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

Percentage Accurate: 95.7% → 97.6%

Time: 9.1s

Alternatives: 12

Speedup: 1.0×

• 20.9% 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: 95.7% 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: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;1 - t\_0 \leq 10^{+307}:\\ \;\;\;\;x - x \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= (- 1.0 t_0) 1e+307) (- x (* x t_0)) (+ x (* (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if ((1.0 - t_0) <= 1e+307) {
		tmp = x - (x * t_0);
	} else {
		tmp = x + ((x * 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) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if ((1.0d0 - t_0) <= 1d+307) then
        tmp = x - (x * t_0)
    else
        tmp = x + ((x * z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if ((1.0 - t_0) <= 1e+307) {
		tmp = x - (x * t_0);
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if (1.0 - t_0) <= 1e+307:
		tmp = x - (x * t_0)
	else:
		tmp = x + ((x * z) * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (Float64(1.0 - t_0) <= 1e+307)
		tmp = Float64(x - Float64(x * t_0));
	else
		tmp = Float64(x + Float64(Float64(x * z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if ((1.0 - t_0) <= 1e+307)
		tmp = x - (x * t_0);
	else
		tmp = x + ((x * z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - t$95$0), $MachinePrecision], 1e+307], N[(x - N[(x * t$95$0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < 9.99999999999999986e306

   1. Initial program 98.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 98.4%

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

   if 9.99999999999999986e306 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 62.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 62.0%

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

   4. Taylor expanded in y around 0 55.4%

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

      1. *-commutative 55.4%

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

      2. associate-*r* 93.3%

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

      3. *-commutative 93.3%

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

      4. distribute-rgt-in 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \cdot \left(1 - y\right) \leq 10^{+307}:\\ \;\;\;\;x - x \cdot \left(z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -2700000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* z y))))
   (if (<= z -2700000000000.0)
     t_0
     (if (<= z -8.2e-94)
       t_1
       (if (<= z 4.6e-113) x (if (<= z 1.08e+27) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -2700000000000.0) {
		tmp = t_0;
	} else if (z <= -8.2e-94) {
		tmp = t_1;
	} else if (z <= 4.6e-113) {
		tmp = x;
	} else if (z <= 1.08e+27) {
		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 = x * -z
    t_1 = x * (z * y)
    if (z <= (-2700000000000.0d0)) then
        tmp = t_0
    else if (z <= (-8.2d-94)) then
        tmp = t_1
    else if (z <= 4.6d-113) then
        tmp = x
    else if (z <= 1.08d+27) 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 = x * -z;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -2700000000000.0) {
		tmp = t_0;
	} else if (z <= -8.2e-94) {
		tmp = t_1;
	} else if (z <= 4.6e-113) {
		tmp = x;
	} else if (z <= 1.08e+27) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (z * y)
	tmp = 0
	if z <= -2700000000000.0:
		tmp = t_0
	elif z <= -8.2e-94:
		tmp = t_1
	elif z <= 4.6e-113:
		tmp = x
	elif z <= 1.08e+27:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (z <= -2700000000000.0)
		tmp = t_0;
	elseif (z <= -8.2e-94)
		tmp = t_1;
	elseif (z <= 4.6e-113)
		tmp = x;
	elseif (z <= 1.08e+27)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = x * (z * y);
	tmp = 0.0;
	if (z <= -2700000000000.0)
		tmp = t_0;
	elseif (z <= -8.2e-94)
		tmp = t_1;
	elseif (z <= 4.6e-113)
		tmp = x;
	elseif (z <= 1.08e+27)
		tmp = t_1;
	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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2700000000000.0], t$95$0, If[LessEqual[z, -8.2e-94], t$95$1, If[LessEqual[z, 4.6e-113], x, If[LessEqual[z, 1.08e+27], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e12 or 1.08e27 < z

   1. Initial program 92.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*r* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 65.5%

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

      1. neg-mul-1 65.5%

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

   8. Simplified 65.5%

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

   if -2.7e12 < z < -8.20000000000000001e-94 or 4.60000000000000016e-113 < z < 1.08e27

   1. Initial program 99.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   if -8.20000000000000001e-94 < z < 4.60000000000000016e-113

