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

Percentage Accurate: 96.0% → 98.0%

Time: 8.9s

Alternatives: 11

Speedup: 0.5×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+215)
   (* (* z x) (+ y -1.0))
   (+ x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+215) {
		tmp = (z * x) * (y + -1.0);
	} 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+215)) then
        tmp = (z * x) * (y + (-1.0d0))
    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+215) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+215:
		tmp = (z * x) * (y + -1.0)
	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+215)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	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+215)
		tmp = (z * x) * (y + -1.0);
	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+215], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $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) < -9.99999999999999907e214

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -9.99999999999999907e214 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+215)
   (* (* z x) (+ y -1.0))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+215) {
		tmp = (z * x) * (y + -1.0);
	} 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+215)) then
        tmp = (z * x) * (y + (-1.0d0))
    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+215) {
		tmp = (z * x) * (y + -1.0);
	} 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+215:
		tmp = (z * x) * (y + -1.0)
	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+215)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	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+215)
		tmp = (z * x) * (y + -1.0);
	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+215], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $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) < -9.99999999999999907e214

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -9.99999999999999907e214 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -240 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -240.0) (not (<= z 1.0)))
   (* (* z x) (+ y -1.0))
   (+ x (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -240.0) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (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 ((z <= (-240.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -240.0) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -240.0) or not (z <= 1.0):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x + (x * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -240.0) || !(z <= 1.0))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -240.0) || ~((z <= 1.0)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -240.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -240 or 1 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf 90.2%

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

      1. associate-*r* 98.7%

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

      2. *-commutative 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

   5. Simplified 98.7%

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

   if -240 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 97.3%

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

      1. *-commutative 97.3%

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

   6. Simplified 97.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -240 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 15600000000000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.1e+85)
   (* z (* y x))
   (if (<= y 15600000000000.0) (- x (* z x)) (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.1e+85) {
		tmp = z * (y * x);
	} else if (y <= 15600000000000.0) {
		tmp = x - (z * x);
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.1d+85)) then
        tmp = z * (y * x)
    else if (y <= 15600000000000.0d0) then
        tmp = x - (z * x)
    else
        tmp = (z * x) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.1e+85) {
		tmp = z * (y * x);
	} else if (y <= 15600000000000.0) {
		tmp = x - (z * x);
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.1e+85:
		tmp = z * (y * x)
	elif y <= 15600000000000.0:
		tmp = x - (z * x)
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.1e+85)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 15600000000000.0)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.1e+85)
		tmp = z * (y * x);
	elseif (y <= 15600000000000.0)
		tmp = x - (z * x);
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.1e+85], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 15600000000000.0], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.09999999999999981e85

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*l* 87.6%

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

   5. Simplified 87.6%

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

   if -6.09999999999999981e85 < y < 1.56e13

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-in 94.2%

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

      6. flip-+ 61.9%

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

   5. Applied egg-rr 63.3%

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

   6. Taylor expanded in y around 0 94.7%

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

   if 1.56e13 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

      3. sub-neg 82.2%

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

      4. metadata-eval 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 15600000000000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+85} \lor \neg \left(y \leq 3800000000000\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.1e+85) (not (<= y 3800000000000.0)))
   (* y (* z x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.1e+85) || !(y <= 3800000000000.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.1d+85)) .or. (.not. (y <= 3800000000000.0d0))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.1e+85) || !(y <= 3800000000000.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.1e+85) or not (y <= 3800000000000.0):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.1e+85) || !(y <= 3800000000000.0))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.1e+85) || ~((y <= 3800000000000.0)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.1e+85], N[Not[LessEqual[y, 3800000000000.0]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.09999999999999981e85 or 3.8e12 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 77.0%

