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

Percentage Accurate: 96.1% → 98.5%

Time: 6.8s

Alternatives: 9

Speedup: 0.6×

• 20.8% 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: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20500000000 \lor \neg \left(z \leq 88000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -20500000000.0) (not (<= z 88000.0)))
   (* z (* x (+ y -1.0)))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -20500000000.0) || !(z <= 88000.0)) {
		tmp = z * (x * (y + -1.0));
	} 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) :: tmp
    if ((z <= (-20500000000.0d0)) .or. (.not. (z <= 88000.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    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 <= -20500000000.0) || !(z <= 88000.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -20500000000.0) or not (z <= 88000.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -20500000000.0) || !(z <= 88000.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	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 <= -20500000000.0) || ~((z <= 88000.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -20500000000.0], N[Not[LessEqual[z, 88000.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e10 or 88000 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -2.05e10 < z < 88000

   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 inf 99.3%

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

      1. *-commutative 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20500000000 \lor \neg \left(z \leq 88000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -10500000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* z y))))
   (if (<= z -10500000000000.0)
     t_0
     (if (<= z -4.7e-43)
       t_1
       (if (<= z 1.9e-13) x (if (<= z 2e+26) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -10500000000000.0) {
		tmp = t_0;
	} else if (z <= -4.7e-43) {
		tmp = t_1;
	} else if (z <= 1.9e-13) {
		tmp = x;
	} else if (z <= 2e+26) {
		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 * (z * y)
    if (z <= (-10500000000000.0d0)) then
        tmp = t_0
    else if (z <= (-4.7d-43)) then
        tmp = t_1
    else if (z <= 1.9d-13) then
        tmp = x
    else if (z <= 2d+26) 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 * (z * y);
	double tmp;
	if (z <= -10500000000000.0) {
		tmp = t_0;
	} else if (z <= -4.7e-43) {
		tmp = t_1;
	} else if (z <= 1.9e-13) {
		tmp = x;
	} else if (z <= 2e+26) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (z * y)
	tmp = 0
	if z <= -10500000000000.0:
		tmp = t_0
	elif z <= -4.7e-43:
		tmp = t_1
	elif z <= 1.9e-13:
		tmp = x
	elif z <= 2e+26:
		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(z * y))
	tmp = 0.0
	if (z <= -10500000000000.0)
		tmp = t_0;
	elseif (z <= -4.7e-43)
		tmp = t_1;
	elseif (z <= 1.9e-13)
		tmp = x;
	elseif (z <= 2e+26)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -10500000000000.0)
		tmp = t_0;
	elseif (z <= -4.7e-43)
		tmp = t_1;
	elseif (z <= 1.9e-13)
		tmp = x;
	elseif (z <= 2e+26)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10500000000000.0], t$95$0, If[LessEqual[z, -4.7e-43], t$95$1, If[LessEqual[z, 1.9e-13], x, If[LessEqual[z, 2e+26], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e13 or 2.0000000000000001e26 < z

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 91.9%

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

   4. Taylor expanded in y around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-out 60.4%

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

   6. Simplified 60.4%

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

   if -1.05e13 < z < -4.7000000000000001e-43 or 1.9e-13 < z < 2.0000000000000001e26

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 83.9%

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

      1. *-commutative 83.9%

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

   5. Simplified 83.9%

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

   if -4.7000000000000001e-43 < z < 1.9e-13

   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 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10500000000000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-43} \lor \neg \left(z \leq 3.9 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-43) (not (<= z 3.9e-14))) (* z (* x (+ y -1.0))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-43) || !(z <= 3.9e-14)) {
		tmp = z * (x * (y + -1.0));
	} 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 <= (-5d-43)) .or. (.not. (z <= 3.9d-14))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-43) || !(z <= 3.9e-14)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-43) or not (z <= 3.9e-14):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-43) || !(z <= 3.9e-14))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-43) || ~((z <= 3.9e-14)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-43], N[Not[LessEqual[z, 3.9e-14]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000019e-43 or 3.8999999999999998e-14 < z

   1. Initial program 92.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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* 98.4%

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

      3. *-commutative 98.4%

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

      4. sub-neg 98.4%

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

      5. metadata-eval 98.4%

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

   5. Simplified 98.4%

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

   if -5.00000000000000019e-43 < z < 3.8999999999999998e-14

   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 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-43} \lor \neg \left(z \leq 3.9 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+67} \lor \neg \left(y \leq 70\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e+67) (not (<= y 70.0))) (* z (* x y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e+67) || !(y <= 70.0)) {
		tmp = z * (x * 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 <= (-2.3d+67)) .or. (.not. (y <= 70.0d0))) then
        tmp = z * (x * 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 <= -2.3e+67) || !(y <= 70.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e+67) or not (y <= 70.0):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e+67) || !(y <= 70.0))
		tmp = Float64(z * Float64(x * 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 <= -2.3e+67) || ~((y <= 70.0)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e+67], N[Not[LessEqual[y, 70.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e67 or 70 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 69.3%

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

   4. Taylor expanded in y around inf 68.6%

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

      1. associate-*r* 73.6%

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

   6. Simplified 73.6%

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

   if -2.2999999999999999e67 < y < 70

   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 97.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+67} \lor \neg \left(y \leq 70\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+64} \lor \neg \left(y \leq 60\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.8e+64) (not (<= y 60.0))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.8e+64) || !(y <= 60.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8.8d+64)) .or. (.not. (y <= 60.0d0))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.8e+64) || !(y <= 60.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.8e+64) or not (y <= 60.0):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.8e+64) || !(y <= 60.0))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.8e+64) || ~((y <= 60.0)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.8e+64], N[Not[LessEqual[y, 60.0]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000007e64 or 60 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 81.6%

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

   4. Taylor expanded in y around inf 71.5%

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

   if -8.80000000000000007e64 < y < 60

   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 97.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+64} \lor \neg \left(y \leq 60\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+68} \lor \neg \left(y \leq 70\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+68) (not (<= y 70.0))) (* x (* z y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+68) || !(y <= 70.0)) {
		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 <= (-5d+68)) .or. (.not. (y <= 70.0d0))) 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 <= -5e+68) || !(y <= 70.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+68) or not (y <= 70.0):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+68) || !(y <= 70.0))
		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 <= -5e+68) || ~((y <= 70.0)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+68], N[Not[LessEqual[y, 70.0]], $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 < -5.0000000000000004e68 or 70 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -5.0000000000000004e68 < y < 70

   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 97.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+68} \lor \neg \left(y \leq 70\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.3 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 4.3e+24))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 4.3e+24)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 4.3d+24))) 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 <= -1.0) || !(z <= 4.3e+24)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 4.3e+24):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 4.3e+24))
		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 <= -1.0) || ~((z <= 4.3e+24)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 4.3e+24]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 4.29999999999999987e24 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf 92.2%

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

   4. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-rgt-neg-out 58.1%

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

   6. Simplified 58.1%

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

   if -1 < z < 4.29999999999999987e24

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 69.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4.3 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1750000:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1750000.0) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* x (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1750000.0) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1750000.0d0) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1750000.0) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1750000.0:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1750000.0)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1750000.0)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1750000.0], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.75e6

   1. Initial program 98.0%

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

   if 1.75e6 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. *-commutative 89.0%

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

      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%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1750000:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.4% 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 95.8%

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

3. Taylor expanded in z around 0 37.7%

   \[\leadsto \color{blue}{x} \]
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 2024108 
(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))))