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

Percentage Accurate: 96.1% → 97.9%

Time: 7.5s

Alternatives: 11

Speedup: 0.8×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;t_0 \leq 10^{+306}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (+ y -1.0))))))
   (if (<= t_0 1e+306) t_0 (* z (- (* x y) x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= 1e+306) {
		tmp = t_0;
	} else {
		tmp = z * ((x * y) - 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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= 1d+306) then
        tmp = t_0
    else
        tmp = z * ((x * y) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= 1e+306) {
		tmp = t_0;
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= 1e+306:
		tmp = t_0
	else:
		tmp = z * ((x * y) - x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= 1e+306)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(x * y) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= 1e+306)
		tmp = t_0;
	else
		tmp = z * ((x * y) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+306], t$95$0, N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 1.00000000000000002e306

   1. Initial program 98.2%

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

   if 1.00000000000000002e306 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0 68.5%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 98.5%

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

Alternative 2: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -57000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -57000.0) (not (<= z 1.0)))
   (* z (- (* x y) x))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -57000.0) || !(z <= 1.0)) {
		tmp = z * ((x * y) - x);
	} 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 ((z <= (-57000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * ((x * y) - x)
    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 ((z <= -57000.0) || !(z <= 1.0)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -57000.0) or not (z <= 1.0):
		tmp = z * ((x * y) - x)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -57000.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(Float64(x * y) - x));
	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 ((z <= -57000.0) || ~((z <= 1.0)))
		tmp = z * ((x * y) - x);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -57000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -57000 or 1 < z

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 85.6%

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

   3. Taylor expanded in z around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

      4. *-commutative 98.7%

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

   5. Applied egg-rr 98.7%

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

   if -57000 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in y around inf 97.7%

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

      1. *-commutative 97.7%

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

   5. Simplified 97.7%

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

      1. *-commutative 97.7%

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

      2. *-commutative 97.7%

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

      3. distribute-rgt1-in 97.7%

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

   7. Applied egg-rr 97.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -57000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 3: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.4:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+32)
   (* z (* x y))
   (if (<= y 7.4) (- x (* x z)) (* z (- (* x y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+32) {
		tmp = z * (x * y);
	} else if (y <= 7.4) {
		tmp = x - (x * z);
	} else {
		tmp = z * ((x * y) - 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 <= (-1.65d+32)) then
        tmp = z * (x * y)
    else if (y <= 7.4d0) then
        tmp = x - (x * z)
    else
        tmp = z * ((x * y) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+32) {
		tmp = z * (x * y);
	} else if (y <= 7.4) {
		tmp = x - (x * z);
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+32:
		tmp = z * (x * y)
	elif y <= 7.4:
		tmp = x - (x * z)
	else:
		tmp = z * ((x * y) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+32)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 7.4)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(z * Float64(Float64(x * y) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e+32)
		tmp = z * (x * y);
	elseif (y <= 7.4)
		tmp = x - (x * z);
	else
		tmp = z * ((x * y) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+32], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6500000000000001e32

   1. Initial program 84.6%

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

   2. Taylor expanded in y around inf 74.5%

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

      1. associate-*r* 85.9%

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

      2. *-commutative 85.9%

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

   4. Simplified 85.9%

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

   if -1.6500000000000001e32 < y < 7.4000000000000004

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-rgt-in 97.8%

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

      3. *-un-lft-identity 97.8%

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

      4. *-commutative 97.8%

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

      5. distribute-rgt-neg-out 97.8%

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

      6. unsub-neg 97.8%

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

   4. Applied egg-rr 97.8%

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

   if 7.4000000000000004 < y

   1. Initial program 92.8%

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

   2. Taylor expanded in y around 0 83.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. +-commutative 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. *-commutative 78.1%

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

   5. Applied egg-rr 78.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.4:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 4: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -57000:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -57000.0)
   (* z (- (* x y) x))
   (if (<= z 1.0) (* x (+ 1.0 (* y z))) (* (* x z) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -57000.0) {
		tmp = z * ((x * y) - x);
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (x * z) * (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 <= (-57000.0d0)) then
        tmp = z * ((x * y) - x)
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = (x * z) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -57000.0) {
		tmp = z * ((x * y) - x);
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (x * z) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -57000.0:
		tmp = z * ((x * y) - x)
	elif z <= 1.0:
		tmp = x * (1.0 + (y * z))
	else:
		tmp = (x * z) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -57000.0)
		tmp = Float64(z * Float64(Float64(x * y) - x));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -57000.0)
		tmp = z * ((x * y) - x);
	elseif (z <= 1.0)
		tmp = x * (1.0 + (y * z));
	else
		tmp = (x * z) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -57000.0], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -57000

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 87.0%

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

   3. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

      4. *-commutative 97.8%

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

   5. Applied egg-rr 97.8%

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

   if -57000 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in y around inf 97.7%

