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

Percentage Accurate: 96.4% → 99.1%

Time: 7.2s

Alternatives: 11

Speedup: 1.0×

• 21.5% 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: 96.4% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+293}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -4e+85)
     (* z (* x (+ -1.0 y)))
     (if (<= t_0 4e+293) (+ x (* x (* z (+ -1.0 y)))) (+ x (* (* x z) y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -4e+85) {
		tmp = z * (x * (-1.0 + y));
	} else if (t_0 <= 4e+293) {
		tmp = x + (x * (z * (-1.0 + y)));
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if (t_0 <= (-4d+85)) then
        tmp = z * (x * ((-1.0d0) + y))
    else if (t_0 <= 4d+293) then
        tmp = x + (x * (z * ((-1.0d0) + y)))
    else
        tmp = x + ((x * z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -4e+85) {
		tmp = z * (x * (-1.0 + y));
	} else if (t_0 <= 4e+293) {
		tmp = x + (x * (z * (-1.0 + y)));
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -4e+85:
		tmp = z * (x * (-1.0 + y))
	elif t_0 <= 4e+293:
		tmp = x + (x * (z * (-1.0 + y)))
	else:
		tmp = x + ((x * z) * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -4e+85)
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	elseif (t_0 <= 4e+293)
		tmp = Float64(x + Float64(x * Float64(z * Float64(-1.0 + y))));
	else
		tmp = Float64(x + Float64(Float64(x * z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -4e+85)
		tmp = z * (x * (-1.0 + y));
	elseif (t_0 <= 4e+293)
		tmp = x + (x * (z * (-1.0 + y)));
	else
		tmp = x + ((x * z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+85], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+293], N[(x + N[(x * N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.0000000000000001e85

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -4.0000000000000001e85 < (*.f64 (-.f64 1 y) z) < 3.9999999999999997e293

   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%

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

   if 3.9999999999999997e293 < (*.f64 (-.f64 1 y) z)

   1. Initial program 68.2%

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

   3. Taylor expanded in z around 0 68.2%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-*l* 86.7%

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

      3. *-commutative 86.7%

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

      4. distribute-rgt-out 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 55.7%

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

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 4 \cdot 10^{+293}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+293}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -4e+85)
     (* z (* x (+ -1.0 y)))
     (if (<= t_0 4e+293) (* x (+ 1.0 (* z (+ -1.0 y)))) (+ x (* (* x z) y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -4e+85) {
		tmp = z * (x * (-1.0 + y));
	} else if (t_0 <= 4e+293) {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if (t_0 <= (-4d+85)) then
        tmp = z * (x * ((-1.0d0) + y))
    else if (t_0 <= 4d+293) then
        tmp = x * (1.0d0 + (z * ((-1.0d0) + y)))
    else
        tmp = x + ((x * z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -4e+85) {
		tmp = z * (x * (-1.0 + y));
	} else if (t_0 <= 4e+293) {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -4e+85:
		tmp = z * (x * (-1.0 + y))
	elif t_0 <= 4e+293:
		tmp = x * (1.0 + (z * (-1.0 + y)))
	else:
		tmp = x + ((x * z) * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -4e+85)
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	elseif (t_0 <= 4e+293)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	else
		tmp = Float64(x + Float64(Float64(x * z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -4e+85)
		tmp = z * (x * (-1.0 + y));
	elseif (t_0 <= 4e+293)
		tmp = x * (1.0 + (z * (-1.0 + y)));
	else
		tmp = x + ((x * z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+85], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+293], N[(x * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.0000000000000001e85

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -4.0000000000000001e85 < (*.f64 (-.f64 1 y) z) < 3.9999999999999997e293

   1. Initial program 99.9%

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

   if 3.9999999999999997e293 < (*.f64 (-.f64 1 y) z)

   1. Initial program 68.2%

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

   3. Taylor expanded in z around 0 68.2%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-*l* 86.7%

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

      3. *-commutative 86.7%

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

      4. distribute-rgt-out 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 55.7%

