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

Percentage Accurate: 95.9% → 99.7%

Time: 10.4s

Alternatives: 10

Speedup: 0.5×

• 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: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\frac{--1}{x}}{y}}{z}\right)}^{-1}\\ \end{array} \end{array} \]

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+302)
       (* x (+ 1.0 (* z (+ y -1.0))))
       (pow (/ (/ (/ (- -1.0) x) y) z) -1.0)))))

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+302) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = pow((((-(-1.0) / x) / y) / z), -1.0);
	}
	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+302) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = Math.pow((((-(-1.0) / x) / y) / z), -1.0);
	}
	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+302:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = math.pow((((-(-1.0) / x) / y) / z), -1.0)
	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+302)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(Float64(Float64(-(-1.0)) / x) / y) / z) ^ -1.0;
	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+302)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = (((-(-1.0) / x) / y) / z) ^ -1.0;
	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+302], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(N[((--1.0) / x), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision], -1.0], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 5e302

   1. Initial program 99.9%

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

   if 5e302 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 60.6%

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

      1. *-commutative 60.6%

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

      2. flip-- 0.0%

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

      3. associate-*l/ 0.0%

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

      4. metadata-eval 0.0%

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

      5. pow2 0.0%

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

      6. +-commutative 0.0%

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

      7. fma-define 0.0%

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

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\left(\left(1 - y\right) \cdot z\right)}^{2}\right) \cdot x}{\mathsf{fma}\left(1 - y, z, 1\right)}} \]
   5. Step-by-step derivation

      1. clear-num 0.0%

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

      2. inv-pow 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-/r* 0.0%

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

      5. fma-undefine 0.0%

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

      6. *-commutative 0.0%

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

      7. fma-define 0.0%

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

      8. *-commutative 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in z around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

      3. associate-/r* 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around inf 99.9%

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

       1. associate-/r* 100.0%

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

   12. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\frac{\frac{--1}{x}}{y}}{z}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-70}:\\ \;\;\;\;x + {\left(\sqrt[3]{z \cdot \left(x \cdot \left(y + -1\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 3.1e-70)
   (+ x (pow (cbrt (* z (* x (+ y -1.0)))) 3.0))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.1e-70) {
		tmp = x + pow(cbrt((z * (x * (y + -1.0)))), 3.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.1e-70) {
		tmp = x + Math.pow(Math.cbrt((z * (x * (y + -1.0)))), 3.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.1e-70)
		tmp = Float64(x + (cbrt(Float64(z * Float64(x * Float64(y + -1.0)))) ^ 3.0));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.1e-70], N[(x + N[Power[N[Power[N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.1e-70

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 92.4%

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

      1. add-cube-cbrt 91.7%

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

      2. pow3 91.8%

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

      3. *-commutative 91.8%

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

      4. associate-*l* 94.2%

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

      5. *-commutative 94.2%

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

      6. sub-neg 94.2%

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

      7. metadata-eval 94.2%

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

   5. Applied egg-rr 94.2%

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

   if 3.1e-70 < x

   1. Initial program 99.9%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-70}:\\ \;\;\;\;x + {\left(\sqrt[3]{z \cdot \left(x \cdot \left(y + -1\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+112}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (* z (* x y))
     (if (<= t_0 1e+112)
       (* x (+ 1.0 (* z (+ y -1.0))))
       (* (+ y -1.0) (* x z))))))

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 <= 1e+112) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	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 <= 1e+112) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	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 <= 1e+112:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = (y + -1.0) * (x * z)
	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 <= 1e+112)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	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 <= 1e+112)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = (y + -1.0) * (x * z);
	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, 1e+112], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 9.9999999999999993e111

   1. Initial program 99.9%

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

   if 9.9999999999999993e111 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 88.6%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 10^{+112}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 5000000000\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05) (not (<= z 5000000000.0)))
   (* (+ y -1.0) (* x z))
   (* x (+ 1.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 5000000000.0)) {
		tmp = (y + -1.0) * (x * z);
	} 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 <= (-1.05d0)) .or. (.not. (z <= 5000000000.0d0))) then
        tmp = (y + (-1.0d0)) * (x * z)
    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 <= -1.05) || !(z <= 5000000000.0)) {
		tmp = (y + -1.0) * (x * z);
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05) or not (z <= 5000000000.0):
		tmp = (y + -1.0) * (x * z)
	else:
		tmp = x * (1.0 + (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 5000000000.0))
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	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 <= -1.05) || ~((z <= 5000000000.0)))
		tmp = (y + -1.0) * (x * z);
	else
		tmp = x * (1.0 + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 5000000000.0]], $MachinePrecision]], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 5e9 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in z around inf 87.1%

