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

Percentage Accurate: 96.1% → 99.5%

Time: 11.2s

Alternatives: 10

Speedup: 0.8×

• 20.9% 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: 96.1% 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: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;x + y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (+ x (* y (* z x)))
     (if (<= t_0 4e+296) (* x (+ 1.0 (* z (+ -1.0 y)))) (* z (* y x))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = x + (y * (z * x));
	} else if (t_0 <= 4e+296) {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y * (z * x));
	} else if (t_0 <= 4e+296) {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = x + (y * (z * x))
	elif t_0 <= 4e+296:
		tmp = x * (1.0 + (z * (-1.0 + y)))
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(x + Float64(y * Float64(z * x)));
	elseif (t_0 <= 4e+296)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = x + (y * (z * x));
	elseif (t_0 <= 4e+296)
		tmp = x * (1.0 + (z * (-1.0 + y)));
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(x + N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+296], N[(x * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 57.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 57.1%

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

      2. distribute-rgt-in 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. *-commutative 57.1%

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

      5. +-commutative 57.1%

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

      6. distribute-lft-neg-in 57.1%

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

      7. *-commutative 57.1%

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

      8. sub-neg 57.1%

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

      9. distribute-neg-in 57.1%

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

      10. +-commutative 57.1%

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

      11. *-un-lft-identity 57.1%

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

      12. distribute-lft-neg-in 57.1%

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

      13. distribute-lft-neg-in 57.1%

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

      14. metadata-eval 57.1%

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

      15. metadata-eval 57.1%

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

      16. *-un-lft-identity 57.1%

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

      17. metadata-eval 57.1%

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

   3. Applied egg-rr 57.1%

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

   4. Taylor expanded in y around inf 57.1%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 100.0%

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

   6. Simplified 100.0%

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 3.99999999999999993e296

   1. Initial program 99.9%

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

   if 3.99999999999999993e296 < (*.f64 (-.f64 1 y) z)

   1. Initial program 66.6%

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

   2. Taylor expanded in y around inf 66.6%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;x + y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 4 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{z}{\frac{\frac{-1}{-1 + y}}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+77)
   (+ x (/ z (/ (/ -1.0 (+ -1.0 y)) (- x))))
   (* x (+ 1.0 (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+77) {
		tmp = x + (z / ((-1.0 / (-1.0 + y)) / -x));
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5d+77)) then
        tmp = x + (z / (((-1.0d0) / ((-1.0d0) + y)) / -x))
    else
        tmp = x * (1.0d0 + (z * ((-1.0d0) + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+77) {
		tmp = x + (z / ((-1.0 / (-1.0 + y)) / -x));
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+77:
		tmp = x + (z / ((-1.0 / (-1.0 + y)) / -x))
	else:
		tmp = x * (1.0 + (z * (-1.0 + y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+77)
		tmp = Float64(x + Float64(z / Float64(Float64(-1.0 / Float64(-1.0 + y)) / Float64(-x))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+77)
		tmp = x + (z / ((-1.0 / (-1.0 + y)) / -x));
	else
		tmp = x * (1.0 + (z * (-1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+77], N[(x + N[(z / N[(N[(-1.0 / N[(-1.0 + y), $MachinePrecision]), $MachinePrecision] / (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000004e77

