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

Percentage Accurate: 95.9% → 97.7%

Time: 8.3s

Alternatives: 12

Speedup: 0.5×

• 20.7% 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: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y + -1\right)\\ \mathbf{if}\;1 + t\_0 \leq -5 \cdot 10^{+277}:\\ \;\;\;\;{\left(\frac{1}{z \cdot \left(x \cdot \left(y + -1\right)\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (+ y -1.0))))
   (if (<= (+ 1.0 t_0) -5e+277)
     (pow (/ 1.0 (* z (* x (+ y -1.0)))) -1.0)
     (+ x (* x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y + -1.0);
	double tmp;
	if ((1.0 + t_0) <= -5e+277) {
		tmp = pow((1.0 / (z * (x * (y + -1.0)))), -1.0);
	} else {
		tmp = x + (x * t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (y + (-1.0d0))
    if ((1.0d0 + t_0) <= (-5d+277)) then
        tmp = (1.0d0 / (z * (x * (y + (-1.0d0))))) ** (-1.0d0)
    else
        tmp = x + (x * t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y + -1.0);
	double tmp;
	if ((1.0 + t_0) <= -5e+277) {
		tmp = Math.pow((1.0 / (z * (x * (y + -1.0)))), -1.0);
	} else {
		tmp = x + (x * t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y + -1.0)
	tmp = 0
	if (1.0 + t_0) <= -5e+277:
		tmp = math.pow((1.0 / (z * (x * (y + -1.0)))), -1.0)
	else:
		tmp = x + (x * t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y + -1.0))
	tmp = 0.0
	if (Float64(1.0 + t_0) <= -5e+277)
		tmp = Float64(1.0 / Float64(z * Float64(x * Float64(y + -1.0)))) ^ -1.0;
	else
		tmp = Float64(x + Float64(x * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y + -1.0);
	tmp = 0.0;
	if ((1.0 + t_0) <= -5e+277)
		tmp = (1.0 / (z * (x * (y + -1.0)))) ^ -1.0;
	else
		tmp = x + (x * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 + t$95$0), $MachinePrecision], -5e+277], N[Power[N[(1.0 / N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(x + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -4.99999999999999982e277

   1. Initial program 74.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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* 99.8%

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

      2. flip-- 83.8%

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

      3. associate-*r/ 83.9%

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

      4. metadata-eval 83.9%

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

      5. fma-neg 83.9%

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

      6. metadata-eval 83.9%

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

   5. Applied egg-rr 83.9%

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

      1. clear-num 83.9%

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

      2. inv-pow 83.9%

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

      3. clear-num 83.8%

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

      4. associate-/l* 83.8%

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

      5. *-commutative 83.8%

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

      6. metadata-eval 83.8%

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

      7. fma-neg 83.8%

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

      8. metadata-eval 83.8%

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

      9. flip-- 99.8%

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

      10. associate-*l* 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -4.99999999999999982e277 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + z \cdot \left(y + -1\right) \leq -5 \cdot 10^{+277}:\\ \;\;\;\;{\left(\frac{1}{z \cdot \left(x \cdot \left(y + -1\right)\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	t_0 = z * (y + -1.0)
	tmp = 0
	if (1.0 + t_0) <= -math.inf:
		tmp = z * (y * x)
	else:
		tmp = x + (x * t_0)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -inf.0

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-*l* 100.0%

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

   5. Simplified 100.0%

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

   if -inf.0 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 98.7%

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

4. Final simplification 98.8%

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

Alternative 3: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	t_0 = 1.0 + (z * (y + -1.0))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = z * (y * x)
	else:
		tmp = t_0 * x
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -inf.0

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

      3. associate-*l* 100.0%

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

   5. Simplified 100.0%

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

   if -inf.0 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 98.7%

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

4. Final simplification 98.8%

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

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 6.8 \cdot 10^{-6}\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.95) (not (<= z 6.8e-6)))
   (* (+ y -1.0) (* z x))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.95) || !(z <= 6.8e-6)) {
		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 <= (-0.95d0)) .or. (.not. (z <= 6.8d-6))) 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 <= -0.95) || !(z <= 6.8e-6)) {
		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 <= -0.95) or not (z <= 6.8e-6):
		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 <= -0.95) || !(z <= 6.8e-6))
		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 <= -0.95) || ~((z <= 6.8e-6)))
		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, -0.95], N[Not[LessEqual[z, 6.8e-6]], $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 < -0.94999999999999996 or 6.80000000000000012e-6 < z

   1. Initial program 92.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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* 98.0%

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

      2. *-commutative 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   5. Simplified 98.0%

