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

Percentage Accurate: 95.9% → 99.1%

Time: 9.6s

Alternatives: 14

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: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+289}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{1}{\mathsf{fma}\left(x, y, x\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 -1e+186)
     (* z (* x (+ y -1.0)))
     (if (<= t_0 1e+289)
       (+ x (* x (- (* y z) z)))
       (+ x (/ z (/ 1.0 (fma x y x))))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -1e+186) {
		tmp = z * (x * (y + -1.0));
	} else if (t_0 <= 1e+289) {
		tmp = x + (x * ((y * z) - z));
	} else {
		tmp = x + (z / (1.0 / fma(x, y, x)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= -1e+186)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (t_0 <= 1e+289)
		tmp = Float64(x + Float64(x * Float64(Float64(y * z) - z)));
	else
		tmp = Float64(x + Float64(z / Float64(1.0 / fma(x, y, x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+186], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+289], N[(x + N[(x * N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(1.0 / N[(x * y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -9.9999999999999998e185

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -9.9999999999999998e185 < (*.f64 (-.f64 1 y) z) < 1.0000000000000001e289

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-commutative 99.9%

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

      4. metadata-eval 99.9%

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

      5. neg-mul-1 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. unsub-neg 99.9%

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

   7. Applied egg-rr 99.9%

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

   if 1.0000000000000001e289 < (*.f64 (-.f64 1 y) z)