   1. Initial program 77.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.1%

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

      2. distribute-rgt-in 77.1%

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

      3. *-un-lft-identity 77.1%

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

      4. *-commutative 77.1%

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

      5. +-commutative 77.1%

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

      6. distribute-lft-neg-in 77.1%

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

      7. *-commutative 77.1%

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

      8. sub-neg 77.1%

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

      9. distribute-neg-in 77.1%

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

      10. +-commutative 77.1%

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

      11. *-un-lft-identity 77.1%

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

      12. distribute-lft-neg-in 77.1%

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

      13. distribute-lft-neg-in 77.1%

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

      14. metadata-eval 77.1%

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

      15. metadata-eval 77.1%

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

      16. *-un-lft-identity 77.1%

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

      17. metadata-eval 77.1%

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

   3. Applied egg-rr 77.1%

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

      1. associate-*r* 99.9%

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

      2. flip-+ 87.5%

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

      3. associate-*r/ 79.2%

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

      4. metadata-eval 79.2%

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

      5. fma-neg 79.2%

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

      6. metadata-eval 79.2%

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

      7. sub-neg 79.2%

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

      8. metadata-eval 79.2%

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

   5. Applied egg-rr 79.2%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

      1. frac-2neg 87.5%

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

      2. distribute-frac-neg 87.5%

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

      3. clear-num 87.5%

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

      4. clear-num 87.5%

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

      5. distribute-neg-frac 87.5%

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

      6. metadata-eval 87.5%

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

      7. clear-num 87.5%

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

      8. fma-udef 87.5%

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

      9. difference-of-sqr--1 87.5%

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

      10. difference-of-sqr-1 87.5%

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

      11. metadata-eval 87.5%

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

      12. flip-- 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. distribute-neg-frac 99.9%

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

       2. *-commutative 99.9%

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

       3. distribute-rgt-neg-out 99.9%

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

       4. associate-/l* 99.7%

          \[\leadsto \color{blue}{\frac{z}{\frac{\frac{-1}{y + -1}}{-x}}} + x \]

       5. +-commutative 99.7%

          \[\leadsto \frac{z}{\frac{\frac{-1}{\color{blue}{-1 + y}}}{-x}} + x \]

   11. Simplified 99.7%

       \[\leadsto \color{blue}{\frac{z}{\frac{\frac{-1}{-1 + y}}{-x}}} + x \]

   if -5.00000000000000004e77 < z

   1. Initial program 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{z}{\frac{\frac{-1}{-1 + y}}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \]

Alternative 3: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{z}{\frac{\frac{1}{x}}{-1 + y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+77)
   (+ x (/ z (/ (/ 1.0 x) (+ -1.0 y))))
   (* x (+ 1.0 (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+77) {
		tmp = x + (z / ((1.0 / x) / (-1.0 + y)));
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5d+77)) then
        tmp = x + (z / ((1.0d0 / x) / ((-1.0d0) + y)))
    else
        tmp = x * (1.0d0 + (z * ((-1.0d0) + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+77) {
		tmp = x + (z / ((1.0 / x) / (-1.0 + y)));
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+77:
		tmp = x + (z / ((1.0 / x) / (-1.0 + y)))
	else:
		tmp = x * (1.0 + (z * (-1.0 + y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+77)
		tmp = Float64(x + Float64(z / Float64(Float64(1.0 / x) / Float64(-1.0 + y))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+77)
		tmp = x + (z / ((1.0 / x) / (-1.0 + y)));
	else
		tmp = x * (1.0 + (z * (-1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+77], N[(x + N[(z / N[(N[(1.0 / x), $MachinePrecision] / N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000004e77

   1. Initial program 77.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 77.1%

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

      2. distribute-rgt-in 77.1%

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

      3. *-un-lft-identity 77.1%

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

      4. *-commutative 77.1%

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

      5. +-commutative 77.1%

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

      6. distribute-lft-neg-in 77.1%

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

      7. *-commutative 77.1%

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

      8. sub-neg 77.1%

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

      9. distribute-neg-in 77.1%

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

      10. +-commutative 77.1%

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

      11. *-un-lft-identity 77.1%

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

      12. distribute-lft-neg-in 77.1%

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

      13. distribute-lft-neg-in 77.1%

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

      14. metadata-eval 77.1%

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

      15. metadata-eval 77.1%

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

      16. *-un-lft-identity 77.1%

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

      17. metadata-eval 77.1%

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

   3. Applied egg-rr 77.1%

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

      1. associate-*r* 99.9%

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

      2. flip-+ 87.5%

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

      3. associate-*r/ 79.2%

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

      4. metadata-eval 79.2%

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

      5. fma-neg 79.2%

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

      6. metadata-eval 79.2%

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

      7. sub-neg 79.2%

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

      8. metadata-eval 79.2%

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

   5. Applied egg-rr 79.2%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

      1. frac-2neg 87.5%

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

      2. distribute-frac-neg 87.5%

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

      3. clear-num 87.5%

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

      4. clear-num 87.5%

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

      5. distribute-neg-frac 87.5%

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

      6. metadata-eval 87.5%

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

      7. clear-num 87.5%

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

      8. fma-udef 87.5%

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

      9. difference-of-sqr--1 87.5%

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

      10. difference-of-sqr-1 87.5%

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

      11. metadata-eval 87.5%

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

      12. flip-- 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. distribute-neg-frac 99.9%