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

      1. associate-*r* 80.2%

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

      2. *-commutative 80.2%

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

      3. sub-neg 80.2%

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

      4. metadata-eval 80.2%

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

   5. Simplified 80.2%

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

      1. add-sqr-sqrt 39.0%

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

      2. pow2 39.0%

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

      3. *-commutative 39.0%

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

   7. Applied egg-rr 39.0%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot z}\right)}^{2}} \cdot \left(y + -1\right) \]
   8. Step-by-step derivation

      1. unpow2 39.0%

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

      2. add-sqr-sqrt 80.2%

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

      3. distribute-rgt-in 67.4%

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

      4. neg-mul-1 67.4%

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

      5. unsub-neg 67.4%

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

      6. *-commutative 67.4%

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

      7. associate-*r* 64.2%

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

      8. *-commutative 64.2%

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

      9. *-commutative 64.2%

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

      10. flip-- 25.8%

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

      11. unpow2 25.8%

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

      12. sqr-neg 25.8%

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

      13. cancel-sign-sub 25.8%

          \[\leadsto \frac{{\left(x \cdot \left(z \cdot y\right)\right)}^{2} - \left(-x \cdot z\right) \cdot \left(-x \cdot z\right)}{\color{blue}{x \cdot \left(z \cdot y\right) - \left(-x\right) \cdot z}} \]

      14. distribute-lft-neg-in 25.8%

          \[\leadsto \frac{{\left(x \cdot \left(z \cdot y\right)\right)}^{2} - \left(-x \cdot z\right) \cdot \left(-x \cdot z\right)}{x \cdot \left(z \cdot y\right) - \color{blue}{\left(-x \cdot z\right)}} \]

      15. clear-num 25.8%

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

   9. Applied egg-rr 77.0%

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

   10. Taylor expanded in y around inf 77.0%

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

       1. associate-*r* 82.7%

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

       2. *-commutative 82.7%

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

       3. associate-*r* 80.2%

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

   12. Simplified 80.2%

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

   if -6.09999999999999981e85 < y < 3.8e12

   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 94.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+85} \lor \neg \left(y \leq 3800000000000\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 33500000000000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+89)
   (* z (* y x))
   (if (<= y 33500000000000.0) (- x (* z x)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+89) {
		tmp = z * (y * x);
	} else if (y <= 33500000000000.0) {
		tmp = x - (z * x);
	} 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 <= (-3.1d+89)) then
        tmp = z * (y * x)
    else if (y <= 33500000000000.0d0) then
        tmp = x - (z * x)
    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 <= -3.1e+89) {
		tmp = z * (y * x);
	} else if (y <= 33500000000000.0) {
		tmp = x - (z * x);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e+89:
		tmp = z * (y * x)
	elif y <= 33500000000000.0:
		tmp = x - (z * x)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+89)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 33500000000000.0)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e+89)
		tmp = z * (y * x);
	elseif (y <= 33500000000000.0)
		tmp = x - (z * x);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+89], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 33500000000000.0], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e89

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*l* 87.6%

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

   5. Simplified 87.6%

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

   if -3.1e89 < y < 3.35e13

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-in 94.2%

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

      6. flip-+ 61.9%

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

   5. Applied egg-rr 63.3%

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

   6. Taylor expanded in y around 0 94.7%

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

   if 3.35e13 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

      3. sub-neg 82.2%

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

      4. metadata-eval 82.2%

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

   5. Simplified 82.2%

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

      1. add-sqr-sqrt 39.1%

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

      2. pow2 39.1%

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

      3. *-commutative 39.1%

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

   7. Applied egg-rr 39.1%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot z}\right)}^{2}} \cdot \left(y + -1\right) \]
   8. Step-by-step derivation

      1. unpow2 39.1%

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

      2. add-sqr-sqrt 82.2%

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

      3. distribute-rgt-in 60.8%

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

      4. neg-mul-1 60.8%

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

      5. unsub-neg 60.8%

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

      6. *-commutative 60.8%

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

      7. associate-*r* 52.6%

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

      8. *-commutative 52.6%

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

      9. *-commutative 52.6%

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

      10. flip-- 20.8%

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

      11. unpow2 20.8%

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

      12. sqr-neg 20.8%

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

      13. cancel-sign-sub 20.8%

          \[\leadsto \frac{{\left(x \cdot \left(z \cdot y\right)\right)}^{2} - \left(-x \cdot z\right) \cdot \left(-x \cdot z\right)}{\color{blue}{x \cdot \left(z \cdot y\right) - \left(-x\right) \cdot z}} \]

