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

Percentage Accurate: 96.2% → 98.0%

Time: 7.9s

Alternatives: 11

Speedup: 0.5×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% 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: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y + -1\right)\\ \mathbf{if}\;x \cdot \left(1 + t\_0\right) \leq -4 \cdot 10^{+299}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z + \frac{1 - z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (+ y -1.0))))
   (if (<= (* x (+ 1.0 t_0)) -4e+299)
     (* y (* x (+ z (/ (- 1.0 z) y))))
     (+ x (* x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y + -1.0);
	double tmp;
	if ((x * (1.0 + t_0)) <= -4e+299) {
		tmp = y * (x * (z + ((1.0 - z) / y)));
	} else {
		tmp = x + (x * t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (y + (-1.0d0))
    if ((x * (1.0d0 + t_0)) <= (-4d+299)) then
        tmp = y * (x * (z + ((1.0d0 - z) / y)))
    else
        tmp = x + (x * t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y + -1.0);
	double tmp;
	if ((x * (1.0 + t_0)) <= -4e+299) {
		tmp = y * (x * (z + ((1.0 - z) / y)));
	} else {
		tmp = x + (x * t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y + -1.0)
	tmp = 0
	if (x * (1.0 + t_0)) <= -4e+299:
		tmp = y * (x * (z + ((1.0 - z) / y)))
	else:
		tmp = x + (x * t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y + -1.0))
	tmp = 0.0
	if (Float64(x * Float64(1.0 + t_0)) <= -4e+299)
		tmp = Float64(y * Float64(x * Float64(z + Float64(Float64(1.0 - z) / y))));
	else
		tmp = Float64(x + Float64(x * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y + -1.0);
	tmp = 0.0;
	if ((x * (1.0 + t_0)) <= -4e+299)
		tmp = y * (x * (z + ((1.0 - z) / y)));
	else
		tmp = x + (x * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision], -4e+299], N[(y * N[(x * N[(z + N[(N[(1.0 - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))) < -4.0000000000000002e299

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 84.4%

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

      3. distribute-lft-out 100.0%

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

   5. Simplified 100.0%

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

   if -4.0000000000000002e299 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)))

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 98.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq -4 \cdot 10^{+299}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z + \frac{1 - z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+182}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+82}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -4.8e+182)
     t_0
     (if (<= z -1.7e+125)
       t_1
       (if (<= z -1.05e+82)
         t_0
         (if (<= z -5e-5)
           t_1
           (if (<= z 8.5e-36) x (if (<= z 4.5e+198) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -4.8e+182) {
		tmp = t_0;
	} else if (z <= -1.7e+125) {
		tmp = t_1;
	} else if (z <= -1.05e+82) {
		tmp = t_0;
	} else if (z <= -5e-5) {
		tmp = t_1;
	} else if (z <= 8.5e-36) {
		tmp = x;
	} else if (z <= 4.5e+198) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * -x
    t_1 = x * (y * z)
    if (z <= (-4.8d+182)) then
        tmp = t_0
    else if (z <= (-1.7d+125)) then
        tmp = t_1
    else if (z <= (-1.05d+82)) then
        tmp = t_0
    else if (z <= (-5d-5)) then
        tmp = t_1
    else if (z <= 8.5d-36) then
        tmp = x
    else if (z <= 4.5d+198) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -4.8e+182) {
		tmp = t_0;
	} else if (z <= -1.7e+125) {
		tmp = t_1;
	} else if (z <= -1.05e+82) {
		tmp = t_0;
	} else if (z <= -5e-5) {
		tmp = t_1;
	} else if (z <= 8.5e-36) {
		tmp = x;
	} else if (z <= 4.5e+198) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -4.8e+182:
		tmp = t_0
	elif z <= -1.7e+125:
		tmp = t_1
	elif z <= -1.05e+82:
		tmp = t_0
	elif z <= -5e-5:
		tmp = t_1
	elif z <= 8.5e-36:
		tmp = x
	elif z <= 4.5e+198:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -4.8e+182)
		tmp = t_0;
	elseif (z <= -1.7e+125)
		tmp = t_1;
	elseif (z <= -1.05e+82)
		tmp = t_0;
	elseif (z <= -5e-5)
		tmp = t_1;
	elseif (z <= 8.5e-36)
		tmp = x;
	elseif (z <= 4.5e+198)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -4.8e+182)
		tmp = t_0;
	elseif (z <= -1.7e+125)
		tmp = t_1;
	elseif (z <= -1.05e+82)
		tmp = t_0;
	elseif (z <= -5e-5)
		tmp = t_1;
	elseif (z <= 8.5e-36)
		tmp = x;
	elseif (z <= 4.5e+198)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+182], t$95$0, If[LessEqual[z, -1.7e+125], t$95$1, If[LessEqual[z, -1.05e+82], t$95$0, If[LessEqual[z, -5e-5], t$95$1, If[LessEqual[z, 8.5e-36], x, If[LessEqual[z, 4.5e+198], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.80000000000000019e182 or -1.6999999999999999e125 < z < -1.05e82 or 4.50000000000000001e198 < z