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

       2. *-commutative 99.9%

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

       3. distribute-rgt-neg-out 99.9%

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

       4. associate-/l* 99.7%

          \[\leadsto \color{blue}{\frac{z}{\frac{\frac{-1}{y + -1}}{-x}}} + x \]

       5. +-commutative 99.7%

          \[\leadsto \frac{z}{\frac{\frac{-1}{\color{blue}{-1 + y}}}{-x}} + x \]

   11. Simplified 99.7%

       \[\leadsto \color{blue}{\frac{z}{\frac{\frac{-1}{-1 + y}}{-x}}} + x \]

   12. Taylor expanded in x around 0 99.6%

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

       1. associate-/r* 99.6%

          \[\leadsto \frac{z}{\color{blue}{\frac{\frac{1}{x}}{y - 1}}} + x \]

       2. sub-neg 99.6%

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

       3. metadata-eval 99.6%

          \[\leadsto \frac{z}{\frac{\frac{1}{x}}{y + \color{blue}{-1}}} + x \]

   14. Simplified 99.6%

       \[\leadsto \frac{z}{\color{blue}{\frac{\frac{1}{x}}{y + -1}}} + x \]

   if -5.00000000000000004e77 < z

   1. Initial program 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{z}{\frac{\frac{1}{x}}{-1 + y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \]

Alternative 4: 94.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+31} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+31) (not (<= z 1.0)))
   (* x (* z (+ -1.0 y)))
   (* x (+ 1.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+31) || !(z <= 1.0)) {
		tmp = x * (z * (-1.0 + y));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.2d+31)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (z * ((-1.0d0) + y))
    else
        tmp = x * (1.0d0 + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+31) || !(z <= 1.0)) {
		tmp = x * (z * (-1.0 + y));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e+31) or not (z <= 1.0):
		tmp = x * (z * (-1.0 + y))
	else:
		tmp = x * (1.0 + (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+31) || !(z <= 1.0))
		tmp = Float64(x * Float64(z * Float64(-1.0 + y)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.2e+31) || ~((z <= 1.0)))
		tmp = x * (z * (-1.0 + y));
	else
		tmp = x * (1.0 + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+31], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e31 or 1 < z

   1. Initial program 90.6%

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

   2. Taylor expanded in z around inf 90.5%

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

   if -2.2000000000000001e31 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. *-commutative 99.3%

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

      3. distribute-rgt-neg-in 99.3%

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

   4. Simplified 99.3%

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

      1. sub-neg 99.3%

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

      2. +-commutative 99.3%

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

      3. distribute-rgt-neg-out 99.3%

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

      4. remove-double-neg 99.3%

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

   6. Applied egg-rr 99.3%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+31} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]

Alternative 5: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+14} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x + y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e+14) (not (<= y 1.0)))
   (+ x (* y (* z x)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e+14) || !(y <= 1.0)) {
		tmp = x + (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 <= (-3.4d+14)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + (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 <= -3.4e+14) || !(y <= 1.0)) {
		tmp = x + (y * (z * x));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e+14) or not (y <= 1.0):
		tmp = x + (y * (z * x))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e+14) || !(y <= 1.0))
		tmp = Float64(x + 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 <= -3.4e+14) || ~((y <= 1.0)))
		tmp = x + (y * (z * x));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e+14], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x + N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e14 or 1 < y