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

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 4 \cdot 10^{+293}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+293}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -4e+85)
     (* z (* x (+ -1.0 y)))
     (if (<= t_0 4e+293) (* x (- (+ 1.0 (* z y)) z)) (+ x (* (* x z) y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -4e+85) {
		tmp = z * (x * (-1.0 + y));
	} else if (t_0 <= 4e+293) {
		tmp = x * ((1.0 + (z * y)) - z);
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if (t_0 <= (-4d+85)) then
        tmp = z * (x * ((-1.0d0) + y))
    else if (t_0 <= 4d+293) then
        tmp = x * ((1.0d0 + (z * y)) - z)
    else
        tmp = x + ((x * z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -4e+85) {
		tmp = z * (x * (-1.0 + y));
	} else if (t_0 <= 4e+293) {
		tmp = x * ((1.0 + (z * y)) - z);
	} else {
		tmp = x + ((x * z) * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -4e+85:
		tmp = z * (x * (-1.0 + y))
	elif t_0 <= 4e+293:
		tmp = x * ((1.0 + (z * y)) - z)
	else:
		tmp = x + ((x * z) * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -4e+85)
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	elseif (t_0 <= 4e+293)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(z * y)) - z));
	else
		tmp = Float64(x + Float64(Float64(x * z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -4e+85)
		tmp = z * (x * (-1.0 + y));
	elseif (t_0 <= 4e+293)
		tmp = x * ((1.0 + (z * y)) - z);
	else
		tmp = x + ((x * z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+85], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+293], N[(x * N[(N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.0000000000000001e85

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -4.0000000000000001e85 < (*.f64 (-.f64 1 y) z) < 3.9999999999999997e293

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

   if 3.9999999999999997e293 < (*.f64 (-.f64 1 y) z)

   1. Initial program 68.2%

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

   3. Taylor expanded in z around 0 68.2%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-*l* 86.7%

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

      3. *-commutative 86.7%

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

      4. distribute-rgt-out 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 55.7%

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

      1. associate-*r* 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -4 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 4 \cdot 10^{+293}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1160000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -1160000000.0)
     t_0
     (if (<= z 9.2e-24) x (if (<= z 2.1e+61) (* x (* z y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1160000000.0) {
		tmp = t_0;
	} else if (z <= 9.2e-24) {
		tmp = x;
	} else if (z <= 2.1e+61) {
		tmp = x * (z * y);
	} 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 <= (-1160000000.0d0)) then
        tmp = t_0
    else if (z <= 9.2d-24) then
        tmp = x
    else if (z <= 2.1d+61) then
        tmp = x * (z * y)
    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 <= -1160000000.0) {
		tmp = t_0;
	} else if (z <= 9.2e-24) {
		tmp = x;
	} else if (z <= 2.1e+61) {
		tmp = x * (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -1160000000.0:
		tmp = t_0
	elif z <= 9.2e-24:
		tmp = x
	elif z <= 2.1e+61:
		tmp = x * (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -1160000000.0)
		tmp = t_0;
	elseif (z <= 9.2e-24)
		tmp = x;
	elseif (z <= 2.1e+61)
		tmp = Float64(x * Float64(z * y));
	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 <= -1160000000.0)
		tmp = t_0;
	elseif (z <= 9.2e-24)
		tmp = x;
	elseif (z <= 2.1e+61)
		tmp = x * (z * y);
	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, -1160000000.0], t$95$0, If[LessEqual[z, 9.2e-24], x, If[LessEqual[z, 2.1e+61], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16e9 or 2.1000000000000001e61 < z

   1. Initial program 92.1%

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

      1. *-commutative 91.9%

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

      2. associate-*l* 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. mul-1-neg 68.4%

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

   8. Simplified 68.4%

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

   if -1.16e9 < z < 9.2000000000000004e-24

   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 77.6%

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

   if 9.2000000000000004e-24 < z < 2.1000000000000001e61

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1160000000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -21500 \lor \neg \left(z \leq 9.5 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -21500.0) (not (<= z 9.5e-24)))
   (* z (* x (+ -1.0 y)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -21500.0) || !(z <= 9.5e-24)) {
		tmp = z * (x * (-1.0 + 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 ((z <= (-21500.0d0)) .or. (.not. (z <= 9.5d-24))) then
        tmp = z * (x * ((-1.0d0) + 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 ((z <= -21500.0) || !(z <= 9.5e-24)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -21500.0) or not (z <= 9.5e-24):
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -21500.0) || !(z <= 9.5e-24))
		tmp = Float64(z * Float64(x * Float64(-1.0 + 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 ((z <= -21500.0) || ~((z <= 9.5e-24)))
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -21500.0], N[Not[LessEqual[z, 9.5e-24]], $MachinePrecision]], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -21500 or 9.50000000000000029e-24 < z

