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

Percentage Accurate: 96.0% → 99.5%

Time: 9.1s

Alternatives: 11

Speedup: 0.5×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x + x \cdot \left(\left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (* z (* x y))
     (if (<= t_0 5e+87) (+ x (* x (* (+ y -1.0) z))) (* z (- (* x 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 = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x + (x * ((y + -1.0) * z));
	} else {
		tmp = z * ((x * 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 = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x + (x * ((y + -1.0) * z));
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = z * (x * y)
	elif t_0 <= 5e+87:
		tmp = x + (x * ((y + -1.0) * z))
	else:
		tmp = z * ((x * 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(z * Float64(x * y));
	elseif (t_0 <= 5e+87)
		tmp = Float64(x + Float64(x * Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(z * Float64(Float64(x * 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 = z * (x * y);
	elseif (t_0 <= 5e+87)
		tmp = x + (x * ((y + -1.0) * z));
	else
		tmp = z * ((x * 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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+87], N[(x + N[(x * N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 44.8%

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

   2. Taylor expanded in y around inf 44.8%

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

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 4.9999999999999998e87

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. *-commutative 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. +-commutative 99.9%

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

      11. *-un-lft-identity 99.9%

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

      12. distribute-lft-neg-in 99.9%

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

      13. distribute-lft-neg-in 99.9%

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

      14. metadata-eval 99.9%

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

      15. metadata-eval 99.9%

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

      16. *-un-lft-identity 99.9%

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

      17. metadata-eval 99.9%

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

   3. Applied egg-rr 99.9%

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

   if 4.9999999999999998e87 < (*.f64 (-.f64 1 y) z)

   1. Initial program 88.5%

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

      1. sub-neg 88.5%

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

      2. distribute-rgt-in 88.5%

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

      3. *-un-lft-identity 88.5%

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

      4. *-commutative 88.5%

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

      5. +-commutative 88.5%

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

      6. distribute-lft-neg-in 88.5%

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

      7. *-commutative 88.5%

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

      8. sub-neg 88.5%

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

      9. distribute-neg-in 88.5%

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

      10. +-commutative 88.5%

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

      11. *-un-lft-identity 88.5%

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

      12. distribute-lft-neg-in 88.5%

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

      13. distribute-lft-neg-in 88.5%

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

      14. metadata-eval 88.5%

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

      15. metadata-eval 88.5%

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

      16. *-un-lft-identity 88.5%

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

      17. metadata-eval 88.5%

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

   3. Applied egg-rr 88.5%

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

      1. associate-*r* 99.7%

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

      2. flip-+ 84.1%

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

      3. associate-*r/ 81.4%

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

      4. metadata-eval 81.4%

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

      5. fma-neg 81.4%

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

      6. metadata-eval 81.4%

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

      7. sub-neg 81.4%

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

      8. metadata-eval 81.4%

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

   5. Applied egg-rr 81.4%

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

   6. Taylor expanded in y around inf 81.0%

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

   7. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x + x \cdot \left(\left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 2: 97.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;x + {\left(\sqrt[3]{\left(x \cdot \left(y + -1\right)\right) \cdot z}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.1e-27)
   (+ x (pow (cbrt (* (* x (+ y -1.0)) z)) 3.0))
   (* x (+ 1.0 (* (+ y -1.0) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.1e-27) {
		tmp = x + pow(cbrt(((x * (y + -1.0)) * z)), 3.0);
	} else {
		tmp = x * (1.0 + ((y + -1.0) * z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.1e-27) {
		tmp = x + Math.pow(Math.cbrt(((x * (y + -1.0)) * z)), 3.0);
	} else {
		tmp = x * (1.0 + ((y + -1.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.1e-27)
		tmp = Float64(x + (cbrt(Float64(Float64(x * Float64(y + -1.0)) * z)) ^ 3.0));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.1e-27], N[(x + N[Power[N[Power[N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.10000000000000015e-27

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. distribute-rgt-in 91.2%

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

      3. *-un-lft-identity 91.2%

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

      4. *-commutative 91.2%

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

      5. +-commutative 91.2%

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

      6. distribute-lft-neg-in 91.2%

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

      7. *-commutative 91.2%

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

      8. sub-neg 91.2%

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

      9. distribute-neg-in 91.2%

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

      10. +-commutative 91.2%

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

      11. *-un-lft-identity 91.2%

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

      12. distribute-lft-neg-in 91.2%

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

      13. distribute-lft-neg-in 91.2%

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

      14. metadata-eval 91.2%

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

      15. metadata-eval 91.2%

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

      16. *-un-lft-identity 91.2%

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

      17. metadata-eval 91.2%

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

   3. Applied egg-rr 91.2%

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

      1. add-cube-cbrt 90.4%

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

      2. pow3 90.4%

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

      3. *-commutative 90.4%

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

      4. associate-*r* 96.5%

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

   5. Applied egg-rr 96.5%

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

   if 2.10000000000000015e-27 < x

   1. Initial program 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;x + {\left(\sqrt[3]{\left(x \cdot \left(y + -1\right)\right) \cdot z}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \end{array} \]