      14. distribute-lft-neg-in 20.8%

          \[\leadsto \frac{{\left(x \cdot \left(z \cdot y\right)\right)}^{2} - \left(-x \cdot z\right) \cdot \left(-x \cdot z\right)}{x \cdot \left(z \cdot y\right) - \color{blue}{\left(-x \cdot z\right)}} \]

      15. clear-num 20.8%

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

   9. Applied egg-rr 73.9%

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

   10. Taylor expanded in y around inf 74.0%

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

       1. associate-*r* 79.5%

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

       2. *-commutative 79.5%

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

       3. associate-*r* 82.2%

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

   12. Simplified 82.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 33500000000000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 13200000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e+86)
   (* z (* y x))
   (if (<= y 13200000000000.0) (* x (- 1.0 z)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+86) {
		tmp = z * (y * x);
	} else if (y <= 13200000000000.0) {
		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 <= (-5d+86)) then
        tmp = z * (y * x)
    else if (y <= 13200000000000.0d0) 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 <= -5e+86) {
		tmp = z * (y * x);
	} else if (y <= 13200000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e+86:
		tmp = z * (y * x)
	elif y <= 13200000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e+86)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 13200000000000.0)
		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 <= -5e+86)
		tmp = z * (y * x);
	elseif (y <= 13200000000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e+86], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 13200000000000.0], 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 < -4.9999999999999998e86

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*l* 87.6%

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

   5. Simplified 87.6%

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

   if -4.9999999999999998e86 < y < 1.32e13

   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 94.7%

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

   if 1.32e13 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

      3. sub-neg 82.2%

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

      4. metadata-eval 82.2%

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

   5. Simplified 82.2%

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

      1. add-sqr-sqrt 39.1%

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

      2. pow2 39.1%

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

      3. *-commutative 39.1%

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

   7. Applied egg-rr 39.1%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot z}\right)}^{2}} \cdot \left(y + -1\right) \]
   8. Step-by-step derivation

      1. unpow2 39.1%

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

      2. add-sqr-sqrt 82.2%

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

      3. distribute-rgt-in 60.8%

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

      4. neg-mul-1 60.8%

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

      5. unsub-neg 60.8%

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

      6. *-commutative 60.8%

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

      7. associate-*r* 52.6%

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

      8. *-commutative 52.6%

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

      9. *-commutative 52.6%

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

      10. flip-- 20.8%

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

      11. unpow2 20.8%

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

      12. sqr-neg 20.8%

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

      13. cancel-sign-sub 20.8%

          \[\leadsto \frac{{\left(x \cdot \left(z \cdot y\right)\right)}^{2} - \left(-x \cdot z\right) \cdot \left(-x \cdot z\right)}{\color{blue}{x \cdot \left(z \cdot y\right) - \left(-x\right) \cdot z}} \]

      14. distribute-lft-neg-in 20.8%

          \[\leadsto \frac{{\left(x \cdot \left(z \cdot y\right)\right)}^{2} - \left(-x \cdot z\right) \cdot \left(-x \cdot z\right)}{x \cdot \left(z \cdot y\right) - \color{blue}{\left(-x \cdot z\right)}} \]