   1. Initial program 58.5%

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

   3. Taylor expanded in z around 0 58.5%

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

      1. sub-neg 58.5%

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

      2. distribute-rgt-in 58.5%

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

      3. *-commutative 58.5%

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

      4. metadata-eval 58.5%

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

      5. neg-mul-1 58.5%

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

   5. Applied egg-rr 58.5%

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

      1. unsub-neg 58.5%

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

   7. Applied egg-rr 58.5%

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

      1. sub-neg 58.5%

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

      2. distribute-lft-in 39.8%

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

      3. *-commutative 39.8%

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

      4. associate-*r* 80.9%

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

      5. distribute-rgt-neg-in 80.9%

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

      6. distribute-lft-neg-in 80.9%

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

      7. distribute-rgt-in 99.6%

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

      8. flip-+ 49.9%

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

      9. associate-*r/ 44.0%

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

      10. add-sqr-sqrt 24.8%

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

      11. sqrt-unprod 44.0%

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

      12. sqr-neg 44.0%

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

      13. sqrt-unprod 19.2%

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

      14. add-sqr-sqrt 44.0%

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

      15. unsub-neg 44.0%

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

   9. Applied egg-rr 50.3%

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

       1. associate-/l* 56.2%

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

       2. unpow2 56.2%

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

       3. associate-/r* 62.3%

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

       4. *-inverses 99.8%

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

   11. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 10^{+289}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{1}{\mathsf{fma}\left(x, y, x\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+169}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+122} \lor \neg \left(z \leq 6.8 \cdot 10^{+212}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -2.1e+169)
     t_0
     (if (<= z -2.25e-48)
       t_1
       (if (<= z 4.6e-82)
         x
         (if (<= z 8e-36)
           t_1
           (if (<= z 1.65e-14)
             x
             (if (or (<= z 1.9e+122) (not (<= z 6.8e+212))) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.1e+169) {
		tmp = t_0;
	} else if (z <= -2.25e-48) {
		tmp = t_1;
	} else if (z <= 4.6e-82) {
		tmp = x;
	} else if (z <= 8e-36) {
		tmp = t_1;
	} else if (z <= 1.65e-14) {
		tmp = x;
	} else if ((z <= 1.9e+122) || !(z <= 6.8e+212)) {
		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 = z * -x
    t_1 = x * (y * z)
    if (z <= (-2.1d+169)) then
        tmp = t_0
    else if (z <= (-2.25d-48)) then
        tmp = t_1
    else if (z <= 4.6d-82) then
        tmp = x
    else if (z <= 8d-36) then
        tmp = t_1
    else if (z <= 1.65d-14) then
        tmp = x
    else if ((z <= 1.9d+122) .or. (.not. (z <= 6.8d+212))) 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 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.1e+169) {
		tmp = t_0;
	} else if (z <= -2.25e-48) {
		tmp = t_1;
	} else if (z <= 4.6e-82) {
		tmp = x;
	} else if (z <= 8e-36) {
		tmp = t_1;
	} else if (z <= 1.65e-14) {
		tmp = x;
	} else if ((z <= 1.9e+122) || !(z <= 6.8e+212)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -2.1e+169:
		tmp = t_0
	elif z <= -2.25e-48:
		tmp = t_1
	elif z <= 4.6e-82:
		tmp = x
	elif z <= 8e-36:
		tmp = t_1
	elif z <= 1.65e-14:
		tmp = x
	elif (z <= 1.9e+122) or not (z <= 6.8e+212):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.1e+169)
		tmp = t_0;
	elseif (z <= -2.25e-48)
		tmp = t_1;
	elseif (z <= 4.6e-82)
		tmp = x;
	elseif (z <= 8e-36)
		tmp = t_1;
	elseif (z <= 1.65e-14)
		tmp = x;
	elseif ((z <= 1.9e+122) || !(z <= 6.8e+212))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.1e+169)
		tmp = t_0;
	elseif (z <= -2.25e-48)
		tmp = t_1;
	elseif (z <= 4.6e-82)
		tmp = x;
	elseif (z <= 8e-36)
		tmp = t_1;
	elseif (z <= 1.65e-14)
		tmp = x;
	elseif ((z <= 1.9e+122) || ~((z <= 6.8e+212)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+169], t$95$0, If[LessEqual[z, -2.25e-48], t$95$1, If[LessEqual[z, 4.6e-82], x, If[LessEqual[z, 8e-36], t$95$1, If[LessEqual[z, 1.65e-14], x, If[Or[LessEqual[z, 1.9e+122], N[Not[LessEqual[z, 6.8e+212]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000001e169 or 1.8999999999999999e122 < z < 6.80000000000000073e212

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 65.8%

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

      1. neg-mul-1 65.8%

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

   8. Simplified 65.8%

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

   if -2.1000000000000001e169 < z < -2.24999999999999994e-48 or 4.59999999999999994e-82 < z < 7.9999999999999995e-36 or 1.6499999999999999e-14 < z < 1.8999999999999999e122 or 6.80000000000000073e212 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 59.6%

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

      1. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   if -2.24999999999999994e-48 < z < 4.59999999999999994e-82 or 7.9999999999999995e-36 < z < 1.6499999999999999e-14

   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 83.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+122} \lor \neg \left(z \leq 6.8 \cdot 10^{+212}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;z \leq -105000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x (+ y -1.0)))))
   (if (<= z -105000.0)
     t_0
     (if (<= z 4.6e-82)
       (- x (* z x))
       (if (<= z 1.2e-35)
         (* x (* y z))
         (if (<= z 2.1) (* x (- 1.0 z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * (y + -1.0));
	double tmp;
	if (z <= -105000.0) {
		tmp = t_0;
	} else if (z <= 4.6e-82) {
		tmp = x - (z * x);
	} else if (z <= 1.2e-35) {
		tmp = x * (y * z);
	} else if (z <= 2.1) {
		tmp = x * (1.0 - z);
	} 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) :: tmp
    t_0 = z * (x * (y + (-1.0d0)))
    if (z <= (-105000.0d0)) then
        tmp = t_0
    else if (z <= 4.6d-82) then
        tmp = x - (z * x)
    else if (z <= 1.2d-35) then
        tmp = x * (y * z)
    else if (z <= 2.1d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * (y + -1.0));
	double tmp;
	if (z <= -105000.0) {
		tmp = t_0;
	} else if (z <= 4.6e-82) {
		tmp = x - (z * x);
	} else if (z <= 1.2e-35) {
		tmp = x * (y * z);
	} else if (z <= 2.1) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * (y + -1.0))
	tmp = 0
	if z <= -105000.0:
		tmp = t_0
	elif z <= 4.6e-82:
		tmp = x - (z * x)
	elif z <= 1.2e-35:
		tmp = x * (y * z)
	elif z <= 2.1:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * Float64(y + -1.0)))
	tmp = 0.0
	if (z <= -105000.0)
		tmp = t_0;
	elseif (z <= 4.6e-82)
		tmp = Float64(x - Float64(z * x));
	elseif (z <= 1.2e-35)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 2.1)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * (y + -1.0));
	tmp = 0.0;
	if (z <= -105000.0)
		tmp = t_0;
	elseif (z <= 4.6e-82)
		tmp = x - (z * x);
	elseif (z <= 1.2e-35)
		tmp = x * (y * z);
	elseif (z <= 2.1)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -105000.0], t$95$0, If[LessEqual[z, 4.6e-82], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-35], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -105000 or 2.10000000000000009 < z