Alternative 3: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (* z (* x y))
     (if (<= t_0 5e+87) (* x (+ 1.0 (* (+ y -1.0) z))) (* z (- (* x 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 = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x * (1.0 + ((y + -1.0) * z));
	} else {
		tmp = z * ((x * 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 = z * (x * y);
	} else if (t_0 <= 5e+87) {
		tmp = x * (1.0 + ((y + -1.0) * z));
	} else {
		tmp = z * ((x * y) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = z * (x * y)
	elif t_0 <= 5e+87:
		tmp = x * (1.0 + ((y + -1.0) * z))
	else:
		tmp = z * ((x * 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(z * Float64(x * y));
	elseif (t_0 <= 5e+87)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(z * Float64(Float64(x * 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 = z * (x * y);
	elseif (t_0 <= 5e+87)
		tmp = x * (1.0 + ((y + -1.0) * z));
	else
		tmp = z * ((x * 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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+87], N[(x * N[(1.0 + N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 44.8%

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

   2. Taylor expanded in y around inf 44.8%

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

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 4.9999999999999998e87

   1. Initial program 99.9%

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

   if 4.9999999999999998e87 < (*.f64 (-.f64 1 y) z)

   1. Initial program 88.5%

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

      1. sub-neg 88.5%

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

      2. distribute-rgt-in 88.5%

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

      3. *-un-lft-identity 88.5%

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

      4. *-commutative 88.5%

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

      5. +-commutative 88.5%

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

      6. distribute-lft-neg-in 88.5%

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

      7. *-commutative 88.5%

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

      8. sub-neg 88.5%

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

      9. distribute-neg-in 88.5%

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

      10. +-commutative 88.5%

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

      11. *-un-lft-identity 88.5%

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

      12. distribute-lft-neg-in 88.5%

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

      13. distribute-lft-neg-in 88.5%

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

      14. metadata-eval 88.5%

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

      15. metadata-eval 88.5%

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

      16. *-un-lft-identity 88.5%

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

      17. metadata-eval 88.5%

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

   3. Applied egg-rr 88.5%

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

      1. associate-*r* 99.7%

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

      2. flip-+ 84.1%

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

      3. associate-*r/ 81.4%

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

      4. metadata-eval 81.4%

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

      5. fma-neg 81.4%

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

      6. metadata-eval 81.4%

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

      7. sub-neg 81.4%

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

      8. metadata-eval 81.4%

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

   5. Applied egg-rr 81.4%

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

   6. Taylor expanded in y around inf 81.0%

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

   7. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 4: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -8800:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* y z))))
   (if (<= z -8800.0)
     t_0
     (if (<= z -2.8e-88)
       t_1
       (if (<= z 6.6e-64) x (if (<= z 4.1e+49) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -8800.0) {
		tmp = t_0;
	} else if (z <= -2.8e-88) {
		tmp = t_1;
	} else if (z <= 6.6e-64) {
		tmp = x;
	} else if (z <= 4.1e+49) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = x * (y * z)
    if (z <= (-8800.0d0)) then
        tmp = t_0
    else if (z <= (-2.8d-88)) then
        tmp = t_1
    else if (z <= 6.6d-64) then
        tmp = x
    else if (z <= 4.1d+49) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -8800.0) {
		tmp = t_0;
	} else if (z <= -2.8e-88) {
		tmp = t_1;
	} else if (z <= 6.6e-64) {
		tmp = x;
	} else if (z <= 4.1e+49) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (y * z)
	tmp = 0
	if z <= -8800.0:
		tmp = t_0
	elif z <= -2.8e-88:
		tmp = t_1
	elif z <= 6.6e-64:
		tmp = x
	elif z <= 4.1e+49:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -8800.0)
		tmp = t_0;
	elseif (z <= -2.8e-88)
		tmp = t_1;
	elseif (z <= 6.6e-64)
		tmp = x;
	elseif (z <= 4.1e+49)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -8800.0)
		tmp = t_0;
	elseif (z <= -2.8e-88)
		tmp = t_1;
	elseif (z <= 6.6e-64)
		tmp = x;
	elseif (z <= 4.1e+49)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8800.0], t$95$0, If[LessEqual[z, -2.8e-88], t$95$1, If[LessEqual[z, 6.6e-64], x, If[LessEqual[z, 4.1e+49], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8800 or 4.1e49 < z

