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

Percentage Accurate: 95.9% → 98.5%

Time: 6.6s

Alternatives: 8

Speedup: 0.8×

• 21.1% 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: 95.9% 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: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e-8)
   (* z (* x (+ y -1.0)))
   (if (<= z 1.3e-8) (+ x (* x (* y z))) (* (+ y -1.0) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e-8) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.3e-8) {
		tmp = x + (x * (y * z));
	} else {
		tmp = (y + -1.0) * (x * 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 <= (-9d-8)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 1.3d-8) then
        tmp = x + (x * (y * z))
    else
        tmp = (y + (-1.0d0)) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e-8) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.3e-8) {
		tmp = x + (x * (y * z));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e-8:
		tmp = z * (x * (y + -1.0))
	elif z <= 1.3e-8:
		tmp = x + (x * (y * z))
	else:
		tmp = (y + -1.0) * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e-8)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 1.3e-8)
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e-8)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 1.3e-8)
		tmp = x + (x * (y * z));
	else
		tmp = (y + -1.0) * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e-8], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-8], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999986e-8

   1. Initial program 91.4%

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

   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%

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

      2. associate-*l* 98.1%

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

      3. sub-neg 98.1%

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

      4. metadata-eval 98.1%

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

   4. Simplified 98.1%

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

   if -8.99999999999999986e-8 < z < 1.3000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-lft-neg-out 99.7%

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

      3. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   if 1.3000000000000001e-8 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 96.4%

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

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

   4. Simplified 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 2: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z)))))
   (if (<= t_0 2e+304) t_0 (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    if (t_0 <= 2d+304) then
        tmp = t_0
    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 t_0 = x * (1.0 - ((1.0 - y) * z));
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0;
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	tmp = 0
	if t_0 <= 2e+304:
		tmp = t_0
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	tmp = 0.0
	if (t_0 <= 2e+304)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	tmp = 0.0;
	if (t_0 <= 2e+304)
		tmp = t_0;
	else
		tmp = z * (x * (y + -1.0));
	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]}, If[LessEqual[t$95$0, 2e+304], t$95$0, N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 1.9999999999999999e304

   1. Initial program 99.1%

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

   if 1.9999999999999999e304 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 84.9%

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

   2. Taylor expanded in z around inf 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l* 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 3: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* z (* x y))))
   (if (<= z -6e+250)
     t_0
     (if (<= z -9e+186)
       t_1
       (if (<= z -2.05e+30)
         t_0
         (if (<= z -6.2e-29)
           t_1
           (if (<= z 1.2e-88)
             x
             (if (<= z 6.2e-68) (* x (* y z)) (if (<= z 1.3e-8) x t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = z * (x * y);
	double tmp;
	if (z <= -6e+250) {
		tmp = t_0;
	} else if (z <= -9e+186) {
		tmp = t_1;
	} else if (z <= -2.05e+30) {
		tmp = t_0;
	} else if (z <= -6.2e-29) {
		tmp = t_1;
	} else if (z <= 1.2e-88) {
		tmp = x;
	} else if (z <= 6.2e-68) {
		tmp = x * (y * z);
	} else if (z <= 1.3e-8) {
		tmp = x;
	} 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 = x * -z
    t_1 = z * (x * y)
    if (z <= (-6d+250)) then
        tmp = t_0
    else if (z <= (-9d+186)) then
        tmp = t_1
    else if (z <= (-2.05d+30)) then
        tmp = t_0
    else if (z <= (-6.2d-29)) then
        tmp = t_1
    else if (z <= 1.2d-88) then
        tmp = x
    else if (z <= 6.2d-68) then
        tmp = x * (y * z)
    else if (z <= 1.3d-8) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = z * (x * y);
	double tmp;
	if (z <= -6e+250) {
		tmp = t_0;
	} else if (z <= -9e+186) {
		tmp = t_1;
	} else if (z <= -2.05e+30) {
		tmp = t_0;
	} else if (z <= -6.2e-29) {
		tmp = t_1;
	} else if (z <= 1.2e-88) {
		tmp = x;
	} else if (z <= 6.2e-68) {
		tmp = x * (y * z);
	} else if (z <= 1.3e-8) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = z * (x * y)
	tmp = 0
	if z <= -6e+250:
		tmp = t_0
	elif z <= -9e+186:
		tmp = t_1
	elif z <= -2.05e+30:
		tmp = t_0
	elif z <= -6.2e-29:
		tmp = t_1
	elif z <= 1.2e-88:
		tmp = x
	elif z <= 6.2e-68:
		tmp = x * (y * z)
	elif z <= 1.3e-8:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (z <= -6e+250)
		tmp = t_0;
	elseif (z <= -9e+186)
		tmp = t_1;
	elseif (z <= -2.05e+30)
		tmp = t_0;
	elseif (z <= -6.2e-29)
		tmp = t_1;
	elseif (z <= 1.2e-88)
		tmp = x;
	elseif (z <= 6.2e-68)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.3e-8)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = z * (x * y);
	tmp = 0.0;
	if (z <= -6e+250)
		tmp = t_0;
	elseif (z <= -9e+186)
		tmp = t_1;
	elseif (z <= -2.05e+30)
		tmp = t_0;
	elseif (z <= -6.2e-29)
		tmp = t_1;
	elseif (z <= 1.2e-88)
		tmp = x;
	elseif (z <= 6.2e-68)
		tmp = x * (y * z);
	elseif (z <= 1.3e-8)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+250], t$95$0, If[LessEqual[z, -9e+186], t$95$1, If[LessEqual[z, -2.05e+30], t$95$0, If[LessEqual[z, -6.2e-29], t$95$1, If[LessEqual[z, 1.2e-88], x, If[LessEqual[z, 6.2e-68], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-8], x, t$95$0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.99999999999999953e250 or -9.0000000000000009e186 < z < -2.05000000000000003e30 or 1.3000000000000001e-8 < z