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

      1. *-commutative 97.7%

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

   5. Simplified 97.7%

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

      1. *-commutative 97.7%

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

      2. *-commutative 97.7%

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

      3. distribute-rgt1-in 97.7%

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

   7. Applied egg-rr 97.7%

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

   if 1 < z

   1. Initial program 89.9%

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

      1. add-cbrt-cube 58.5%

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

      2. pow3 58.5%

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

      3. sub-neg 58.5%

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

      4. +-commutative 58.5%

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

      5. distribute-rgt-neg-in 58.5%

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

      6. fma-def 58.5%

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

   3. Applied egg-rr 58.5%

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

   4. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*r* 89.4%

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

      5. associate-*r* 99.5%

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

      6. mul-1-neg 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -57000:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 5: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -3.8e+194)
     t_0
     (if (<= z -3e-23) (* x (* y z)) (if (<= z 1.0) x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -3.8e+194) {
		tmp = t_0;
	} else if (z <= -3e-23) {
		tmp = x * (y * z);
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-3.8d+194)) then
        tmp = t_0
    else if (z <= (-3d-23)) then
        tmp = x * (y * z)
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -3.8e+194) {
		tmp = t_0;
	} else if (z <= -3e-23) {
		tmp = x * (y * z);
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -3.8e+194:
		tmp = t_0
	elif z <= -3e-23:
		tmp = x * (y * z)
	elif z <= 1.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -3.8e+194)
		tmp = t_0;
	elseif (z <= -3e-23)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -3.8e+194)
		tmp = t_0;
	elseif (z <= -3e-23)
		tmp = x * (y * z);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -3.8e+194], t$95$0, If[LessEqual[z, -3e-23], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999999e194 or 1 < z

   1. Initial program 88.7%

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

   2. Taylor expanded in y around 0 61.8%

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

   3. Taylor expanded in z around inf 61.5%

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

      1. associate-*r* 61.5%

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

      2. neg-mul-1 61.5%

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

   5. Simplified 61.5%

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

   if -3.7999999999999999e194 < z < -3.00000000000000003e-23

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

   4. Simplified 59.0%

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

   if -3.00000000000000003e-23 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 74.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+31} \lor \neg \left(y \leq 12\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.6e+31) (not (<= y 12.0))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e+31) || !(y <= 12.0)) {
		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 <= (-3.6d+31)) .or. (.not. (y <= 12.0d0))) 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 <= -3.6e+31) || !(y <= 12.0)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.6e+31) or not (y <= 12.0):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.6e+31) || !(y <= 12.0))
		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 <= -3.6e+31) || ~((y <= 12.0)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.6e+31], N[Not[LessEqual[y, 12.0]], $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 < -3.59999999999999996e31 or 12 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

   4. Simplified 72.8%

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

   if -3.59999999999999996e31 < y < 12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+31} \lor \neg \left(y \leq 12\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+33} \lor \neg \left(y \leq 6.6\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+33) (not (<= y 6.6))) (* y (* x z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+33) || !(y <= 6.6)) {
		tmp = y * (x * 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 <= (-4.8d+33)) .or. (.not. (y <= 6.6d0))) then
        tmp = y * (x * 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 <= -4.8e+33) || !(y <= 6.6)) {
		tmp = y * (x * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+33) or not (y <= 6.6):
		tmp = y * (x * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+33) || !(y <= 6.6))
		tmp = Float64(y * Float64(x * 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 <= -4.8e+33) || ~((y <= 6.6)))
		tmp = y * (x * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+33], N[Not[LessEqual[y, 6.6]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e33 or 6.5999999999999996 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in y around 0 84.0%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*l* 77.9%

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

      3. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -4.8e33 < y < 6.5999999999999996

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+33} \lor \neg \left(y \leq 6.6\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+33} \lor \neg \left(y \leq 10.2\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+33) (not (<= y 10.2))) (* z (* x y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+33) || !(y <= 10.2)) {
		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 <= (-6.2d+33)) .or. (.not. (y <= 10.2d0))) 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 <= -6.2e+33) || !(y <= 10.2)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+33) or not (y <= 10.2):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+33) || !(y <= 10.2))
		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 <= -6.2e+33) || ~((y <= 10.2)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+33], N[Not[LessEqual[y, 10.2]], $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 < -6.2e33 or 10.199999999999999 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf 72.8%

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

      1. associate-*r* 80.8%

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

      2. *-commutative 80.8%

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

   4. Simplified 80.8%

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

   if -6.2e33 < y < 10.199999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+33} \lor \neg \left(y \leq 10.2\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+31} \lor \neg \left(y \leq 14.5\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+31) (not (<= y 14.5))) (* z (* x y)) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+31) || !(y <= 14.5)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.1d+31)) .or. (.not. (y <= 14.5d0))) then
        tmp = z * (x * y)
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+31) || !(y <= 14.5)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+31) or not (y <= 14.5):
		tmp = z * (x * y)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+31) || !(y <= 14.5))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.1e+31) || ~((y <= 14.5)))
		tmp = z * (x * y);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+31], N[Not[LessEqual[y, 14.5]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000005e31 or 14.5 < y

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf 72.8%

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

      1. associate-*r* 80.8%

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

      2. *-commutative 80.8%

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

   4. Simplified 80.8%

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

   if -1.10000000000000005e31 < y < 14.5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-rgt-in 97.8%

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

      3. *-un-lft-identity 97.8%

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

      4. *-commutative 97.8%

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

      5. distribute-rgt-neg-out 97.8%

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

      6. unsub-neg 97.8%

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

   4. Applied egg-rr 97.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+31} \lor \neg \left(y \leq 14.5\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 10: 64.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(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 <= -1.0) || ~((z <= 1.0)))
		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, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 91.0%

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

   2. Taylor expanded in y around 0 55.7%

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

   3. Taylor expanded in z around inf 54.7%

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

      1. associate-*r* 54.7%

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

      2. neg-mul-1 54.7%

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

   5. Simplified 54.7%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 72.1%

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

4. Final simplification 63.0%

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

Alternative 11: 39.0% 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 95.2%

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

2. Taylor expanded in z around 0 35.7%

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

3. Final simplification 35.7%

   \[\leadsto x \]

Developer target: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))