   1. Initial program 89.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 89.6%

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

      2. distribute-rgt-in 89.6%

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

      3. *-un-lft-identity 89.6%

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

      4. *-commutative 89.6%

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

      5. +-commutative 89.6%

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

      6. distribute-lft-neg-in 89.6%

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

      7. *-commutative 89.6%

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

      8. sub-neg 89.6%

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

      9. distribute-neg-in 89.6%

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

      10. +-commutative 89.6%

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

      11. *-un-lft-identity 89.6%

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

      12. distribute-lft-neg-in 89.6%

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

      13. distribute-lft-neg-in 89.6%

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

      14. metadata-eval 89.6%

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

      15. metadata-eval 89.6%

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

      16. *-un-lft-identity 89.6%

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

      17. metadata-eval 89.6%

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

   3. Applied egg-rr 89.6%

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

   4. Taylor expanded in y around inf 89.6%

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

      1. associate-*r* 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*r* 94.2%

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

   6. Simplified 94.2%

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

   if -3.4e14 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.1%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+14} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x + y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 6: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.12 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.12e+40)
   (* z (* y x))
   (if (<= y 8e+146) (* x (- 1.0 z)) (* x (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.12e+40) {
		tmp = z * (y * x);
	} else if (y <= 8e+146) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * (-1.0 + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.12d+40)) then
        tmp = z * (y * x)
    else if (y <= 8d+146) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x * (z * ((-1.0d0) + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.12e+40) {
		tmp = z * (y * x);
	} else if (y <= 8e+146) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * (-1.0 + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.12e+40:
		tmp = z * (y * x)
	elif y <= 8e+146:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (z * (-1.0 + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.12e+40)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 8e+146)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(z * Float64(-1.0 + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.12e+40)
		tmp = z * (y * x);
	elseif (y <= 8e+146)
		tmp = x * (1.0 - z);
	else
		tmp = x * (z * (-1.0 + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.12e+40], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+146], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.11999999999999991e40

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf 65.6%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

   4. Simplified 74.0%

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

   if -2.11999999999999991e40 < y < 7.99999999999999947e146

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 91.9%

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

   if 7.99999999999999947e146 < y

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 74.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.12 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \]

Alternative 7: 58.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-14} \lor \neg \left(z \leq 2.95 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.5e-14) (not (<= z 2.95e-22))) (* x (* z y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-14) || !(z <= 2.95e-22)) {
		tmp = x * (z * y);
	} 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 <= (-9.5d-14)) .or. (.not. (z <= 2.95d-22))) then
        tmp = x * (z * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-14) || !(z <= 2.95e-22)) {
		tmp = x * (z * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.5e-14) or not (z <= 2.95e-22):
		tmp = x * (z * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.5e-14) || !(z <= 2.95e-22))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.5e-14) || ~((z <= 2.95e-22)))
		tmp = x * (z * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.5e-14], N[Not[LessEqual[z, 2.95e-22]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e-14 or 2.95000000000000004e-22 < z

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 39.2%

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

      1. *-commutative 39.2%

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

   4. Simplified 39.2%

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

   if -9.4999999999999999e-14 < z < 2.95000000000000004e-22

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.7%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-14} \lor \neg \left(z \leq 2.95 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+40} \lor \neg \left(y \leq 8 \cdot 10^{+146}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.08e+40) (not (<= y 8e+146))) (* x (* z y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.08e+40) || !(y <= 8e+146)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.08d+40)) .or. (.not. (y <= 8d+146))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.08e+40) || !(y <= 8e+146)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.08e+40) or not (y <= 8e+146):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.08e+40) || !(y <= 8e+146))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.08e+40) || ~((y <= 8e+146)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.08e+40], N[Not[LessEqual[y, 8e+146]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08000000000000001e40 or 7.99999999999999947e146 < y

   1. Initial program 87.9%

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

   2. Taylor expanded in y around inf 69.1%

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

      1. *-commutative 69.1%

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

   4. Simplified 69.1%

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

   if -1.08000000000000001e40 < y < 7.99999999999999947e146

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 91.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+40} \lor \neg \left(y \leq 8 \cdot 10^{+146}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+39)
   (* z (* y x))
   (if (<= y 5.8e+152) (* x (- 1.0 z)) (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+39) {
		tmp = z * (y * x);
	} else if (y <= 5.8e+152) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.2d+39)) then
        tmp = z * (y * x)
    else if (y <= 5.8d+152) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+39) {
		tmp = z * (y * x);
	} else if (y <= 5.8e+152) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+39:
		tmp = z * (y * x)
	elif y <= 5.8e+152:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+39)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 5.8e+152)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e+39)
		tmp = z * (y * x);
	elseif (y <= 5.8e+152)
		tmp = x * (1.0 - z);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+39], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+152], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1999999999999997e39

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf 65.6%

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

      1. associate-*r* 74.0%

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

      2. *-commutative 74.0%

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

   4. Simplified 74.0%

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

   if -4.1999999999999997e39 < y < 5.7999999999999997e152

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 91.9%

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

   if 5.7999999999999997e152 < y

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   4. Simplified 74.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 10: 37.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.5%

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

2. Taylor expanded in z around 0 42.3%

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

3. Final simplification 42.3%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× 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 2023301 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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