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2700000000000:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq 10^{+307}:\\ \;\;\;\;x \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* z (- 1.0 y)))))
   (if (<= t_0 1e+307) (* x t_0) (+ x (* (* x z) y)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * (1.0 - y));
	double tmp;
	if (t_0 <= 1e+307) {
		tmp = x * t_0;
	} else {
		tmp = x + ((x * 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (z * (1.0d0 - y))
    if (t_0 <= 1d+307) then
        tmp = x * t_0
    else
        tmp = x + ((x * z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * (1.0 - y));
	double tmp;
	if (t_0 <= 1e+307) {
		tmp = x * t_0;
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (z * (1.0 - y))
	tmp = 0
	if t_0 <= 1e+307:
		tmp = x * t_0
	else:
		tmp = x + ((x * z) * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (t_0 <= 1e+307)
		tmp = Float64(x * t_0);
	else
		tmp = Float64(x + Float64(Float64(x * z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (z * (1.0 - y));
	tmp = 0.0;
	if (t_0 <= 1e+307)
		tmp = x * t_0;
	else
		tmp = x + ((x * z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+307], N[(x * t$95$0), $MachinePrecision], N[(x + N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < 9.99999999999999986e306

   1. Initial program 98.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   if 9.99999999999999986e306 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 62.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 62.0%

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

   4. Taylor expanded in y around 0 55.4%

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

      1. *-commutative 55.4%

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

      2. associate-*r* 93.3%

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

      3. *-commutative 93.3%

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

      4. distribute-rgt-in 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \cdot \left(1 - y\right) \leq 10^{+307}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13.2 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -13.2) (not (<= z 1.0)))
   (* z (* x (+ -1.0 y)))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13.2) || !(z <= 1.0)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x + (x * (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 <= (-13.2d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x * ((-1.0d0) + y))
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13.2) || !(z <= 1.0)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -13.2) or not (z <= 1.0):
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -13.2) || !(z <= 1.0))
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -13.2) || ~((z <= 1.0)))
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -13.2], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -13.199999999999999 or 1 < z

   1. Initial program 92.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-*r* 97.9%

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

      3. *-commutative 97.9%

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

      4. sub-neg 97.9%

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

      5. metadata-eval 97.9%

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

   5. Simplified 97.9%

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

   if -13.199999999999999 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-lft-neg-out 98.9%

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

      3. *-commutative 98.9%

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

   5. Simplified 98.9%

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

      1. sub-neg 98.9%

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

      2. distribute-rgt-neg-out 98.9%

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

      3. remove-double-neg 98.9%

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

      4. distribute-rgt-in 98.9%

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

      5. *-un-lft-identity 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13.2 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-7} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-7) (not (<= y 1.0))) (+ x (* (* x z) y)) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-7) || !(y <= 1.0)) {
		tmp = x + ((x * z) * 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 <= (-3.4d-7)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + ((x * z) * 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 <= -3.4e-7) || !(y <= 1.0)) {
		tmp = x + ((x * z) * y);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-7) or not (y <= 1.0):
		tmp = x + ((x * z) * y)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-7) || !(y <= 1.0))
		tmp = Float64(x + Float64(Float64(x * z) * 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 <= -3.4e-7) || ~((y <= 1.0)))
		tmp = x + ((x * z) * y);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-7], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x + N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999974e-7 or 1 < y

   1. Initial program 92.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.8%

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

   4. Taylor expanded in y around 0 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*r* 91.4%

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

      3. *-commutative 91.4%

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

      4. distribute-rgt-in 95.1%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in y around inf 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*r* 94.7%

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

      3. *-commutative 94.7%

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

   9. Simplified 94.7%

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

   if -3.39999999999999974e-7 < y < 1

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-7} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+72} \lor \neg \left(y \leq 3.8 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.3e+72) (not (<= y 3.8e+69))) (* x (* z y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e+72) || !(y <= 3.8e+69)) {
		tmp = x * (z * y);
	} 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 <= (-3.3d+72)) .or. (.not. (y <= 3.8d+69))) then
        tmp = x * (z * y)
    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 <= -3.3e+72) || !(y <= 3.8e+69)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.3e+72) or not (y <= 3.8e+69):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.3e+72) || !(y <= 3.8e+69))
		tmp = Float64(x * Float64(z * y));
	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 <= -3.3e+72) || ~((y <= 3.8e+69)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.3e+72], N[Not[LessEqual[y, 3.8e+69]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e72 or 3.80000000000000028e69 < y

