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

Percentage Accurate: 95.9% → 96.6%

Time: 8.1s

Alternatives: 13

Speedup: 1.0×

• 20.6% 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: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -1 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 y) -1e+95) (+ x (* (* x z) y)) (+ x (* x (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -1e+95) {
		tmp = x + ((x * z) * y);
	} else {
		tmp = x + (x * (z * (-1.0 + 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 ((1.0d0 - y) <= (-1d+95)) then
        tmp = x + ((x * z) * y)
    else
        tmp = x + (x * (z * ((-1.0d0) + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -1e+95) {
		tmp = x + ((x * z) * y);
	} else {
		tmp = x + (x * (z * (-1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - y) <= -1e+95:
		tmp = x + ((x * z) * y)
	else:
		tmp = x + (x * (z * (-1.0 + y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - y) <= -1e+95)
		tmp = Float64(x + Float64(Float64(x * z) * y));
	else
		tmp = Float64(x + Float64(x * Float64(z * Float64(-1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - y) <= -1e+95)
		tmp = x + ((x * z) * y);
	else
		tmp = x + (x * (z * (-1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -1.00000000000000002e95

   1. Initial program 83.5%

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

   3. Taylor expanded in z around 0 83.5%

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

   4. Taylor expanded in y around 0 73.0%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 87.6%

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

      4. distribute-rgt-in 98.1%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in y around inf 83.5%

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

      1. associate-*r* 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 98.1%

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

   9. Simplified 98.1%

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

   if -1.00000000000000002e95 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 99.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -1 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+196}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -5.2e+196)
     t_0
     (if (<= z -3.7e+155)
       (* x (* z y))
       (if (or (<= z -1.0) (not (<= z 1.0))) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -5.2e+196) {
		tmp = t_0;
	} else if (z <= -3.7e+155) {
		tmp = x * (z * y);
	} else if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-5.2d+196)) then
        tmp = t_0
    else if (z <= (-3.7d+155)) then
        tmp = x * (z * y)
    else if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = t_0
    else
        tmp = x
    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 <= -5.2e+196) {
		tmp = t_0;
	} else if (z <= -3.7e+155) {
		tmp = x * (z * y);
	} else if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -5.2e+196:
		tmp = t_0
	elif z <= -3.7e+155:
		tmp = x * (z * y)
	elif (z <= -1.0) or not (z <= 1.0):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -5.2e+196)
		tmp = t_0;
	elseif (z <= -3.7e+155)
		tmp = Float64(x * Float64(z * y));
	elseif ((z <= -1.0) || !(z <= 1.0))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -5.2e+196)
		tmp = t_0;
	elseif (z <= -3.7e+155)
		tmp = x * (z * y);
	elseif ((z <= -1.0) || ~((z <= 1.0)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -5.2e+196], t$95$0, If[LessEqual[z, -3.7e+155], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000024e196 or -3.6999999999999998e155 < z < -1 or 1 < 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 91.0%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*r* 98.9%

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

      4. sub-neg 98.9%

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

      5. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 56.9%

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

      1. neg-mul-1 56.9%

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

   8. Simplified 56.9%

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

   if -5.20000000000000024e196 < z < -3.6999999999999998e155

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   if -1 < 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 80.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+196}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-25} \lor \neg \left(z \leq 48000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e-25) (not (<= z 48000000000.0)))
   (* z (* x (+ -1.0 y)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e-25) || !(z <= 48000000000.0)) {
		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 <= (-6.5d-25)) .or. (.not. (z <= 48000000000.0d0))) 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 <= -6.5e-25) || !(z <= 48000000000.0)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e-25) or not (z <= 48000000000.0):
		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 <= -6.5e-25) || !(z <= 48000000000.0))
		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 <= -6.5e-25) || ~((z <= 48000000000.0)))
		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, -6.5e-25], N[Not[LessEqual[z, 48000000000.0]], $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 < -6.5e-25 or 4.8e10 < z

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. associate-*r* 97.7%

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

      2. *-commutative 97.7%

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

      3. associate-*r* 97.7%

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

      4. sub-neg 97.7%

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

      5. metadata-eval 97.7%

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

   5. Simplified 97.7%

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

   if -6.5e-25 < z < 4.8e10

   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 82.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-25} \lor \neg \left(z \leq 48000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{elif}\;z \leq 48000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e-22)
   (* z (- (* x y) x))
   (if (<= z 48000000000.0) (* x (- 1.0 z)) (* z (* x (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e-22) {
		tmp = z * ((x * y) - x);
	} else if (z <= 48000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * (-1.0 + 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 <= (-1.85d-22)) then
        tmp = z * ((x * y) - x)
    else if (z <= 48000000000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * ((-1.0d0) + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e-22) {
		tmp = z * ((x * y) - x);
	} else if (z <= 48000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * (-1.0 + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e-22:
		tmp = z * ((x * y) - x)
	elif z <= 48000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * (-1.0 + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e-22)
		tmp = Float64(z * Float64(Float64(x * y) - x));
	elseif (z <= 48000000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.85e-22)
		tmp = z * ((x * y) - x);
	elseif (z <= 48000000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * (-1.0 + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e-22], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 48000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e-22

