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

Percentage Accurate: 95.9% → 98.5%

Time: 7.0s

Alternatives: 11

Speedup: 0.5×

• 20.3% 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: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.06)
   (* z (* x (+ y -1.0)))
   (if (<= z 1.32e-11) (* x (+ 1.0 (* y z))) (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.06) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.32e-11) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.06d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 1.32d-11) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = (z * x) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.06) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.32e-11) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.06:
		tmp = z * (x * (y + -1.0))
	elif z <= 1.32e-11:
		tmp = x * (1.0 + (y * z))
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.06)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 1.32e-11)
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.06)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 1.32e-11)
		tmp = x * (1.0 + (y * z));
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.06], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e-11], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0600000000000001

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 89.2%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

      3. sub-neg 99.6%

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

      4. remove-double-neg 99.6%

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

      5. distribute-neg-in 99.6%

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

      6. +-commutative 99.6%

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

      7. sub-neg 99.6%

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

      8. associate-*r* 99.7%

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

      9. *-commutative 99.7%

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

      10. *-commutative 99.7%

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

      11. neg-sub0 99.7%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(0 - \left(1 - y\right)\right)}\right) \]

      12. associate--r- 99.7%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(\left(0 - 1\right) + y\right)}\right) \]

      13. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

   if -1.0600000000000001 < z < 1.32e-11

   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 98.5%

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

      1. associate-*r* 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 98.5%

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

   if 1.32e-11 < z

   1. Initial program 92.0%

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

   3. Taylor expanded in z around inf 90.3%

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

      1. associate-*r* 98.3%

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

      2. *-commutative 98.3%

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

      3. sub-neg 98.3%

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

      4. metadata-eval 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x - t\_0 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 4e+307) (- x (* t_0 x)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 4e+307) {
		tmp = x - (t_0 * x);
	} else {
		tmp = z * (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 = (1.0d0 - y) * z
    if (t_0 <= 4d+307) then
        tmp = x - (t_0 * x)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 4e+307) {
		tmp = x - (t_0 * x);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= 4e+307:
		tmp = x - (t_0 * x)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= 4e+307)
		tmp = Float64(x - Float64(t_0 * x));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= 4e+307)
		tmp = x - (t_0 * x);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, 4e+307], N[(x - N[(t$95$0 * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 3.99999999999999994e307

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 98.3%

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

   if 3.99999999999999994e307 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 42.6%

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

   3. Taylor expanded in y around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

      3. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x - \left(\left(1 - y\right) \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 4e+307) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 4e+307) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (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 (((1.0d0 - y) * z) <= 4d+307) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 4e+307) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 4e+307:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 4e+307)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 4e+307)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 4e+307], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 3.99999999999999994e307

   1. Initial program 98.3%

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

   if 3.99999999999999994e307 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 42.6%

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

   3. Taylor expanded in y around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

      3. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+307}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.95) (not (<= z 1.0)))
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.95) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} 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 <= (-0.95d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    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 <= -0.95) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.95) or not (z <= 1.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.95) || !(z <= 1.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	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 <= -0.95) || ~((z <= 1.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.95], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.94999999999999996 or 1 < z

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. associate-*r* 99.0%

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

      2. *-commutative 99.0%

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

      3. sub-neg 99.0%

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

      4. remove-double-neg 99.0%

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

      5. distribute-neg-in 99.0%

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

      6. +-commutative 99.0%

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

      7. sub-neg 99.0%

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

      8. associate-*r* 99.0%

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

      9. *-commutative 99.0%

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

      10. *-commutative 99.0%

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

      11. neg-sub0 99.0%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(0 - \left(1 - y\right)\right)}\right) \]

      12. associate--r- 99.0%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(\left(0 - 1\right) + y\right)}\right) \]

      13. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   if -0.94999999999999996 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 98.5%

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

      1. associate-*r* 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in x around 0 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 90.6%

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

   4. Taylor expanded in y around inf 90.0%

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

      1. associate-*r* 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in x around 0 90.1%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around 0 98.6%

