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

Percentage Accurate: 95.9% → 99.0%

Time: 5.9s

Alternatives: 7

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (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 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (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 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+269}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot z \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+269)
   (- (* z (* x y)))
   (if (<= (* y z) 1.5e+76) (* x (- 1.0 (* y z))) (* y (* x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+269) {
		tmp = -(z * (x * y));
	} else if ((y * z) <= 1.5e+76) {
		tmp = x * (1.0 - (y * z));
	} 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 ((y * z) <= (-1d+269)) then
        tmp = -(z * (x * y))
    else if ((y * z) <= 1.5d+76) then
        tmp = x * (1.0d0 - (y * z))
    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 ((y * z) <= -1e+269) {
		tmp = -(z * (x * y));
	} else if ((y * z) <= 1.5e+76) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+269:
		tmp = -(z * (x * y))
	elif (y * z) <= 1.5e+76:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+269)
		tmp = Float64(-Float64(z * Float64(x * y)));
	elseif (Float64(y * z) <= 1.5e+76)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+269)
		tmp = -(z * (x * y));
	elseif ((y * z) <= 1.5e+76)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+269], (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], 1.5e+76], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1e269

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

   if -1e269 < (*.f64 y z) < 1.4999999999999999e76

   1. Initial program 99.9%

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

   if 1.4999999999999999e76 < (*.f64 y z)

   1. Initial program 85.5%

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

   3. Taylor expanded in y around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. associate-*r* 97.7%

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

      3. distribute-rgt-neg-in 97.7%

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

      4. *-commutative 97.7%

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

      5. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+269}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot z \leq 1.5 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot \left(-z\right)\right)\\ t_1 := -z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+292}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y (- z)))) (t_1 (- (* z (* x y)))))
   (if (<= (* y z) -1e+269)
     t_1
     (if (<= (* y z) -1000000.0)
       t_0
       (if (<= (* y z) 1.0) x (if (<= (* y z) 5e+292) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * -z);
	double t_1 = -(z * (x * y));
	double tmp;
	if ((y * z) <= -1e+269) {
		tmp = t_1;
	} else if ((y * z) <= -1000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 1.0) {
		tmp = x;
	} else if ((y * z) <= 5e+292) {
		tmp = t_0;
	} 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 * (y * -z)
    t_1 = -(z * (x * y))
    if ((y * z) <= (-1d+269)) then
        tmp = t_1
    else if ((y * z) <= (-1000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 1.0d0) then
        tmp = x
    else if ((y * z) <= 5d+292) then
        tmp = t_0
    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 * (y * -z);
	double t_1 = -(z * (x * y));
	double tmp;
	if ((y * z) <= -1e+269) {
		tmp = t_1;
	} else if ((y * z) <= -1000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 1.0) {
		tmp = x;
	} else if ((y * z) <= 5e+292) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * -z)
	t_1 = -(z * (x * y))
	tmp = 0
	if (y * z) <= -1e+269:
		tmp = t_1
	elif (y * z) <= -1000000.0:
		tmp = t_0
	elif (y * z) <= 1.0:
		tmp = x
	elif (y * z) <= 5e+292:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * Float64(-z)))
	t_1 = Float64(-Float64(z * Float64(x * y)))
	tmp = 0.0
	if (Float64(y * z) <= -1e+269)
		tmp = t_1;
	elseif (Float64(y * z) <= -1000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 1.0)
		tmp = x;
	elseif (Float64(y * z) <= 5e+292)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * -z);
	t_1 = -(z * (x * y));
	tmp = 0.0;
	if ((y * z) <= -1e+269)
		tmp = t_1;
	elseif ((y * z) <= -1000000.0)
		tmp = t_0;
	elseif ((y * z) <= 1.0)
		tmp = x;
	elseif ((y * z) <= 5e+292)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -1e+269], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -1000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 1.0], x, If[LessEqual[N[(y * z), $MachinePrecision], 5e+292], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1e269 or 4.9999999999999996e292 < (*.f64 y z)

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. associate-*r* 99.8%

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

   5. Simplified 99.8%

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

   if -1e269 < (*.f64 y z) < -1e6 or 1 < (*.f64 y z) < 4.9999999999999996e292

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 97.4%

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

      1. mul-1-neg 97.4%

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

      2. associate-*r* 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in x around 0 97.4%