   1. Initial program 90.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   if -3.3e72 < y < 3.80000000000000028e69

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 94.0%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+72} \lor \neg \left(y \leq 3.8 \cdot 10^{+69}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 10^{+69}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+71)
   (* z (* x y))
   (if (<= y 1e+69) (- x (* x z)) (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+71) {
		tmp = z * (x * y);
	} else if (y <= 1e+69) {
		tmp = x - (x * z);
	} else {
		tmp = x * (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 (y <= (-7d+71)) then
        tmp = z * (x * y)
    else if (y <= 1d+69) then
        tmp = x - (x * z)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+71) {
		tmp = z * (x * y);
	} else if (y <= 1e+69) {
		tmp = x - (x * z);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+71:
		tmp = z * (x * y)
	elif y <= 1e+69:
		tmp = x - (x * z)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+71)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1e+69)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+71)
		tmp = z * (x * y);
	elseif (y <= 1e+69)
		tmp = x - (x * z);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+71], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+69], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999998e71

   1. Initial program 87.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 81.8%

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

      3. *-commutative 81.8%

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

      4. sub-neg 81.8%

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

      5. metadata-eval 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around inf 81.8%

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

   if -6.9999999999999998e71 < y < 1.0000000000000001e69

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-rgt-in 94.0%

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

      3. *-un-lft-identity 94.0%

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

   5. Applied egg-rr 94.0%

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

   if 1.0000000000000001e69 < y

   1. Initial program 93.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 10^{+69}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+70}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+71)
   (* z (* x y))
   (if (<= y 2.1e+70) (- x (* x z)) (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+71) {
		tmp = z * (x * y);
	} else if (y <= 2.1e+70) {
		tmp = x - (x * z);
	} else {
		tmp = x * (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 (y <= (-4.2d+71)) then
        tmp = z * (x * y)
    else if (y <= 2.1d+70) then
        tmp = x - (x * z)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+71) {
		tmp = z * (x * y);
	} else if (y <= 2.1e+70) {
		tmp = x - (x * z);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+71:
		tmp = z * (x * y)
	elif y <= 2.1e+70:
		tmp = x - (x * z)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+71)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 2.1e+70)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e+71)
		tmp = z * (x * y);
	elseif (y <= 2.1e+70)
		tmp = x - (x * z);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+71], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+70], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999978e71

   1. Initial program 87.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 81.8%

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

      3. *-commutative 81.8%

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

      4. sub-neg 81.8%

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

      5. metadata-eval 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around inf 81.8%

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

   if -4.19999999999999978e71 < y < 2.10000000000000008e70

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*r* 95.0%

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

      3. *-commutative 95.0%

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

      4. distribute-rgt-in 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 94.0%

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

      1. neg-mul-1 94.0%

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

      2. sub-neg 94.0%

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

   9. Simplified 94.0%

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

   if 2.10000000000000008e70 < y

   1. Initial program 93.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

   5. Simplified 77.7%

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

Alternative 9: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+71)
   (* z (* x y))
   (if (<= y 3.1e+68) (* x (- 1.0 z)) (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+71) {
		tmp = z * (x * y);
	} else if (y <= 3.1e+68) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (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 (y <= (-5.5d+71)) then
        tmp = z * (x * y)
    else if (y <= 3.1d+68) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+71) {
		tmp = z * (x * y);
	} else if (y <= 3.1e+68) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e+71:
		tmp = z * (x * y)
	elif y <= 3.1e+68:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+71)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 3.1e+68)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e+71)
		tmp = z * (x * y);
	elseif (y <= 3.1e+68)
		tmp = x * (1.0 - z);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+71], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+68], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e71

   1. Initial program 87.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 81.8%

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

      3. *-commutative 81.8%

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

      4. sub-neg 81.8%

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

      5. metadata-eval 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around inf 81.8%

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

   if -5.5e71 < y < 3.0999999999999998e68

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 94.0%

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

   if 3.0999999999999998e68 < y

   1. Initial program 93.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

   5. Simplified 77.7%

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

Alternative 10: 64.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0078\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.0078))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.0078)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 0.0078d0))) 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 <= -1.0) || !(z <= 0.0078)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.0078):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.0078))
		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 <= -1.0) || ~((z <= 0.0078)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.0078]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.0077999999999999996 < z

   1. Initial program 92.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*r* 98.0%

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

      3. *-commutative 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

   8. Simplified 61.7%

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

   if -1 < z < 0.0077999999999999996

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0078\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((x * z) * ((-1.0d0) + y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 96.2%

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

4. Taylor expanded in y around 0 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*r* 92.8%

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

   3. *-commutative 92.8%

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

   4. distribute-rgt-in 97.5%

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

6. Simplified 97.5%

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

Alternative 12: 38.2% 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 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 36.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 99.7% accurate, 0.2× 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 2024103 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (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))))