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 72.1%

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

      1. sub-neg 72.1%

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

      2. distribute-rgt-in 72.1%

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

      3. *-lft-identity 72.1%

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

      4. distribute-lft-neg-out 72.1%

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

      5. *-commutative 72.1%

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

      6. unsub-neg 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in z around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. *-commutative 72.2%

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

      3. distribute-rgt-neg-in 72.2%

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

   7. Simplified 72.2%

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

   if -5.99999999999999953e250 < z < -9.0000000000000009e186 or -2.05000000000000003e30 < z < -6.20000000000000052e-29

   1. Initial program 85.1%

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

      1. add-cube-cbrt 84.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)} \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}} \]

      2. pow3 84.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 84.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   4. Taylor expanded in y around inf 57.1%

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

      1. *-commutative 57.3%

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

   6. Simplified 57.1%

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

      1. rem-cube-cbrt 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-*r* 72.1%

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

   8. Applied egg-rr 72.1%

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

   if -6.20000000000000052e-29 < z < 1.2e-88 or 6.1999999999999999e-68 < z < 1.3000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 80.5%

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

   if 1.2e-88 < z < 6.1999999999999999e-68

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+250}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -3.6e+154)
     (* y (* x z))
     (if (<= z -2.8e+30)
       t_0
       (if (<= z -3.2e-30)
         (* z (* x y))
         (if (<= z 8.4e-89)
           x
           (if (<= z 6.8e-68) (* x (* y z)) (if (<= z 1.3e-8) x t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -3.6e+154) {
		tmp = y * (x * z);
	} else if (z <= -2.8e+30) {
		tmp = t_0;
	} else if (z <= -3.2e-30) {
		tmp = z * (x * y);
	} else if (z <= 8.4e-89) {
		tmp = x;
	} else if (z <= 6.8e-68) {
		tmp = x * (y * z);
	} else if (z <= 1.3e-8) {
		tmp = x;
	} 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 = x * -z
    if (z <= (-3.6d+154)) then
        tmp = y * (x * z)
    else if (z <= (-2.8d+30)) then
        tmp = t_0
    else if (z <= (-3.2d-30)) then
        tmp = z * (x * y)
    else if (z <= 8.4d-89) then
        tmp = x
    else if (z <= 6.8d-68) then
        tmp = x * (y * z)
    else if (z <= 1.3d-8) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -3.6e+154) {
		tmp = y * (x * z);
	} else if (z <= -2.8e+30) {
		tmp = t_0;
	} else if (z <= -3.2e-30) {
		tmp = z * (x * y);
	} else if (z <= 8.4e-89) {
		tmp = x;
	} else if (z <= 6.8e-68) {
		tmp = x * (y * z);
	} else if (z <= 1.3e-8) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -3.6e+154:
		tmp = y * (x * z)
	elif z <= -2.8e+30:
		tmp = t_0
	elif z <= -3.2e-30:
		tmp = z * (x * y)
	elif z <= 8.4e-89:
		tmp = x
	elif z <= 6.8e-68:
		tmp = x * (y * z)
	elif z <= 1.3e-8:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -3.6e+154)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -2.8e+30)
		tmp = t_0;
	elseif (z <= -3.2e-30)
		tmp = Float64(z * Float64(x * y));
	elseif (z <= 8.4e-89)
		tmp = x;
	elseif (z <= 6.8e-68)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.3e-8)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -3.6e+154)
		tmp = y * (x * z);
	elseif (z <= -2.8e+30)
		tmp = t_0;
	elseif (z <= -3.2e-30)
		tmp = z * (x * y);
	elseif (z <= 8.4e-89)
		tmp = x;
	elseif (z <= 6.8e-68)
		tmp = x * (y * z);
	elseif (z <= 1.3e-8)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -3.6e+154], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e+30], t$95$0, If[LessEqual[z, -3.2e-30], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e-89], x, If[LessEqual[z, 6.8e-68], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-8], x, t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.6000000000000001e154