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 91.2%

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

   4. Taylor expanded in y around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-rgt-neg-out 77.0%

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

   6. Simplified 77.0%

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

   if -4.80000000000000019e182 < z < -1.6999999999999999e125 or -1.05e82 < z < -5.00000000000000024e-5 or 8.5000000000000007e-36 < z < 4.50000000000000001e198

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   if -5.00000000000000024e-5 < z < 8.5000000000000007e-36

   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 77.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 10^{+226} \lor \neg \left(y \leq 1.9 \cdot 10^{+282}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))))
   (if (<= y -8e+161)
     t_0
     (if (<= y 1.5e+20)
       (* x (- 1.0 z))
       (if (or (<= y 1e+226) (not (<= y 1.9e+282))) t_0 (* x (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (y <= -8e+161) {
		tmp = t_0;
	} else if (y <= 1.5e+20) {
		tmp = x * (1.0 - z);
	} else if ((y <= 1e+226) || !(y <= 1.9e+282)) {
		tmp = t_0;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x * z)
    if (y <= (-8d+161)) then
        tmp = t_0
    else if (y <= 1.5d+20) then
        tmp = x * (1.0d0 - z)
    else if ((y <= 1d+226) .or. (.not. (y <= 1.9d+282))) then
        tmp = t_0
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (y <= -8e+161) {
		tmp = t_0;
	} else if (y <= 1.5e+20) {
		tmp = x * (1.0 - z);
	} else if ((y <= 1e+226) || !(y <= 1.9e+282)) {
		tmp = t_0;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	tmp = 0
	if y <= -8e+161:
		tmp = t_0
	elif y <= 1.5e+20:
		tmp = x * (1.0 - z)
	elif (y <= 1e+226) or not (y <= 1.9e+282):
		tmp = t_0
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (y <= -8e+161)
		tmp = t_0;
	elseif (y <= 1.5e+20)
		tmp = Float64(x * Float64(1.0 - z));
	elseif ((y <= 1e+226) || !(y <= 1.9e+282))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	tmp = 0.0;
	if (y <= -8e+161)
		tmp = t_0;
	elseif (y <= 1.5e+20)
		tmp = x * (1.0 - z);
	elseif ((y <= 1e+226) || ~((y <= 1.9e+282)))
		tmp = t_0;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+161], t$95$0, If[LessEqual[y, 1.5e+20], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1e+226], N[Not[LessEqual[y, 1.9e+282]], $MachinePrecision]], t$95$0, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000003e161 or 1.5e20 < y < 9.99999999999999961e225 or 1.9e282 < y

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. associate-/l* 90.6%

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

      3. distribute-lft-out 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in y around inf 80.0%

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

   if -8.0000000000000003e161 < y < 1.5e20

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 92.1%

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

   if 9.99999999999999961e225 < y < 1.9e282

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 10^{+226} \lor \neg \left(y \leq 1.9 \cdot 10^{+282}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 2e+306) (+ x (* x (* z (+ y -1.0)))) (* y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+306) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = y * (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 (((1.0d0 - y) * z) <= 2d+306) then
        tmp = x + (x * (z * (y + (-1.0d0))))
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+306) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 2e+306:
		tmp = x + (x * (z * (y + -1.0)))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 2e+306)
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 2e+306)
		tmp = x + (x * (z * (y + -1.0)));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 2e+306], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 2.00000000000000003e306

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 98.3%

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

   if 2.00000000000000003e306 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 62.9%

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

   3. Taylor expanded in y around inf 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 99.9%

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

      3. distribute-lft-out 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 2e+306) (* x (+ 1.0 (* z (+ y -1.0)))) (* y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+306) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = y * (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 (((1.0d0 - y) * z) <= 2d+306) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+306) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 2e+306:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 2e+306)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 2e+306)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 2e+306], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 2.00000000000000003e306

   1. Initial program 98.3%

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

   if 2.00000000000000003e306 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 62.9%

