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

Percentage Accurate: 95.9% → 97.9%

Time: 8.1s

Alternatives: 13

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+308}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+308) (* z (* y x)) (+ x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+308) {
		tmp = z * (y * x);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= (-1d+308)) then
        tmp = z * (y * x)
    else
        tmp = x + (x * (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+308) {
		tmp = z * (y * x);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+308:
		tmp = z * (y * x)
	else:
		tmp = x + (x * (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -1e+308)
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -1e+308)
		tmp = z * (y * x);
	else
		tmp = x + (x * (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -1e+308], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -1e308

   1. Initial program 60.4%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*l* 99.8%

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

   5. Simplified 99.8%

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

   if -1e308 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+308}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+308}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+308)
   (* z (* y x))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+308) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= (-1d+308)) then
        tmp = z * (y * x)
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+308) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+308:
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -1e+308)
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -1e+308)
		tmp = z * (y * x);
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -1e+308], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -1e308

   1. Initial program 60.4%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*l* 99.8%

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

   5. Simplified 99.8%

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

   if -1e308 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+308}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+19} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+19) (not (<= z 1.0)))
   (* (+ y -1.0) (* z x))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+19) || !(z <= 1.0)) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.35d+19)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + (-1.0d0)) * (z * x)
    else
        tmp = x * (1.0d0 + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+19) || !(z <= 1.0)) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+19) or not (z <= 1.0):
		tmp = (y + -1.0) * (z * x)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+19) || !(z <= 1.0))
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e+19) || ~((z <= 1.0)))
		tmp = (y + -1.0) * (z * x);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+19], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e19 or 1 < z

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf 91.7%

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

      1. associate-*r* 98.2%

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

      2. *-commutative 98.2%

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

      3. sub-neg 98.2%

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

      4. metadata-eval 98.2%

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

   5. Simplified 98.2%

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

   if -1.35e19 < 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 y around inf 99.0%

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

      1. neg-mul-1 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+19} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0115\right):\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.0115))) (+ x (* z (* y x))) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.0115)) {
		tmp = x + (z * (y * x));
	} 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 <= 0.0115d0))) then
        tmp = x + (z * (y * x))
    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 <= 0.0115)) {
		tmp = x + (z * (y * x));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.0115):
		tmp = x + (z * (y * x))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.0115))
		tmp = Float64(x + Float64(z * Float64(y * x)));
	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 <= 0.0115)))
		tmp = x + (z * (y * x));
	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, 0.0115]], $MachinePrecision]], N[(x + N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0115 < y

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0 93.3%

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

   4. Taylor expanded in y around inf 92.0%

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

      1. associate-*r* 92.7%

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

      2. *-commutative 92.7%

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

   6. Simplified 92.7%

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

   if -1 < y < 0.0115

   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 99.5%

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

      1. mul-1-neg 99.5%

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

      2. *-commutative 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x around 0 99.5%

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

      1. distribute-lft-in 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. mul-1-neg 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. sub-neg 99.5%

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

   9. Simplified 99.5%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0115\right):\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+29)
   (* z (* y x))
   (if (<= y 1.0) (- x (* z x)) (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+29) {
		tmp = z * (y * x);
	} else if (y <= 1.0) {
		tmp = x - (z * x);
	} else {
		tmp = x * (z * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.2d+29)) then
        tmp = z * (y * x)
    else if (y <= 1.0d0) then
        tmp = x - (z * x)
    else
        tmp = x * (z * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+29) {
		tmp = z * (y * x);
	} else if (y <= 1.0) {
		tmp = x - (z * x);
	} else {
		tmp = x * (z * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+29:
		tmp = z * (y * x)
	elif y <= 1.0:
		tmp = x - (z * x)
	else:
		tmp = x * (z * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+29)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 1.0)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(x * Float64(z * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.2e+29)
		tmp = z * (y * x);
	elseif (y <= 1.0)
		tmp = x - (z * x);
	else
		tmp = x * (z * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+29], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999952e29

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l* 78.9%

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

   5. Simplified 78.9%

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

   if -7.19999999999999952e29 < 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 98.3%

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

      1. mul-1-neg 98.3%

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

      2. *-commutative 98.3%

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

      3. distribute-rgt-neg-in 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in x around 0 98.2%