   1. Initial program 86.8%

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

      1. add-cube-cbrt 86.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)} \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}} \]

      2. pow3 86.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 86.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   4. Taylor expanded in y around inf 46.8%

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

      1. *-commutative 46.8%

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

   6. Simplified 46.8%

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

      1. rem-cube-cbrt 46.8%

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

      2. associate-*r* 67.5%

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

      3. *-commutative 67.5%

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

   8. Applied egg-rr 67.5%

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

   if -3.6000000000000001e154 < z < -2.79999999999999983e30 or 1.3000000000000001e-8 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 70.9%

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

      1. sub-neg 70.9%

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

      2. distribute-rgt-in 70.9%

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

      3. *-lft-identity 70.9%

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

      4. distribute-lft-neg-out 70.9%

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

      5. *-commutative 70.9%

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

      6. unsub-neg 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in z around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. *-commutative 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

   7. Simplified 70.9%

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

   if -2.79999999999999983e30 < z < -3.2e-30

   1. Initial program 99.8%

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

      1. add-cube-cbrt 98.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)} \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}} \]

      2. pow3 98.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   4. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 70.3%

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

   6. Simplified 69.7%

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

      1. rem-cube-cbrt 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r* 70.5%

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

   8. Applied egg-rr 70.5%

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

   if -3.2e-30 < z < 8.4000000000000004e-89 or 6.80000000000000037e-68 < z < 1.3000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 80.5%

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

   if 8.4000000000000004e-89 < z < 6.80000000000000037e-68

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* y z))))
   (if (<= z -2.8e+30)
     t_0
     (if (<= z -6.2e-29)
       t_1
       (if (<= z 1.06e-88)
         x
         (if (<= z 4.8e-62) t_1 (if (<= z 1.3e-8) x t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.8e+30) {
		tmp = t_0;
	} else if (z <= -6.2e-29) {
		tmp = t_1;
	} else if (z <= 1.06e-88) {
		tmp = x;
	} else if (z <= 4.8e-62) {
		tmp = t_1;
	} else if (z <= 1.3e-8) {
		tmp = x;
	} 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 = x * -z
    t_1 = x * (y * z)
    if (z <= (-2.8d+30)) then
        tmp = t_0
    else if (z <= (-6.2d-29)) then
        tmp = t_1
    else if (z <= 1.06d-88) then
        tmp = x
    else if (z <= 4.8d-62) then
        tmp = t_1
    else if (z <= 1.3d-8) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.8e+30) {
		tmp = t_0;
	} else if (z <= -6.2e-29) {
		tmp = t_1;
	} else if (z <= 1.06e-88) {
		tmp = x;
	} else if (z <= 4.8e-62) {
		tmp = t_1;
	} else if (z <= 1.3e-8) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (y * z)
	tmp = 0
	if z <= -2.8e+30:
		tmp = t_0
	elif z <= -6.2e-29:
		tmp = t_1
	elif z <= 1.06e-88:
		tmp = x
	elif z <= 4.8e-62:
		tmp = t_1
	elif z <= 1.3e-8:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.8e+30)
		tmp = t_0;
	elseif (z <= -6.2e-29)
		tmp = t_1;
	elseif (z <= 1.06e-88)
		tmp = x;
	elseif (z <= 4.8e-62)
		tmp = t_1;
	elseif (z <= 1.3e-8)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.8e+30)
		tmp = t_0;
	elseif (z <= -6.2e-29)
		tmp = t_1;
	elseif (z <= 1.06e-88)
		tmp = x;
	elseif (z <= 4.8e-62)
		tmp = t_1;
	elseif (z <= 1.3e-8)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+30], t$95$0, If[LessEqual[z, -6.2e-29], t$95$1, If[LessEqual[z, 1.06e-88], x, If[LessEqual[z, 4.8e-62], t$95$1, If[LessEqual[z, 1.3e-8], x, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999983e30 or 1.3000000000000001e-8 < z