   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 87.2%

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

      1. associate-*r* 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*r* 96.5%

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

      4. sub-neg 96.5%

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

      5. metadata-eval 96.5%

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

   5. Simplified 96.5%

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

      1. distribute-lft-in 96.5%

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

      2. *-commutative 96.5%

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

      3. mul-1-neg 96.5%

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

   7. Applied egg-rr 96.5%

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

   8. Taylor expanded in z around 0 96.5%

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

   if -1.85e-22 < z < 4.8e10

   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 82.7%

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

   if 4.8e10 < z

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf 93.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y - 1\right)\right)} \]
   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. associate-*r* 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{elif}\;z \leq 48000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05)
   (* z (- (* x y) x))
   (if (<= z 1.0) (* x (+ 1.0 (* z y))) (* z (* x (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = z * ((x * y) - x);
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = z * (x * (-1.0 + 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 <= (-1.05d0)) then
        tmp = z * ((x * y) - x)
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (z * y))
    else
        tmp = z * (x * ((-1.0d0) + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = z * ((x * y) - x);
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = z * (x * (-1.0 + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05:
		tmp = z * ((x * y) - x)
	elif z <= 1.0:
		tmp = x * (1.0 + (z * y))
	else:
		tmp = z * (x * (-1.0 + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(z * Float64(Float64(x * y) - x));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	else
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = z * ((x * y) - x);
	elseif (z <= 1.0)
		tmp = x * (1.0 + (z * y));
	else
		tmp = z * (x * (-1.0 + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 89.9%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*r* 98.8%

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

      4. sub-neg 98.8%

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

      5. metadata-eval 98.8%

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

   5. Simplified 98.8%

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

      1. distribute-lft-in 98.9%

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

      2. *-commutative 98.9%

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

      3. mul-1-neg 98.9%

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

   7. Applied egg-rr 98.9%

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

   8. Taylor expanded in z around 0 98.9%

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

   if -1.05000000000000004 < 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 0 99.9%

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

      1. associate-*r* 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-*r* 97.8%

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

      4. distribute-rgt-in 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in y around inf 98.5%

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

      1. associate-*r* 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*r* 96.3%

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

   9. Simplified 96.3%

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

       1. *-commutative 96.3%

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

       2. associate-*r* 98.5%

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

       3. *-commutative 98.5%

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

       4. distribute-rgt1-in 98.5%

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

   11. Applied egg-rr 98.5%

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

   if 1 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf 93.4%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*r* 99.1%

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

      4. sub-neg 99.1%

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

      5. metadata-eval 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -1 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 y) -1e+95) (+ x (* (* x z) y)) (* x (+ 1.0 (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -1e+95) {
		tmp = x + ((x * z) * y);
	} else {
		tmp = x * (1.0 + (z * (-1.0 + 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 ((1.0d0 - y) <= (-1d+95)) then
        tmp = x + ((x * z) * y)
    else
        tmp = x * (1.0d0 + (z * ((-1.0d0) + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - y) <= -1e+95) {
		tmp = x + ((x * z) * y);
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - y) <= -1e+95:
		tmp = x + ((x * z) * y)
	else:
		tmp = x * (1.0 + (z * (-1.0 + y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - y) <= -1e+95)
		tmp = Float64(x + Float64(Float64(x * z) * y));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - y) <= -1e+95)
		tmp = x + ((x * z) * y);
	else
		tmp = x * (1.0 + (z * (-1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -1.00000000000000002e95

   1. Initial program 83.5%

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

   3. Taylor expanded in z around 0 83.5%

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

   4. Taylor expanded in y around 0 73.0%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 87.6%

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

      4. distribute-rgt-in 98.1%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in y around inf 83.5%

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

      1. associate-*r* 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*r* 98.1%

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

   9. Simplified 98.1%

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

   if -1.00000000000000002e95 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 99.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -1 \cdot 10^{+95}:\\ \;\;\;\;x + \left(x \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+165} \lor \neg \left(y \leq 17000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.15e+165) (not (<= y 17000000.0)))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.15e+165) || !(y <= 17000000.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.15d+165)) .or. (.not. (y <= 17000000.0d0))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.15e+165) || !(y <= 17000000.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.15e+165) or not (y <= 17000000.0):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.15e+165) || !(y <= 17000000.0))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.15e+165) || ~((y <= 17000000.0)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.15e+165], N[Not[LessEqual[y, 17000000.0]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1500000000000001e165 or 1.7e7 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -3.1500000000000001e165 < y < 1.7e7