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

      1. distribute-lft-in 98.3%

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

      2. *-rgt-identity 98.3%

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

      3. mul-1-neg 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

      5. sub-neg 98.3%

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

   9. Simplified 98.3%

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

   if 1 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 81.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+34} \lor \neg \left(y \leq 55\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+34) (not (<= y 55.0))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+34) || !(y <= 55.0)) {
		tmp = z * (y * 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 <= (-5.2d+34)) .or. (.not. (y <= 55.0d0))) then
        tmp = z * (y * 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 <= -5.2e+34) || !(y <= 55.0)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+34) or not (y <= 55.0):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+34) || !(y <= 55.0))
		tmp = Float64(z * Float64(y * 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 <= -5.2e+34) || ~((y <= 55.0)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+34], N[Not[LessEqual[y, 55.0]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999995e34 or 55 < y

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*l* 79.2%

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

   5. Simplified 79.2%

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

   if -5.19999999999999995e34 < y < 55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+34} \lor \neg \left(y \leq 55\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 180:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+32)
   (* z (* y x))
   (if (<= y 180.0) (- x (* z x)) (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+32) {
		tmp = z * (y * x);
	} else if (y <= 180.0) {
		tmp = x - (z * x);
	} else {
		tmp = x * (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 (y <= (-1.9d+32)) then
        tmp = z * (y * x)
    else if (y <= 180.0d0) then
        tmp = x - (z * x)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+32) {
		tmp = z * (y * x);
	} else if (y <= 180.0) {
		tmp = x - (z * x);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+32:
		tmp = z * (y * x)
	elif y <= 180.0:
		tmp = x - (z * x)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+32)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 180.0)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+32)
		tmp = z * (y * x);
	elseif (y <= 180.0)
		tmp = x - (z * x);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+32], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 180.0], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000002e32

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l* 78.9%

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

   5. Simplified 78.9%

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

   if -1.9000000000000002e32 < y < 180

   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 98.3%

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

      1. mul-1-neg 98.3%

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

      2. *-commutative 98.3%

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

      3. distribute-rgt-neg-in 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in x around 0 98.2%

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

      1. distribute-lft-in 98.3%

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

      2. *-rgt-identity 98.3%

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

      3. mul-1-neg 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

      5. sub-neg 98.3%

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

   9. Simplified 98.3%

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

   if 180 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. *-commutative 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 180:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.6e+33)
   (* z (* y x))
   (if (<= y 190.0) (* x (- 1.0 z)) (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.6e+33) {
		tmp = z * (y * x);
	} else if (y <= 190.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (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 (y <= (-6.6d+33)) then
        tmp = z * (y * x)
    else if (y <= 190.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.6e+33) {
		tmp = z * (y * x);
	} else if (y <= 190.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.6e+33:
		tmp = z * (y * x)
	elif y <= 190.0:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.6e+33)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 190.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.6e+33)
		tmp = z * (y * x);
	elseif (y <= 190.0)
		tmp = x * (1.0 - z);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.6e+33], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 190.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.59999999999999953e33

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l* 78.9%

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

   5. Simplified 78.9%

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

   if -6.59999999999999953e33 < y < 190

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.2%

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

   if 190 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. *-commutative 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+30)
   (* z (* y x))
   (if (<= y 190.0) (* x (- 1.0 z)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+30) {
		tmp = z * (y * x);
	} else if (y <= 190.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (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 <= (-1.05d+30)) then
        tmp = z * (y * x)
    else if (y <= 190.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+30) {
		tmp = z * (y * x);
	} else if (y <= 190.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+30:
		tmp = z * (y * x)
	elif y <= 190.0:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+30)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 190.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+30)
		tmp = z * (y * x);
	elseif (y <= 190.0)
		tmp = x * (1.0 - z);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+30], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 190.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e30

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l* 78.9%

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

   5. Simplified 78.9%

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

   if -1.05e30 < y < 190

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.2%

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

   if 190 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

      3. sub-neg 81.8%

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

      4. metadata-eval 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around inf 80.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 190:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% 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 93.5%

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

   3. Taylor expanded in z around inf 91.9%

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

   4. Taylor expanded in y around 0 49.5%

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

      1. mul-1-neg 50.9%

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

      2. *-commutative 50.9%

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

      3. distribute-rgt-neg-in 50.9%

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

   6. Simplified 49.5%

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

   if -1 < z < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 76.5%

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

4. Final simplification 62.6%

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

Alternative 11: 41.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+70} \lor \neg \left(z \leq 52000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e+70) (not (<= z 52000000.0))) (* z x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e+70) || !(z <= 52000000.0)) {
		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 <= (-2.3d+70)) .or. (.not. (z <= 52000000.0d0))) 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 <= -2.3e+70) || !(z <= 52000000.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e+70) or not (z <= 52000000.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e+70) || !(z <= 52000000.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e+70) || ~((z <= 52000000.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e+70], N[Not[LessEqual[z, 52000000.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999994e70 or 5.2e7 < z

