	double tmp;
	if (z <= -2.4e+73) {
		tmp = t_0;
	} else if (z <= -1.05e+51) {
		tmp = t_1;
	} else if (z <= -0.0058) {
		tmp = t_0;
	} else if (z <= 2.2e-65) {
		tmp = x;
	} else if (z <= 4.5e+84) {
		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 = y * (z * x)
    if (z <= (-2.4d+73)) then
        tmp = t_0
    else if (z <= (-1.05d+51)) then
        tmp = t_1
    else if (z <= (-0.0058d0)) then
        tmp = t_0
    else if (z <= 2.2d-65) then
        tmp = x
    else if (z <= 4.5d+84) 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 = y * (z * x);
	double tmp;
	if (z <= -2.4e+73) {
		tmp = t_0;
	} else if (z <= -1.05e+51) {
		tmp = t_1;
	} else if (z <= -0.0058) {
		tmp = t_0;
	} else if (z <= 2.2e-65) {
		tmp = x;
	} else if (z <= 4.5e+84) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = y * (z * x)
	tmp = 0
	if z <= -2.4e+73:
		tmp = t_0
	elif z <= -1.05e+51:
		tmp = t_1
	elif z <= -0.0058:
		tmp = t_0
	elif z <= 2.2e-65:
		tmp = x
	elif z <= 4.5e+84:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(y * Float64(z * x))
	tmp = 0.0
	if (z <= -2.4e+73)
		tmp = t_0;
	elseif (z <= -1.05e+51)
		tmp = t_1;
	elseif (z <= -0.0058)
		tmp = t_0;
	elseif (z <= 2.2e-65)
		tmp = x;
	elseif (z <= 4.5e+84)
		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 = y * (z * x);
	tmp = 0.0;
	if (z <= -2.4e+73)
		tmp = t_0;
	elseif (z <= -1.05e+51)
		tmp = t_1;
	elseif (z <= -0.0058)
		tmp = t_0;
	elseif (z <= 2.2e-65)
		tmp = x;
	elseif (z <= 4.5e+84)
		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[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+73], t$95$0, If[LessEqual[z, -1.05e+51], t$95$1, If[LessEqual[z, -0.0058], t$95$0, If[LessEqual[z, 2.2e-65], x, If[LessEqual[z, 4.5e+84], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000002e73 or -1.0500000000000001e51 < z < -0.0058 or 4.4999999999999997e84 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 99.7%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. mul-1-neg 65.5%

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

   5. Simplified 65.5%

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

   if -2.40000000000000002e73 < z < -1.0500000000000001e51 or 2.20000000000000021e-65 < z < 4.4999999999999997e84

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 65.9%

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

   if -0.0058 < z < 2.20000000000000021e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -0.0058:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -0.0058:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -1.02e+74)
     t_0
     (if (<= z -8e+50)
       (* y (* z x))
       (if (<= z -0.0058)
         t_0
         (if (<= z 5.3e-65) x (if (<= z 3.8e+85) (* z (* x y)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1.02e+74) {
		tmp = t_0;
	} else if (z <= -8e+50) {
		tmp = y * (z * x);
	} else if (z <= -0.0058) {
		tmp = t_0;
	} else if (z <= 5.3e-65) {
		tmp = x;
	} else if (z <= 3.8e+85) {
		tmp = z * (x * y);
	} 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) :: tmp
    t_0 = z * -x
    if (z <= (-1.02d+74)) then
        tmp = t_0
    else if (z <= (-8d+50)) then
        tmp = y * (z * x)
    else if (z <= (-0.0058d0)) then
        tmp = t_0
    else if (z <= 5.3d-65) then
        tmp = x
    else if (z <= 3.8d+85) then
        tmp = z * (x * y)
    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 tmp;
	if (z <= -1.02e+74) {
		tmp = t_0;
	} else if (z <= -8e+50) {
		tmp = y * (z * x);
	} else if (z <= -0.0058) {
		tmp = t_0;
	} else if (z <= 5.3e-65) {
		tmp = x;
	} else if (z <= 3.8e+85) {
		tmp = z * (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -1.02e+74:
		tmp = t_0
	elif z <= -8e+50:
		tmp = y * (z * x)
	elif z <= -0.0058:
		tmp = t_0
	elif z <= 5.3e-65:
		tmp = x
	elif z <= 3.8e+85:
		tmp = z * (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -1.02e+74)
		tmp = t_0;
	elseif (z <= -8e+50)
		tmp = Float64(y * Float64(z * x));
	elseif (z <= -0.0058)
		tmp = t_0;
	elseif (z <= 5.3e-65)
		tmp = x;
	elseif (z <= 3.8e+85)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -1.02e+74)
		tmp = t_0;
	elseif (z <= -8e+50)
		tmp = y * (z * x);
	elseif (z <= -0.0058)
		tmp = t_0;
	elseif (z <= 5.3e-65)
		tmp = x;
	elseif (z <= 3.8e+85)
		tmp = z * (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.02e+74], t$95$0, If[LessEqual[z, -8e+50], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0058], t$95$0, If[LessEqual[z, 5.3e-65], x, If[LessEqual[z, 3.8e+85], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02000000000000005e74 or -8.0000000000000006e50 < z < -0.0058 or 3.79999999999999992e85 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 99.7%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. mul-1-neg 65.5%