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

      1. neg-mul-1 98.6%

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

      2. distribute-rgt-neg-in 98.6%

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

   6. Simplified 98.6%

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

      1. distribute-rgt-neg-out 98.6%

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

      2. unsub-neg 98.6%

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

      3. *-commutative 98.6%

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

   8. Applied egg-rr 98.6%

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

4. Final simplification 94.5%

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

Alternative 6: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+47} \lor \neg \left(y \leq 7.5 \cdot 10^{+51}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+47) (not (<= y 7.5e+51))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+47) || !(y <= 7.5e+51)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1d+47)) .or. (.not. (y <= 7.5d+51))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+47) || !(y <= 7.5e+51)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+47) or not (y <= 7.5e+51):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+47) || !(y <= 7.5e+51))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+47) || ~((y <= 7.5e+51)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+47], N[Not[LessEqual[y, 7.5e+51]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e47 or 7.4999999999999999e51 < y

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 89.0%

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

   4. Taylor expanded in y around inf 89.0%

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

      1. associate-*r* 90.6%

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

   6. Simplified 90.6%

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

   7. Taylor expanded in x around 0 89.0%

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

   8. Taylor expanded in y around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*r* 75.0%

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

      3. *-commutative 75.0%

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

   10. Simplified 75.0%

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

   if -1e47 < y < 7.4999999999999999e51

   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 97.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+47} \lor \neg \left(y \leq 7.5 \cdot 10^{+51}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e+47)
   (* y (* z x))
   (if (<= y 1.05e+52) (- x (* z x)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+47) {
		tmp = y * (z * x);
	} else if (y <= 1.05e+52) {
		tmp = x - (z * x);
	} else {
		tmp = z * (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 <= (-4.1d+47)) then
        tmp = y * (z * x)
    else if (y <= 1.05d+52) then
        tmp = x - (z * x)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+47) {
		tmp = y * (z * x);
	} else if (y <= 1.05e+52) {
		tmp = x - (z * x);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e+47:
		tmp = y * (z * x)
	elif y <= 1.05e+52:
		tmp = x - (z * x)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e+47)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 1.05e+52)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.1e+47)
		tmp = y * (z * x);
	elseif (y <= 1.05e+52)
		tmp = x - (z * x);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e+47], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+52], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000001e47

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 91.6%

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

   4. Taylor expanded in y around inf 91.6%

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

      1. associate-*r* 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in x around 0 91.5%

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

   8. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r* 80.7%

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

      3. *-commutative 80.7%

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

   10. Simplified 80.7%

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

   if -4.1000000000000001e47 < y < 1.05e52

   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 0 100.0%

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

   4. Taylor expanded in y around 0 97.0%

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

      1. neg-mul-1 97.0%

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

      2. distribute-rgt-neg-in 97.0%

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

   6. Simplified 97.0%

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

      1. distribute-rgt-neg-out 97.0%

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

      2. unsub-neg 97.0%

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

      3. *-commutative 97.0%

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

   8. Applied egg-rr 97.0%

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

   if 1.05e52 < y

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*l* 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+47)
   (* y (* z x))
   (if (<= y 2.5e+53) (* x (- 1.0 z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+47) {
		tmp = y * (z * x);
	} else if (y <= 2.5e+53) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (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 <= (-4.5d+47)) then
        tmp = y * (z * x)
    else if (y <= 2.5d+53) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+47) {
		tmp = y * (z * x);
	} else if (y <= 2.5e+53) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+47:
		tmp = y * (z * x)
	elif y <= 2.5e+53:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+47)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 2.5e+53)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+47)
		tmp = y * (z * x);
	elseif (y <= 2.5e+53)
		tmp = x * (1.0 - z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+47], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+53], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999979e47

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 91.6%

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

   4. Taylor expanded in y around inf 91.6%

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

      1. associate-*r* 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in x around 0 91.5%

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

   8. Taylor expanded in y around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*r* 80.7%

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

      3. *-commutative 80.7%

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

   10. Simplified 80.7%

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

   if -4.49999999999999979e47 < y < 2.5000000000000002e53

   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 97.0%

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

   if 2.5000000000000002e53 < y

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*l* 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 52\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 52.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 52.0)) {
		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 <= 52.0d0))) 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 <= 52.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 52.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 52.0))
		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 <= 52.0)))
		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, 52.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 52 < z

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 89.5%

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

   4. Taylor expanded in y around 0 62.4%

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

      1. neg-mul-1 63.3%

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

      2. distribute-rgt-neg-in 63.3%

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

   6. Simplified 62.4%

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

   if -1 < z < 52

   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 70.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 52\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in y around 0 67.8%

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

Alternative 11: 39.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in z around 0 39.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

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