   1. Initial program 86.2%

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

   2. Taylor expanded in z around inf 85.7%

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

   3. Taylor expanded in y around 0 60.5%

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

      1. mul-1-neg 60.5%

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

   5. Simplified 60.5%

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

   if -8800 < z < -2.79999999999999976e-88 or 6.5999999999999999e-64 < z < 4.1e49

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. *-commutative 62.2%

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

   4. Simplified 62.2%

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

   if -2.79999999999999976e-88 < z < 6.5999999999999999e-64

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8800:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{-18}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -30000000000.0) (not (<= y 3.6e-18)))
   (+ x (* z (* x y)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -30000000000.0) || !(y <= 3.6e-18)) {
		tmp = x + (z * (x * 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 <= (-30000000000.0d0)) .or. (.not. (y <= 3.6d-18))) then
        tmp = x + (z * (x * 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 <= -30000000000.0) || !(y <= 3.6e-18)) {
		tmp = x + (z * (x * y));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -30000000000.0) or not (y <= 3.6e-18):
		tmp = x + (z * (x * y))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -30000000000.0) || !(y <= 3.6e-18))
		tmp = Float64(x + Float64(z * Float64(x * 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 <= -30000000000.0) || ~((y <= 3.6e-18)))
		tmp = x + (z * (x * y));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -30000000000.0], N[Not[LessEqual[y, 3.6e-18]], $MachinePrecision]], N[(x + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e10 or 3.6000000000000001e-18 < y

   1. Initial program 85.9%

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

      1. sub-neg 85.9%

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

      2. distribute-rgt-in 85.9%

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

      3. *-un-lft-identity 85.9%

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

      4. *-commutative 85.9%

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

      5. +-commutative 85.9%

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

      6. distribute-lft-neg-in 85.9%

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

      7. *-commutative 85.9%

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

      8. sub-neg 85.9%

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

      9. distribute-neg-in 85.9%

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

      10. +-commutative 85.9%

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

      11. *-un-lft-identity 85.9%

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

      12. distribute-lft-neg-in 85.9%

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

      13. distribute-lft-neg-in 85.9%

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

      14. metadata-eval 85.9%

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

      15. metadata-eval 85.9%

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

      16. *-un-lft-identity 85.9%

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

      17. metadata-eval 85.9%

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

   3. Applied egg-rr 85.9%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. associate-*r* 92.8%

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

      2. *-commutative 92.8%

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

   6. Simplified 92.8%

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

   if -3e10 < y < 3.6000000000000001e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{-18}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 0.019)))
   (* z (- (* x y) x))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 0.019)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.1d0)) .or. (.not. (z <= 0.019d0))) then
        tmp = z * ((x * y) - x)
    else
        tmp = x * (1.0d0 + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 0.019)) {
		tmp = z * ((x * y) - x);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1) or not (z <= 0.019):
		tmp = z * ((x * y) - x)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1) || !(z <= 0.019))
		tmp = Float64(z * Float64(Float64(x * y) - x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1) || ~((z <= 0.019)))
		tmp = z * ((x * y) - x);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1], N[Not[LessEqual[z, 0.019]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 0.0189999999999999995 < z

   1. Initial program 86.7%

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

      1. sub-neg 86.7%

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

      2. distribute-rgt-in 86.6%

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

      3. *-un-lft-identity 86.6%

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

      4. *-commutative 86.6%

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

      5. +-commutative 86.6%

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

      6. distribute-lft-neg-in 86.6%

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

      7. *-commutative 86.6%

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

      8. sub-neg 86.6%

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

      9. distribute-neg-in 86.6%

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

      10. +-commutative 86.6%

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

      11. *-un-lft-identity 86.6%

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

      12. distribute-lft-neg-in 86.6%

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

      13. distribute-lft-neg-in 86.6%

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

      14. metadata-eval 86.6%

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

      15. metadata-eval 86.6%

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

      16. *-un-lft-identity 86.6%

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

      17. metadata-eval 86.6%

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

   3. Applied egg-rr 86.6%

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

      1. associate-*r* 99.8%

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

      2. flip-+ 91.0%

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

      3. associate-*r/ 87.4%

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

      4. metadata-eval 87.4%

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

      5. fma-neg 87.4%

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

      6. metadata-eval 87.4%

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

      7. sub-neg 87.4%

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

      8. metadata-eval 87.4%

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

   5. Applied egg-rr 87.4%

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

   6. Taylor expanded in y around inf 78.8%

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

   7. Taylor expanded in z around inf 98.2%

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

   if -1.1000000000000001 < z < 0.0189999999999999995

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. *-commutative 98.7%

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

      3. distribute-rgt-neg-in 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 7: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+39} \lor \neg \left(y \leq 1.24 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.7e+39) (not (<= y 1.24e+14))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.7e+39) || !(y <= 1.24e+14)) {
		tmp = x * (y * z);
	} 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 <= (-8.7d+39)) .or. (.not. (y <= 1.24d+14))) then
        tmp = x * (y * z)
    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 <= -8.7e+39) || !(y <= 1.24e+14)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.7e+39) or not (y <= 1.24e+14):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.7e+39) || !(y <= 1.24e+14))
		tmp = Float64(x * Float64(y * z));
	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 <= -8.7e+39) || ~((y <= 1.24e+14)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.7e+39], N[Not[LessEqual[y, 1.24e+14]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.70000000000000028e39 or 1.24e14 < y