      15. clear-num 20.8%

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

   9. Applied egg-rr 73.9%

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

   10. Taylor expanded in y around inf 74.0%

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

       1. associate-*r* 79.5%

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

       2. *-commutative 79.5%

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

       3. associate-*r* 82.2%

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

   12. Simplified 82.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 13200000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00016 \lor \neg \left(z \leq 0.98\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.00016) (not (<= z 0.98))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00016) || !(z <= 0.98)) {
		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 <= (-0.00016d0)) .or. (.not. (z <= 0.98d0))) 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 <= -0.00016) || !(z <= 0.98)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.00016) or not (z <= 0.98):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.00016) || !(z <= 0.98))
		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 <= -0.00016) || ~((z <= 0.98)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.00016], N[Not[LessEqual[z, 0.98]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000013e-4 or 0.97999999999999998 < z

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 54.1%

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

   4. Taylor expanded in z around inf 52.9%

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

      1. neg-mul-1 52.9%

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

      2. distribute-rgt-neg-in 52.9%

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

   6. Simplified 52.9%

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

   if -1.60000000000000013e-4 < z < 0.97999999999999998

   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 64.5%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00016 \lor \neg \left(z \leq 0.98\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+71} \lor \neg \left(z \leq 8.2 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e+71) (not (<= z 8.2e+14))) (* z x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e+71) || !(z <= 8.2e+14)) {
		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 <= (-3.3d+71)) .or. (.not. (z <= 8.2d+14))) 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 <= -3.3e+71) || !(z <= 8.2e+14)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e+71) or not (z <= 8.2e+14):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e+71) || !(z <= 8.2e+14))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.3e+71) || ~((z <= 8.2e+14)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e+71], N[Not[LessEqual[z, 8.2e+14]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999998e71 or 8.2e14 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 51.5%

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

      1. sub-neg 51.5%

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

      2. distribute-rgt-in 51.5%

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

      3. *-un-lft-identity 51.5%

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

      4. distribute-lft-neg-in 51.5%

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

      5. distribute-rgt-neg-out 51.5%

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

      6. +-commutative 51.5%

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

      7. *-commutative 51.5%

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

      8. distribute-lft-neg-in 51.5%

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

      9. pow1 51.5%

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

      10. metadata-eval 51.5%

          \[\leadsto {\left(-x \cdot z\right)}^{\color{blue}{\left(\frac{2}{2}\right)}} + x \]

      11. sqrt-pow1 33.8%

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

      12. pow2 33.8%

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

      13. sqr-neg 33.8%

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

      14. sqrt-prod 8.3%

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

      15. add-sqr-sqrt 16.5%

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

   5. Applied egg-rr 16.5%

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

   6. Taylor expanded in z around inf 16.5%

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

   if -3.2999999999999998e71 < z < 8.2e14

   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 54.0%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+71} \lor \neg \left(z \leq 8.2 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.3e+102) (* x (- 1.0 z)) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.3e+102) {
		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 <= 3.3d+102) 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 <= 3.3e+102) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.3e+102:
		tmp = x * (1.0 - z)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.3e+102)
		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 <= 3.3e+102)
		tmp = x * (1.0 - z);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.3e+102], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.29999999999999999e102

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 73.6%

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

   if 3.29999999999999999e102 < y

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 0 13.3%

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

      1. sub-neg 13.3%

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

      2. distribute-rgt-in 13.3%

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

      3. *-un-lft-identity 13.3%

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

      4. distribute-lft-neg-in 13.3%

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

      5. distribute-rgt-neg-out 13.3%

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

      6. +-commutative 13.3%

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

      7. *-commutative 13.3%

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

      8. distribute-lft-neg-in 13.3%

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

      9. pow1 13.3%

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

      10. metadata-eval 13.3%

          \[\leadsto {\left(-x \cdot z\right)}^{\color{blue}{\left(\frac{2}{2}\right)}} + x \]

      11. sqrt-pow1 33.0%

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

      12. pow2 33.0%

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

      13. sqr-neg 33.0%

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

      14. sqrt-prod 24.5%

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

      15. add-sqr-sqrt 39.2%

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

   5. Applied egg-rr 39.2%

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

   6. Taylor expanded in z around inf 28.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in z around 0 32.7%

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

Developer Target 1: 99.8% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024146 
(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))))