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

      1. associate-*r* 97.9%

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

      2. *-commutative 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   5. Simplified 97.9%

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

   if -1.05000000000000004 < z < 5e9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. neg-mul-1 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 5000000000\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+25} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+25) (not (<= y 1.0)))
   (+ x (* z (* x y)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+25) || !(y <= 1.0)) {
		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 <= (-4.2d+25)) .or. (.not. (y <= 1.0d0))) 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 <= -4.2e+25) || !(y <= 1.0)) {
		tmp = x + (z * (x * y));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+25) or not (y <= 1.0):
		tmp = x + (z * (x * y))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+25) || !(y <= 1.0))
		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 <= -4.2e+25) || ~((y <= 1.0)))
		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, -4.2e+25], N[Not[LessEqual[y, 1.0]], $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 < -4.1999999999999998e25 or 1 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in y around inf 88.8%

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

      1. associate-*r* 90.1%

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

   6. Simplified 90.1%

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

   if -4.1999999999999998e25 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.1%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+25} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+42} \lor \neg \left(y \leq 7.2 \cdot 10^{+81}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e+42) (not (<= y 7.2e+81))) (* z (* x y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e+42) || !(y <= 7.2e+81)) {
		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 <= (-2.2d+42)) .or. (.not. (y <= 7.2d+81))) 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 <= -2.2e+42) || !(y <= 7.2e+81)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e+42) or not (y <= 7.2e+81):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.2e+42) || !(y <= 7.2e+81))
		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 <= -2.2e+42) || ~((y <= 7.2e+81)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.2e+42], N[Not[LessEqual[y, 7.2e+81]], $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 < -2.2000000000000001e42 or 7.20000000000000011e81 < y

   1. Initial program 87.6%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*l* 73.7%

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

   5. Simplified 73.7%

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

   if -2.2000000000000001e42 < y < 7.20000000000000011e81

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 94.2%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+42} \lor \neg \left(y \leq 7.2 \cdot 10^{+81}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+42}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e+42)
   (* (+ y -1.0) (* x z))
   (if (<= y 7.3e+81) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+42) {
		tmp = (y + -1.0) * (x * z);
	} else if (y <= 7.3e+81) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * 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 <= (-5d+42)) then
        tmp = (y + (-1.0d0)) * (x * z)
    else if (y <= 7.3d+81) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+42) {
		tmp = (y + -1.0) * (x * z);
	} else if (y <= 7.3e+81) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e+42:
		tmp = (y + -1.0) * (x * z)
	elif y <= 7.3e+81:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e+42)
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	elseif (y <= 7.3e+81)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e+42)
		tmp = (y + -1.0) * (x * z);
	elseif (y <= 7.3e+81)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e+42], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.3e+81], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000007e42

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 71.7%

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

      1. associate-*r* 78.5%

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

      2. *-commutative 78.5%

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

      3. sub-neg 78.5%

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

      4. metadata-eval 78.5%

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

   5. Simplified 78.5%

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

   if -5.00000000000000007e42 < y < 7.2999999999999997e81

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 94.2%

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

   if 7.2999999999999997e81 < y

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

      3. associate-*l* 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+42}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00034 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.00034) (not (<= z 1.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00034) || !(z <= 1.0)) {
		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 <= (-0.00034d0)) .or. (.not. (z <= 1.0d0))) 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 <= -0.00034) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.00034) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.00034) || !(z <= 1.0))
		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 <= -0.00034) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.00034], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e-4 or 1 < z

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 62.9%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. neg-mul-1 61.0%

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

   6. Simplified 61.0%

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

   if -3.4e-4 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 74.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00034 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

3. Taylor expanded in y around 0 69.4%

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

Alternative 10: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 94.8%

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

3. Taylor expanded in z around 0 40.5%

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

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

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