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf 93.0%

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

      1. associate-*r* 99.5%

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

      2. *-commutative 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

   5. Simplified 99.5%

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

      1. distribute-lft-in 78.5%

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

      2. associate-*r* 83.8%

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

      3. *-commutative 83.8%

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

      4. add-cube-cbrt 83.3%

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

      5. unpow2 83.3%

         \[\leadsto z \cdot \left(\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{2}} \cdot \sqrt[3]{x \cdot y}\right) + \left(x \cdot z\right) \cdot -1 \]

      6. associate-*r* 83.3%

         \[\leadsto \color{blue}{\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}\right) \cdot \sqrt[3]{x \cdot y}} + \left(x \cdot z\right) \cdot -1 \]

      7. fma-undefine 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \left(x \cdot z\right) \cdot -1\right)} \]

      8. associate-*l* 84.1%

         \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \color{blue}{x \cdot \left(z \cdot -1\right)}\right) \]

      9. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \color{blue}{\left(z \cdot -1\right) \cdot x}\right) \]

      10. associate-*r* 84.1%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \color{blue}{z \cdot \left(-1 \cdot x\right)}\right) \]

      11. neg-mul-1 84.1%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\left(-x\right)}\right) \]

      12. add-sqr-sqrt 32.1%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \]

      13. sqrt-unprod 55.7%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \]

      14. sqr-neg 55.7%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \sqrt{\color{blue}{x \cdot x}}\right) \]

      15. sqrt-unprod 29.4%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \]

      16. add-sqr-sqrt 46.6%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{x}\right) \]

   7. Applied egg-rr 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot x\right)} \]

   8. Taylor expanded in y around 0 14.1%

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

   if -2.29999999999999994e70 < z < 5.2e7

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 67.3%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+70} \lor \neg \left(z \leq 52000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.45e+165) (* x (- 1.0 z)) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.45e+165) {
		tmp = x * (1.0 - z);
	} else {
		tmp = 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 <= 1.45d+165) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.45e+165) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.45e+165:
		tmp = x * (1.0 - z)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.45e+165)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.45e+165)
		tmp = x * (1.0 - z);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.45e+165], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.45000000000000003e165

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0 70.7%

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

   if 1.45000000000000003e165 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-*r* 92.9%

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

      2. *-commutative 92.9%

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

      3. sub-neg 92.9%

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

      4. metadata-eval 92.9%

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

   5. Simplified 92.9%

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

      1. distribute-lft-in 67.0%

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

      2. associate-*r* 63.8%

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

      3. *-commutative 63.8%

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

      4. add-cube-cbrt 63.0%

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

      5. unpow2 63.0%

         \[\leadsto z \cdot \left(\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{2}} \cdot \sqrt[3]{x \cdot y}\right) + \left(x \cdot z\right) \cdot -1 \]

      6. associate-*r* 63.0%

         \[\leadsto \color{blue}{\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}\right) \cdot \sqrt[3]{x \cdot y}} + \left(x \cdot z\right) \cdot -1 \]

      7. fma-undefine 63.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \left(x \cdot z\right) \cdot -1\right)} \]

      8. associate-*l* 63.0%

         \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \color{blue}{x \cdot \left(z \cdot -1\right)}\right) \]

      9. *-commutative 63.0%

         \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \color{blue}{\left(z \cdot -1\right) \cdot x}\right) \]

      10. associate-*r* 63.0%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, \color{blue}{z \cdot \left(-1 \cdot x\right)}\right) \]

      11. neg-mul-1 63.0%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\left(-x\right)}\right) \]

      12. add-sqr-sqrt 40.3%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \]

      13. sqrt-unprod 81.5%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \]

      14. sqr-neg 81.5%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \sqrt{\color{blue}{x \cdot x}}\right) \]

      15. sqrt-unprod 41.2%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \]

      16. add-sqr-sqrt 88.9%

          \[\leadsto \mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot \color{blue}{x}\right) \]

   7. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{x \cdot y}\right)}^{2}, \sqrt[3]{x \cdot y}, z \cdot x\right)} \]

   8. Taylor expanded in y around 0 29.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.6%

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

3. Taylor expanded in z around 0 38.5%

   \[\leadsto \color{blue}{x} \]
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 2024158 
(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))))