   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 93.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+165} \lor \neg \left(y \leq 17000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 7500000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+160)
   (* x (* z y))
   (if (<= y 7500000.0) (* x (- 1.0 z)) (* (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+160) {
		tmp = x * (z * y);
	} else if (y <= 7500000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (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 (y <= (-2.3d+160)) then
        tmp = x * (z * y)
    else if (y <= 7500000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = (x * z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+160) {
		tmp = x * (z * y);
	} else if (y <= 7500000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+160:
		tmp = x * (z * y)
	elif y <= 7500000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = (x * z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+160)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 7500000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+160)
		tmp = x * (z * y);
	elseif (y <= 7500000.0)
		tmp = x * (1.0 - z);
	else
		tmp = (x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+160], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7500000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999987e160

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 89.3%

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

      1. *-commutative 89.3%

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

   5. Simplified 89.3%

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

   if -2.29999999999999987e160 < y < 7.5e6

   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 93.7%

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

   if 7.5e6 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 87.5%

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

   4. Taylor expanded in y around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. fma-define 85.2%

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

      5. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around inf 71.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 7500000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3050000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+160)
   (* z (* x y))
   (if (<= y 3050000.0) (* x (- 1.0 z)) (* (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+160) {
		tmp = z * (x * y);
	} else if (y <= 3050000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (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 (y <= (-1.5d+160)) then
        tmp = z * (x * y)
    else if (y <= 3050000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = (x * z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+160) {
		tmp = z * (x * y);
	} else if (y <= 3050000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+160:
		tmp = z * (x * y)
	elif y <= 3050000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = (x * z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+160)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 3050000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e+160)
		tmp = z * (x * y);
	elseif (y <= 3050000.0)
		tmp = x * (1.0 - z);
	else
		tmp = (x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+160], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3050000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4999999999999999e160

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 89.3%

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

      1. associate-*r* 90.7%

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

      2. *-commutative 90.7%

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

   5. Simplified 90.7%

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

   if -1.4999999999999999e160 < y < 3.05e6

   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 93.7%

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

   if 3.05e6 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 87.5%

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

   4. Taylor expanded in y around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. fma-define 85.2%

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

      5. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around inf 71.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3050000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 16000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e+165)
   (* z (* x y))
   (if (<= y 16000000.0) (- x (* x z)) (* (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+165) {
		tmp = z * (x * y);
	} else if (y <= 16000000.0) {
		tmp = x - (x * z);
	} else {
		tmp = (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 (y <= (-2.1d+165)) then
        tmp = z * (x * y)
    else if (y <= 16000000.0d0) then
        tmp = x - (x * z)
    else
        tmp = (x * z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+165) {
		tmp = z * (x * y);
	} else if (y <= 16000000.0) {
		tmp = x - (x * z);
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e+165:
		tmp = z * (x * y)
	elif y <= 16000000.0:
		tmp = x - (x * z)
	else:
		tmp = (x * z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e+165)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 16000000.0)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.1e+165)
		tmp = z * (x * y);
	elseif (y <= 16000000.0)
		tmp = x - (x * z);
	else
		tmp = (x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e+165], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 16000000.0], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000001e165

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 89.3%

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

      1. associate-*r* 90.7%

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

      2. *-commutative 90.7%

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

   5. Simplified 90.7%

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

   if -2.1000000000000001e165 < y < 1.6e7

   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 0 98.7%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*r* 95.6%

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

      4. distribute-rgt-in 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. sub-neg 93.7%

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

   9. Simplified 93.7%

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

   if 1.6e7 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 87.5%

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

   4. Taylor expanded in y around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. fma-define 85.2%

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

      5. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around inf 71.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 16000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 90.7%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*r* 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in y around 0 53.9%

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

      1. neg-mul-1 53.9%

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

   8. Simplified 53.9%

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

   if -1 < 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 80.3%

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

4. Final simplification 67.5%

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

Alternative 12: 98.0% 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 95.9%

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

3. Taylor expanded in z around 0 95.9%

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

4. Taylor expanded in y around 0 91.6%

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

   1. associate-*r* 91.2%

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

   2. *-commutative 91.2%

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

   3. associate-*r* 92.5%

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

   4. distribute-rgt-in 98.8%

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

6. Simplified 98.8%

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

7. Final simplification 98.8%

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

Alternative 13: 38.7% 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 95.9%

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

3. Taylor expanded in z around 0 43.1%

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

4. Final simplification 43.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.6% 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 2024115 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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