   1. Initial program 93.0%

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

      1. *-commutative 92.2%

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

      2. associate-*l* 99.0%

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

      3. sub-neg 99.0%

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

      4. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   if -21500 < z < 9.50000000000000029e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -21500 \lor \neg \left(z \leq 9.5 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1160000000 \lor \neg \left(z \leq 460\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1160000000.0) (not (<= z 460.0)))
   (* z (* x (+ -1.0 y)))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1160000000.0) || !(z <= 460.0)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1160000000.0d0)) .or. (.not. (z <= 460.0d0))) then
        tmp = z * (x * ((-1.0d0) + y))
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1160000000.0) || !(z <= 460.0)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1160000000.0) or not (z <= 460.0):
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1160000000.0) || !(z <= 460.0))
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1160000000.0) || ~((z <= 460.0)))
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1160000000.0], N[Not[LessEqual[z, 460.0]], $MachinePrecision]], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.16e9 or 460 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l* 99.0%

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

      3. sub-neg 99.0%

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

      4. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   if -1.16e9 < z < 460

   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 98.9%

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

      1. *-commutative 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1160000000 \lor \neg \left(z \leq 460\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+132} \lor \neg \left(y \leq 9.2 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e+132) (not (<= y 9.2e+93)))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e+132) || !(y <= 9.2e+93)) {
		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 <= (-1.25d+132)) .or. (.not. (y <= 9.2d+93))) 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 <= -1.25e+132) || !(y <= 9.2e+93)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e+132) or not (y <= 9.2e+93):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e+132) || !(y <= 9.2e+93))
		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 <= -1.25e+132) || ~((y <= 9.2e+93)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e+132], N[Not[LessEqual[y, 9.2e+93]], $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 < -1.25e132 or 9.2000000000000006e93 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -1.25e132 < y < 9.2000000000000006e93

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 89.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+132} \lor \neg \left(y \leq 9.2 \cdot 10^{+93}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.6e+131)
   (* x (* z y))
   (if (<= y 3.1e+92) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.6e+131) {
		tmp = x * (z * y);
	} else if (y <= 3.1e+92) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.6d+131)) then
        tmp = x * (z * y)
    else if (y <= 3.1d+92) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.6e+131) {
		tmp = x * (z * y);
	} else if (y <= 3.1e+92) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.6e+131:
		tmp = x * (z * y)
	elif y <= 3.1e+92:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.6e+131)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 3.1e+92)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.6e+131)
		tmp = x * (z * y);
	elseif (y <= 3.1e+92)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.6e+131], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+92], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5999999999999997e131

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if -6.5999999999999997e131 < y < 3.1000000000000002e92

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 89.4%

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

   if 3.1000000000000002e92 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf 72.5%

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

      1. associate-*r* 83.1%

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

      2. *-commutative 83.1%

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

   5. Simplified 83.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1160000000 \lor \neg \left(z \leq 0.00178\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1160000000.0) (not (<= z 0.00178))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1160000000.0) || !(z <= 0.00178)) {
		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 <= (-1160000000.0d0)) .or. (.not. (z <= 0.00178d0))) 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 <= -1160000000.0) || !(z <= 0.00178)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1160000000.0) or not (z <= 0.00178):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1160000000.0) || !(z <= 0.00178))
		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 <= -1160000000.0) || ~((z <= 0.00178)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1160000000.0], N[Not[LessEqual[z, 0.00178]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.16e9 or 0.0017799999999999999 < z

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*l* 99.0%

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

      3. sub-neg 99.0%

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

      4. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. mul-1-neg 64.9%

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

   8. Simplified 64.9%

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

   if -1.16e9 < z < 0.0017799999999999999

   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 77.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1160000000 \lor \neg \left(z \leq 0.00178\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in z around 0 96.2%

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

4. Taylor expanded in y around 0 92.0%

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

   1. *-commutative 92.0%

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

   2. associate-*l* 91.3%

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

   3. *-commutative 91.3%

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

   4. distribute-rgt-out 98.3%

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

6. Simplified 98.3%

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

7. Final simplification 98.3%

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

Alternative 11: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in z around 0 38.2%

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

4. Final simplification 38.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% 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 2024027 
(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))))