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

   if -0.94999999999999996 < z < 6.80000000000000012e-6

   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 98.9%

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

      1. neg-mul-1 98.9%

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

   5. Simplified 98.9%

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

      1. cancel-sign-sub 98.9%

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

      2. +-commutative 98.9%

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

      3. *-commutative 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 6.8 \cdot 10^{-6}\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+25} \lor \neg \left(y \leq 3.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e+25) (not (<= y 3.4e-7)))
   (* x (+ 1.0 (* y z)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e+25) || !(y <= 3.4e-7)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2d+25)) .or. (.not. (y <= 3.4d-7))) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e+25) || !(y <= 3.4e-7)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e+25) or not (y <= 3.4e-7):
		tmp = x * (1.0 + (y * z))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e+25) || !(y <= 3.4e-7))
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2e+25) || ~((y <= 3.4e-7)))
		tmp = x * (1.0 + (y * z));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e+25], N[Not[LessEqual[y, 3.4e-7]], $MachinePrecision]], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000018e25 or 3.39999999999999974e-7 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 90.3%

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

      1. neg-mul-1 90.3%

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

   5. Simplified 90.3%

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

      1. cancel-sign-sub 90.3%

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

      2. +-commutative 90.3%

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

      3. *-commutative 90.3%

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

   7. Applied egg-rr 90.3%

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

   if -2.00000000000000018e25 < y < 3.39999999999999974e-7

   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 99.2%

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

      1. mul-1-neg 99.2%

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

      2. *-commutative 99.2%

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

      3. distribute-rgt-neg-in 99.2%

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

   6. Simplified 99.2%

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

      1. distribute-rgt-neg-out 99.2%

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

      2. *-commutative 99.2%

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

      3. unsub-neg 99.2%

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

   8. Applied egg-rr 99.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+25} \lor \neg \left(y \leq 3.4 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+73} \lor \neg \left(y \leq 1.16 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.1e+73) (not (<= y 1.16e+29))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e+73) || !(y <= 1.16e+29)) {
		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 <= (-4.1d+73)) .or. (.not. (y <= 1.16d+29))) 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 <= -4.1e+73) || !(y <= 1.16e+29)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.1e+73) or not (y <= 1.16e+29):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.1e+73) || !(y <= 1.16e+29))
		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 <= -4.1e+73) || ~((y <= 1.16e+29)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.1e+73], N[Not[LessEqual[y, 1.16e+29]], $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 < -4.0999999999999998e73 or 1.16e29 < 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 65.9%

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

      1. associate-*r* 70.9%

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

      2. flip-- 51.9%

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

      3. associate-*r/ 49.5%

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

      4. metadata-eval 49.5%

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

      5. fma-neg 49.5%

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

      6. metadata-eval 49.5%

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

   5. Applied egg-rr 49.5%

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

      1. associate-/l* 51.9%

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

      2. metadata-eval 51.9%

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

      3. fma-neg 51.9%

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

      4. metadata-eval 51.9%

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

      5. flip-- 70.9%

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

      6. *-commutative 70.9%

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

      7. sub-neg 70.9%

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

      8. metadata-eval 70.9%

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

      9. *-commutative 70.9%

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

   7. Applied egg-rr 70.9%

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

   8. Taylor expanded in y around inf 70.9%

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

   if -4.0999999999999998e73 < y < 1.16e29

   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 95.9%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+73} \lor \neg \left(y \leq 1.16 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.28e+79)
   (* z (* y x))
   (if (<= y 4.5e+28) (- x (* z x)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.28e+79) {
		tmp = z * (y * x);
	} else if (y <= 4.5e+28) {
		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 <= (-1.28d+79)) then
        tmp = z * (y * x)
    else if (y <= 4.5d+28) 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 <= -1.28e+79) {
		tmp = z * (y * x);
	} else if (y <= 4.5e+28) {
		tmp = x - (z * x);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.28e+79:
		tmp = z * (y * x)
	elif y <= 4.5e+28:
		tmp = x - (z * x)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.28e+79)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 4.5e+28)
		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 <= -1.28e+79)
		tmp = z * (y * x);
	elseif (y <= 4.5e+28)
		tmp = x - (z * x);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.28e+79], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+28], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.27999999999999998e79

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*l* 79.7%

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

   5. Simplified 79.7%

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

   if -1.27999999999999998e79 < y < 4.4999999999999997e28

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around 0 96.0%

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

      1. mul-1-neg 96.0%

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

      2. *-commutative 96.0%

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

      3. distribute-rgt-neg-in 96.0%

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

   6. Simplified 96.0%

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

      1. distribute-rgt-neg-out 96.0%

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

      2. *-commutative 96.0%

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

      3. unsub-neg 96.0%

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

   8. Applied egg-rr 96.0%

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

   if 4.4999999999999997e28 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 61.7%