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

   5. Simplified 65.5%

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

   if -1.02000000000000005e74 < z < -8.0000000000000006e50

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.8%

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

   if -0.0058 < z < 5.30000000000000037e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.5%

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

   if 5.30000000000000037e-65 < z < 3.79999999999999992e85

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 61.3%

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

      1. associate-*r* 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-*l* 61.4%

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

   4. Simplified 61.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -0.0058:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -0.0058:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -2.1e+78)
     t_0
     (if (<= z -1.05e+51)
       (* y (* z x))
       (if (<= z -0.0058)
         t_0
         (if (<= z 5.3e-65) x (if (<= z 1.1e+86) (* x (* z y)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -2.1e+78) {
		tmp = t_0;
	} else if (z <= -1.05e+51) {
		tmp = y * (z * x);
	} else if (z <= -0.0058) {
		tmp = t_0;
	} else if (z <= 5.3e-65) {
		tmp = x;
	} else if (z <= 1.1e+86) {
		tmp = x * (z * y);
	} 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) :: tmp
    t_0 = z * -x
    if (z <= (-2.1d+78)) then
        tmp = t_0
    else if (z <= (-1.05d+51)) then
        tmp = y * (z * x)
    else if (z <= (-0.0058d0)) then
        tmp = t_0
    else if (z <= 5.3d-65) then
        tmp = x
    else if (z <= 1.1d+86) then
        tmp = x * (z * y)
    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 tmp;
	if (z <= -2.1e+78) {
		tmp = t_0;
	} else if (z <= -1.05e+51) {
		tmp = y * (z * x);
	} else if (z <= -0.0058) {
		tmp = t_0;
	} else if (z <= 5.3e-65) {
		tmp = x;
	} else if (z <= 1.1e+86) {
		tmp = x * (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -2.1e+78:
		tmp = t_0
	elif z <= -1.05e+51:
		tmp = y * (z * x)
	elif z <= -0.0058:
		tmp = t_0
	elif z <= 5.3e-65:
		tmp = x
	elif z <= 1.1e+86:
		tmp = x * (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -2.1e+78)
		tmp = t_0;
	elseif (z <= -1.05e+51)
		tmp = Float64(y * Float64(z * x));
	elseif (z <= -0.0058)
		tmp = t_0;
	elseif (z <= 5.3e-65)
		tmp = x;
	elseif (z <= 1.1e+86)
		tmp = Float64(x * Float64(z * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -2.1e+78)
		tmp = t_0;
	elseif (z <= -1.05e+51)
		tmp = y * (z * x);
	elseif (z <= -0.0058)
		tmp = t_0;
	elseif (z <= 5.3e-65)
		tmp = x;
	elseif (z <= 1.1e+86)
		tmp = x * (z * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -2.1e+78], t$95$0, If[LessEqual[z, -1.05e+51], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0058], t$95$0, If[LessEqual[z, 5.3e-65], x, If[LessEqual[z, 1.1e+86], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1000000000000001e78 or -1.0500000000000001e51 < z < -0.0058 or 1.10000000000000002e86 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 99.7%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. mul-1-neg 65.5%

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

   5. Simplified 65.5%

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

   if -2.1000000000000001e78 < z < -1.0500000000000001e51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.8%

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

   if -0.0058 < z < 5.30000000000000037e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.5%

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

   if 5.30000000000000037e-65 < z < 1.10000000000000002e86

   1. Initial program 100.0%

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

      1. distribute-rgt-out-- 100.0%

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

      2. *-lft-identity 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-in 100.0%

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

      6. associate-*l* 99.7%

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

      7. fma-def 99.7%

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

      8. neg-sub0 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(1 - y\right)}, z \cdot x, x\right) \]

      9. associate--r- 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - 1\right) + y}, z \cdot x, x\right) \]