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

   3. Taylor expanded in y around inf 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 99.9%

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

      3. distribute-lft-out 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3200 \lor \neg \left(y \leq 0.96\right):\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3200.0) (not (<= y 0.96))) (+ x (* x (* y z))) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3200.0) || !(y <= 0.96)) {
		tmp = x + (x * (y * z));
	} 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 <= (-3200.0d0)) .or. (.not. (y <= 0.96d0))) then
        tmp = x + (x * (y * z))
    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 <= -3200.0) || !(y <= 0.96)) {
		tmp = x + (x * (y * z));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3200.0) or not (y <= 0.96):
		tmp = x + (x * (y * z))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3200.0) || !(y <= 0.96))
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3200.0) || ~((y <= 0.96)))
		tmp = x + (x * (y * z));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3200.0], N[Not[LessEqual[y, 0.96]], $MachinePrecision]], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3200 or 0.95999999999999996 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 91.5%

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

   4. Taylor expanded in y around inf 90.9%

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

      1. *-commutative 90.9%

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

   6. Simplified 90.9%

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

   if -3200 < y < 0.95999999999999996

   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 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-rgt-in 99.5%

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

      3. *-un-lft-identity 99.5%

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

   5. Applied egg-rr 99.5%

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

      1. distribute-lft-neg-out 99.5%

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

      2. *-commutative 99.5%

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

      3. unsub-neg 99.5%

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

      4. *-commutative 99.5%

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

   7. Applied egg-rr 99.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3200 \lor \neg \left(y \leq 0.96\right):\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159} \lor \neg \left(y \leq 2.25 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+159) (not (<= y 2.25e+20)))
   (* x (* y z))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+159) || !(y <= 2.25e+20)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.4d+159)) .or. (.not. (y <= 2.25d+20))) then
        tmp = x * (y * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+159) || !(y <= 2.25e+20)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e+159) or not (y <= 2.25e+20):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e+159) || !(y <= 2.25e+20))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.4e+159) || ~((y <= 2.25e+20)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e+159], N[Not[LessEqual[y, 2.25e+20]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e159 or 2.25e20 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   if -4.3999999999999998e159 < y < 2.25e20

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 92.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159} \lor \neg \left(y \leq 2.25 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+20}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.4e+159)
   (* y (* x z))
   (if (<= y 2.25e+20) (- x (* x z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+159) {
		tmp = y * (x * z);
	} else if (y <= 2.25e+20) {
		tmp = x - (x * z);
	} else {
		tmp = z * (x * 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 <= (-4.4d+159)) then
        tmp = y * (x * z)
    else if (y <= 2.25d+20) then
        tmp = x - (x * z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+159) {
		tmp = y * (x * z);
	} else if (y <= 2.25e+20) {
		tmp = x - (x * z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.4e+159:
		tmp = y * (x * z)
	elif y <= 2.25e+20:
		tmp = x - (x * z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.4e+159)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 2.25e+20)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.4e+159)
		tmp = y * (x * z);
	elseif (y <= 2.25e+20)
		tmp = x - (x * z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.4e+159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+20], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999998e159

   1. Initial program 91.3%

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

   3. Taylor expanded in y around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-/l* 88.5%

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

      3. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around inf 85.6%

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

   if -4.3999999999999998e159 < y < 2.25e20

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 92.1%

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

      1. sub-neg 92.1%

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

      2. distribute-rgt-in 92.2%

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

      3. *-un-lft-identity 92.2%

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

   5. Applied egg-rr 92.2%

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

      1. distribute-lft-neg-out 92.2%

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

      2. *-commutative 92.2%

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

      3. unsub-neg 92.2%

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

      4. *-commutative 92.2%

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

   7. Applied egg-rr 92.2%

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

   if 2.25e20 < y

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. associate-*r* 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+20}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.4e+159)
   (* y (* x z))
   (if (<= y 1.4e+20) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+159) {
		tmp = y * (x * z);
	} else if (y <= 1.4e+20) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * 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 <= (-4.4d+159)) then
        tmp = y * (x * z)
    else if (y <= 1.4d+20) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.4e+159) {
		tmp = y * (x * z);
	} else if (y <= 1.4e+20) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.4e+159:
		tmp = y * (x * z)
	elif y <= 1.4e+20:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.4e+159)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.4e+20)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.4e+159)
		tmp = y * (x * z);
	elseif (y <= 1.4e+20)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.4e+159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+20], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999998e159

   1. Initial program 91.3%

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

   3. Taylor expanded in y around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-/l* 88.5%

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

      3. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around inf 85.6%

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

   if -4.3999999999999998e159 < y < 1.4e20

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 92.1%

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

   if 1.4e20 < y

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. associate-*r* 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0023 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0023) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0023) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.0023d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0023) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0023) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0023) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0023) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0023], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.0023 or 1 < z

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 90.8%

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

   4. Taylor expanded in y around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. distribute-rgt-neg-out 54.2%

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

   6. Simplified 54.2%

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

   if -0.0023 < 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 z around 0 74.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0023 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in z around 0 38.3%

   \[\leadsto \color{blue}{x} \]
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 2024111 
(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))))