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

   4. Simplified 67.3%

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

   if -8.70000000000000028e39 < y < 1.24e14

   1. Initial program 99.3%

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

   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 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+39} \lor \neg \left(y \leq 1.24 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+24} \lor \neg \left(y \leq 2.15 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.4e+24) (not (<= y 2.15e+15))) (* z (* x y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.4e+24) || !(y <= 2.15e+15)) {
		tmp = z * (x * 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 <= (-7.4d+24)) .or. (.not. (y <= 2.15d+15))) then
        tmp = z * (x * 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 <= -7.4e+24) || !(y <= 2.15e+15)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.4e+24) or not (y <= 2.15e+15):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.4e+24) || !(y <= 2.15e+15))
		tmp = Float64(z * Float64(x * 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 <= -7.4e+24) || ~((y <= 2.15e+15)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.4e+24], N[Not[LessEqual[y, 2.15e+15]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.39999999999999998e24 or 2.15e15 < y

   1. Initial program 85.4%

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

   2. Taylor expanded in y around inf 67.1%

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

      1. associate-*r* 76.7%

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

      2. *-commutative 76.7%

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

   4. Simplified 76.7%

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

   if -7.39999999999999998e24 < y < 2.15e15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+24} \lor \neg \left(y \leq 2.15 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+15} \lor \neg \left(y \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e+15) (not (<= y 1.2e+17))) (* y (* x z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+15) || !(y <= 1.2e+17)) {
		tmp = y * (x * z);
	} 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 <= (-7d+15)) .or. (.not. (y <= 1.2d+17))) then
        tmp = y * (x * z)
    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 <= -7e+15) || !(y <= 1.2e+17)) {
		tmp = y * (x * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e+15) or not (y <= 1.2e+17):
		tmp = y * (x * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e+15) || !(y <= 1.2e+17))
		tmp = Float64(y * Float64(x * z));
	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 <= -7e+15) || ~((y <= 1.2e+17)))
		tmp = y * (x * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e+15], N[Not[LessEqual[y, 1.2e+17]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e15 or 1.2e17 < y

   1. Initial program 85.4%

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

      1. flip-- 56.1%

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

      2. associate-*r/ 51.5%

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

      3. associate-/l* 56.2%

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

      4. *-un-lft-identity 56.2%

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

      5. associate-/l* 56.2%

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

      6. flip-- 85.4%

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

      7. cancel-sign-sub-inv 85.4%

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

      8. *-commutative 85.4%

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

      9. sub-neg 85.4%

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

      10. distribute-neg-in 85.4%

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

      11. +-commutative 85.4%

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

      12. *-un-lft-identity 85.4%

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

      13. distribute-lft-neg-in 85.4%

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

      14. distribute-lft-neg-in 85.4%

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

      15. metadata-eval 85.4%

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

      16. metadata-eval 85.4%

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

      17. *-un-lft-identity 85.4%

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

      18. metadata-eval 85.4%

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

   3. Applied egg-rr 85.4%

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

   4. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-/r* 68.7%

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

   6. Simplified 68.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{\frac{1}{z}}{y}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 80.5%

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

      2. div-inv 80.5%

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

      3. clear-num 80.5%

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

      4. /-rgt-identity 80.5%

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

   8. Applied egg-rr 80.5%

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

   if -7e15 < y < 1.2e17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+15} \lor \neg \left(y \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 10: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.019))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.019)) {
		tmp = x * -z;
	} 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 <= 0.019d0))) then
        tmp = x * -z
    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 <= 0.019)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.019):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.019))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.019)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.019]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.0189999999999999995 < z

   1. Initial program 86.7%

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

   2. Taylor expanded in z around inf 85.0%

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

   3. Taylor expanded in y around 0 58.2%

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

      1. mul-1-neg 58.2%

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

   5. Simplified 58.2%

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

   if -1 < z < 0.0189999999999999995

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 68.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.019\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 38.2% 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 93.3%

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

2. Taylor expanded in z around 0 35.9%

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

3. Final simplification 35.9%

   \[\leadsto x \]

Developer target: 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 2023336 
(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))))