      10. metadata-eval 99.7%

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

      11. +-commutative 99.7%

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

      12. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. associate-*r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 79.3%

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

   7. Taylor expanded in y around inf 61.3%

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

      1. associate-*r* 61.5%

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

   9. Simplified 61.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -0.0058:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-57} \lor \neg \left(z \leq 13200000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-57) (not (<= z 13200000.0)))
   (* z (* x (+ y -1.0)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-57) || !(z <= 13200000.0)) {
		tmp = z * (x * (y + -1.0));
	} 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 ((z <= (-4.5d-57)) .or. (.not. (z <= 13200000.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    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 ((z <= -4.5e-57) || !(z <= 13200000.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-57) or not (z <= 13200000.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-57) || !(z <= 13200000.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-57) || ~((z <= 13200000.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-57], N[Not[LessEqual[z, 13200000.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999973e-57 or 1.32e7 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 97.7%

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

   if -4.49999999999999973e-57 < z < 1.32e7

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. distribute-rgt-out-- 79.4%

         \[\leadsto \color{blue}{1 \cdot x - z \cdot x} \]

      3. *-lft-identity 79.4%

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

   4. Simplified 79.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-57} \lor \neg \left(z \leq 13200000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0058 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0058) (not (<= z 1.0)))
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0058) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	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 <= (-0.0058d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0058) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0058) or not (z <= 1.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0058) || !(z <= 1.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0058) || ~((z <= 1.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0058], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0058 or 1 < z

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 99.7%

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

   if -0.0058 < z < 1

   1. Initial program 99.9%

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

      1. distribute-rgt-out-- 99.9%

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

      2. *-lft-identity 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. associate-*l* 94.8%

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

      7. fma-def 94.8%

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

      8. neg-sub0 94.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(1 - y\right)}, z \cdot x, x\right) \]

      9. associate--r- 94.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - 1\right) + y}, z \cdot x, x\right) \]

      10. metadata-eval 94.8%

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

      11. +-commutative 94.8%

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

      12. *-commutative 94.8%

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

   3. Simplified 94.8%

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

      1. fma-udef 94.8%

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

      2. associate-*r* 92.5%

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

   5. Applied egg-rr 92.5%

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

   6. Taylor expanded in y around inf 93.3%

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

   7. Taylor expanded in x around 0 98.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0058 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]

Alternative 7: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+48} \lor \neg \left(y \leq 360000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+48) (not (<= y 360000.0))) (* z (* x y)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+48) || !(y <= 360000.0)) {
		tmp = z * (x * y);
	} 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 <= (-5.5d+48)) .or. (.not. (y <= 360000.0d0))) then
        tmp = z * (x * y)
    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 <= -5.5e+48) || !(y <= 360000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+48) or not (y <= 360000.0):
		tmp = z * (x * y)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+48) || !(y <= 360000.0))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e+48) || ~((y <= 360000.0)))
		tmp = z * (x * y);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+48], N[Not[LessEqual[y, 360000.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000002e48 or 3.6e5 < y

   1. Initial program 94.9%

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

   2. Taylor expanded in y around inf 74.6%

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

      1. associate-*r* 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*l* 76.3%

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

   4. Simplified 76.3%

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

   if -5.5000000000000002e48 < y < 3.6e5

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 97.7%

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

      1. *-commutative 97.7%

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

      2. distribute-rgt-out-- 97.7%

         \[\leadsto \color{blue}{1 \cdot x - z \cdot x} \]

      3. *-lft-identity 97.7%

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

   4. Simplified 97.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+48} \lor \neg \left(y \leq 360000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 8: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0058 \lor \neg \left(z \leq 340000000000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0058) (not (<= z 340000000000.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0058) || !(z <= 340000000000.0)) {
		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 <= (-0.0058d0)) .or. (.not. (z <= 340000000000.0d0))) 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 <= -0.0058) || !(z <= 340000000000.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0058) or not (z <= 340000000000.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0058) || !(z <= 340000000000.0))
		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 <= -0.0058) || ~((z <= 340000000000.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0058], N[Not[LessEqual[z, 340000000000.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.0058 or 3.4e11 < z

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf 99.7%

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

   3. Taylor expanded in y around 0 60.6%

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

      1. mul-1-neg 60.6%

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

   5. Simplified 60.6%

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

   if -0.0058 < z < 3.4e11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0058 \lor \neg \left(z \leq 340000000000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 37.8% 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 97.3%

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

2. Taylor expanded in z around 0 36.6%

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

3. Final simplification 36.6%

   \[\leadsto x \]

Developer target: 99.8% 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 2023199 
(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))))