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

   if -1e6 < (*.f64 y z) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+269}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot z \leq -1000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+292}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+269}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot z \leq -1000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+269)
   (- (* z (* x y)))
   (if (<= (* y z) -1000000.0)
     (* x (* y (- z)))
     (if (<= (* y z) 1.0) x (* y (* x (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+269) {
		tmp = -(z * (x * y));
	} else if ((y * z) <= -1000000.0) {
		tmp = x * (y * -z);
	} else if ((y * z) <= 1.0) {
		tmp = x;
	} 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 ((y * z) <= (-1d+269)) then
        tmp = -(z * (x * y))
    else if ((y * z) <= (-1000000.0d0)) then
        tmp = x * (y * -z)
    else if ((y * z) <= 1.0d0) then
        tmp = x
    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 ((y * z) <= -1e+269) {
		tmp = -(z * (x * y));
	} else if ((y * z) <= -1000000.0) {
		tmp = x * (y * -z);
	} else if ((y * z) <= 1.0) {
		tmp = x;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+269:
		tmp = -(z * (x * y))
	elif (y * z) <= -1000000.0:
		tmp = x * (y * -z)
	elif (y * z) <= 1.0:
		tmp = x
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+269)
		tmp = Float64(-Float64(z * Float64(x * y)));
	elseif (Float64(y * z) <= -1000000.0)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (Float64(y * z) <= 1.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+269)
		tmp = -(z * (x * y));
	elseif ((y * z) <= -1000000.0)
		tmp = x * (y * -z);
	elseif ((y * z) <= 1.0)
		tmp = x;
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+269], (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], -1000000.0], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1.0], x, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 y z) < -1e269

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

   if -1e269 < (*.f64 y z) < -1e6

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 97.5%

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

      1. mul-1-neg 97.5%

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

      2. associate-*r* 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in x around 0 97.5%

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

   if -1e6 < (*.f64 y z) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

   if 1 < (*.f64 y z)

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. associate-*r* 93.1%

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

      3. distribute-rgt-neg-in 93.1%

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

      4. *-commutative 93.1%

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

      5. associate-*l* 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+269}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot z \leq -1000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1000000 \lor \neg \left(y \cdot z \leq 1\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -1000000.0) (not (<= (* y z) 1.0))) (* x (* y (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -1000000.0) || !((y * z) <= 1.0)) {
		tmp = x * (y * -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 (((y * z) <= (-1000000.0d0)) .or. (.not. ((y * z) <= 1.0d0))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -1000000.0) || !((y * z) <= 1.0)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -1000000.0) or not ((y * z) <= 1.0):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -1000000.0) || !(Float64(y * z) <= 1.0))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -1000000.0) || ~(((y * z) <= 1.0)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1.0]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1e6 or 1 < (*.f64 y z)

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. mul-1-neg 87.4%

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

      2. associate-*r* 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in x around 0 87.4%

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

   if -1e6 < (*.f64 y z) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1000000 \lor \neg \left(y \cdot z \leq 1\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1500:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1500.0) (- x (* y (* x z))) (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1500.0) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x * (1.0 - (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) :: tmp
    if (x <= 1500.0d0) then
        tmp = x - (y * (x * z))
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1500.0) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1500.0:
		tmp = x - (y * (x * z))
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1500.0)
		tmp = Float64(x - Float64(y * Float64(x * z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1500.0)
		tmp = x - (y * (x * z));
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1500.0], N[(x - N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1500

   1. Initial program 93.3%

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

      1. sub-neg 93.3%

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

      2. distribute-rgt-in 93.3%

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

      3. *-un-lft-identity 93.3%

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

      4. distribute-rgt-neg-in 93.3%

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

   4. Applied egg-rr 93.3%

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

      1. add-sqr-sqrt 52.1%

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

      2. sqrt-unprod 68.1%

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

      3. distribute-rgt-neg-out 68.1%

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

      4. distribute-rgt-neg-out 68.1%

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

      5. sqr-neg 68.1%

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

      6. sqrt-prod 32.8%

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

      7. add-sqr-sqrt 52.0%

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

      8. cancel-sign-sub 52.0%

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

      9. distribute-rgt-neg-out 52.0%

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

      10. associate-*l* 46.9%

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

      11. add-sqr-sqrt 21.0%

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

      12. sqrt-unprod 57.5%

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

      13. sqr-neg 57.5%

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

      14. sqrt-unprod 45.6%

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

      15. add-sqr-sqrt 90.2%

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

   6. Applied egg-rr 90.2%

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

   if 1500 < x

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1500:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y -8.2e+191) (/ (* x y) y) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+191) {
		tmp = (x * y) / y;
	} 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 (y <= (-8.2d+191)) then
        tmp = (x * y) / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+191) {
		tmp = (x * y) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.2e+191:
		tmp = (x * y) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e+191)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.2e+191)
		tmp = (x * y) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e+191], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999998e191

   1. Initial program 85.2%

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

      1. sub-neg 85.2%

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

      2. distribute-rgt-in 85.2%

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

      3. *-un-lft-identity 85.2%

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

      4. distribute-rgt-neg-in 85.2%

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

   4. Applied egg-rr 85.2%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. associate-*r* 92.6%

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

      2. fma-define 92.6%

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

      3. neg-mul-1 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in z around 0 2.6%

      \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 20.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{y}} \]

   10. Applied egg-rr 20.7%

       \[\leadsto \color{blue}{\frac{y \cdot x}{y}} \]

   if -8.1999999999999998e191 < y

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.2% accurate, 7.0× 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 94.7%

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

3. Taylor expanded in y around 0 52.5%

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

4. Final simplification 52.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024083 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))