   1. Initial program 92.8%

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

   2. Taylor expanded in y around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. distribute-rgt-in 66.3%

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

      3. *-lft-identity 66.3%

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

      4. distribute-lft-neg-out 66.3%

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

      5. *-commutative 66.3%

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

      6. unsub-neg 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. *-commutative 66.3%

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

      3. distribute-rgt-neg-in 66.3%

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

   7. Simplified 66.3%

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

   if -2.79999999999999983e30 < z < -6.20000000000000052e-29 or 1.06e-88 < z < 4.79999999999999967e-62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 75.5%

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

   4. Simplified 75.5%

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

   if -6.20000000000000052e-29 < z < 1.06e-88 or 4.79999999999999967e-62 < z < 1.3000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 80.5%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+94} \lor \neg \left(y \leq 255000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+94) (not (<= y 255000000000.0)))
   (* z (* x y))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+94) || !(y <= 255000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (x * 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 <= (-5.2d+94)) .or. (.not. (y <= 255000000000.0d0))) then
        tmp = z * (x * y)
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+94) || !(y <= 255000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+94) or not (y <= 255000000000.0):
		tmp = z * (x * y)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+94) || !(y <= 255000000000.0))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e+94) || ~((y <= 255000000000.0)))
		tmp = z * (x * y);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+94], N[Not[LessEqual[y, 255000000000.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e94 or 2.55e11 < y

   1. Initial program 91.1%

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

      1. add-cube-cbrt 90.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)} \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}} \]

      2. pow3 90.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 90.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   4. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 73.4%

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

   6. Simplified 72.8%

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

      1. rem-cube-cbrt 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 78.4%

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

   8. Applied egg-rr 78.4%

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

   if -5.1999999999999998e94 < y < 2.55e11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-rgt-in 97.9%

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

      3. *-lft-identity 97.9%

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

      4. distribute-lft-neg-out 97.9%

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

      5. *-commutative 97.9%

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

      6. unsub-neg 97.9%

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

   4. Simplified 97.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+94} \lor \neg \left(y \leq 255000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 7: 64.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-8} \lor \neg \left(z \leq 1.3 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9e-8) (not (<= z 1.3e-8))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9e-8) || !(z <= 1.3e-8)) {
		tmp = x * -z;
	} 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 <= (-9d-8)) .or. (.not. (z <= 1.3d-8))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9e-8) || !(z <= 1.3e-8)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9e-8) or not (z <= 1.3e-8):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9e-8) || !(z <= 1.3e-8))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9e-8) || ~((z <= 1.3e-8)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9e-8], N[Not[LessEqual[z, 1.3e-8]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999986e-8 or 1.3000000000000001e-8 < z

   1. Initial program 93.4%

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

   2. Taylor expanded in y around 0 62.8%

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

      1. sub-neg 62.8%

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

      2. distribute-rgt-in 62.8%

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

      3. *-lft-identity 62.8%

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

      4. distribute-lft-neg-out 62.8%

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

      5. *-commutative 62.8%

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

      6. unsub-neg 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in z around inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. *-commutative 62.1%

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

      3. distribute-rgt-neg-in 62.1%

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

   7. Simplified 62.1%

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

   if -8.99999999999999986e-8 < z < 1.3000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-8} \lor \neg \left(z \leq 1.3 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 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 96.6%

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

2. Taylor expanded in z around 0 38.8%

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

3. Final simplification 38.8%

   \[\leadsto x \]

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 2023293 
(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))))