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

      1. associate-*r* 67.0%

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

      2. flip-- 52.3%

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

      3. associate-*r/ 49.7%

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

      4. metadata-eval 49.7%

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

      5. fma-neg 49.7%

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

      6. metadata-eval 49.7%

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

   5. Applied egg-rr 49.7%

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

      1. associate-/l* 52.3%

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

      2. metadata-eval 52.3%

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

      3. fma-neg 52.3%

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

      4. metadata-eval 52.3%

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

      5. flip-- 67.0%

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

      6. *-commutative 67.0%

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

      7. sub-neg 67.0%

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

      8. metadata-eval 67.0%

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

      9. *-commutative 67.0%

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

   7. Applied egg-rr 67.0%

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

   8. Taylor expanded in y around inf 67.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+73)
   (* z (* y x))
   (if (<= y 1.3e+28) (* x (- 1.0 z)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+73) {
		tmp = z * (y * x);
	} else if (y <= 1.3e+28) {
		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 <= (-3.8d+73)) then
        tmp = z * (y * x)
    else if (y <= 1.3d+28) 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 <= -3.8e+73) {
		tmp = z * (y * x);
	} else if (y <= 1.3e+28) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+73:
		tmp = z * (y * x)
	elif y <= 1.3e+28:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+73)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 1.3e+28)
		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 <= -3.8e+73)
		tmp = z * (y * x);
	elseif (y <= 1.3e+28)
		tmp = x * (1.0 - z);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+73], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+28], 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 < -3.80000000000000022e73

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. *-commutative 72.8%

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

      2. *-commutative 72.8%

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

      3. associate-*l* 79.7%

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

   5. Simplified 79.7%

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

   if -3.80000000000000022e73 < y < 1.3000000000000001e28

   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 95.9%

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

   if 1.3000000000000001e28 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 61.7%

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

      1. associate-*r* 67.0%

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

      2. flip-- 52.3%

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

      3. associate-*r/ 49.7%

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

      4. metadata-eval 49.7%

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

      5. fma-neg 49.7%

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

      6. metadata-eval 49.7%

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

   5. Applied egg-rr 49.7%

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

      1. associate-/l* 52.3%

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

      2. metadata-eval 52.3%

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

      3. fma-neg 52.3%

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

      4. metadata-eval 52.3%

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

      5. flip-- 67.0%

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

      6. *-commutative 67.0%

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

      7. sub-neg 67.0%

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

      8. metadata-eval 67.0%

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

      9. *-commutative 67.0%

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

   7. Applied egg-rr 67.0%

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

   8. Taylor expanded in y around inf 67.0%

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

Alternative 9: 65.0% 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 92.0%

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

   3. Taylor expanded in z around inf 90.0%

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

   4. Taylor expanded in y around 0 60.7%

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

      1. mul-1-neg 62.3%

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

      2. *-commutative 62.3%

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

      3. distribute-rgt-neg-in 62.3%

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

   6. Simplified 60.7%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.9%

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

4. Final simplification 67.7%

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

Alternative 10: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.3e+212) (* x (- 1.0 z)) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.3e+212) {
		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 <= 2.3d+212) 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 <= 2.3e+212) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.3e+212:
		tmp = x * (1.0 - z)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.3e+212)
		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 <= 2.3e+212)
		tmp = x * (1.0 - z);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.3e+212], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.2999999999999998e212

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0 73.7%

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

   if 2.2999999999999998e212 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 85.3%

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

   4. Taylor expanded in y around 0 1.9%

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

      1. mul-1-neg 10.9%

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

      2. *-commutative 10.9%

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

      3. distribute-rgt-neg-in 10.9%

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

   6. Simplified 1.9%

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

      1. add-sqr-sqrt 1.5%

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

      2. sqrt-unprod 29.3%

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

      3. sqr-neg 29.3%

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

      4. sqrt-unprod 27.5%

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

      5. add-sqr-sqrt 35.0%

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

      6. pow1 35.0%

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

   8. Applied egg-rr 35.0%

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

      1. unpow1 35.0%

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

      2. *-commutative 35.0%

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

   10. Simplified 35.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+91}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -4.3e+91) (* z x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.3e+91) {
		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 <= (-4.3d+91)) 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 <= -4.3e+91) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.3e+91:
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.3e+91)
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.3e+91)
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.3e+91], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000001e91

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 86.8%

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

   4. Taylor expanded in y around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   6. Simplified 56.9%

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

      1. add-sqr-sqrt 32.4%

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

      2. sqrt-unprod 33.2%

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

      3. sqr-neg 33.2%

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

      4. sqrt-unprod 6.5%

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

      5. add-sqr-sqrt 13.4%

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

      6. pow1 13.4%

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

   8. Applied egg-rr 13.4%

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

      1. unpow1 13.4%

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

      2. *-commutative 13.4%

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

   10. Simplified 13.4%

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

   if -4.3000000000000001e91 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 47.0%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+91}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 95.9%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
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 2024145 
(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))))