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   if -105000 < z < 4.59999999999999994e-82

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.0%

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

      1. sub-neg 80.0%

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

      2. distribute-rgt-in 80.1%

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

      3. *-un-lft-identity 80.1%

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

   5. Applied egg-rr 80.1%

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

      1. distribute-lft-neg-out 80.1%

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

      2. *-commutative 80.1%

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

      3. unsub-neg 80.1%

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

   7. Applied egg-rr 80.1%

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

   if 4.59999999999999994e-82 < z < 1.2000000000000001e-35

   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 inf 87.8%

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

      1. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   if 1.2000000000000001e-35 < z < 2.10000000000000009

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105000:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-89}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.112:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -105000.0)
   (* z (- (* y x) x))
   (if (<= z 8e-89)
     (- x (* z x))
     (if (<= z 9.8e-36)
       (* x (* y z))
       (if (<= z 0.112) (* x (- 1.0 z)) (* z (* x (+ y -1.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -105000.0) {
		tmp = z * ((y * x) - x);
	} else if (z <= 8e-89) {
		tmp = x - (z * x);
	} else if (z <= 9.8e-36) {
		tmp = x * (y * z);
	} else if (z <= 0.112) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-105000.0d0)) then
        tmp = z * ((y * x) - x)
    else if (z <= 8d-89) then
        tmp = x - (z * x)
    else if (z <= 9.8d-36) then
        tmp = x * (y * z)
    else if (z <= 0.112d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -105000.0) {
		tmp = z * ((y * x) - x);
	} else if (z <= 8e-89) {
		tmp = x - (z * x);
	} else if (z <= 9.8e-36) {
		tmp = x * (y * z);
	} else if (z <= 0.112) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -105000.0:
		tmp = z * ((y * x) - x)
	elif z <= 8e-89:
		tmp = x - (z * x)
	elif z <= 9.8e-36:
		tmp = x * (y * z)
	elif z <= 0.112:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -105000.0)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 8e-89)
		tmp = Float64(x - Float64(z * x));
	elseif (z <= 9.8e-36)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 0.112)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -105000.0)
		tmp = z * ((y * x) - x);
	elseif (z <= 8e-89)
		tmp = x - (z * x);
	elseif (z <= 9.8e-36)
		tmp = x * (y * z);
	elseif (z <= 0.112)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -105000.0], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-89], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-36], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.112], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -105000

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. *-commutative 99.9%

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

      3. mul-1-neg 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around 0 99.9%

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

   if -105000 < z < 8.00000000000000031e-89

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.0%

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

      1. sub-neg 80.0%

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

      2. distribute-rgt-in 80.1%

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

      3. *-un-lft-identity 80.1%

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

   5. Applied egg-rr 80.1%

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

      1. distribute-lft-neg-out 80.1%

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

      2. *-commutative 80.1%

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

      3. unsub-neg 80.1%

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

   7. Applied egg-rr 80.1%

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

   if 8.00000000000000031e-89 < z < 9.7999999999999994e-36

   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 inf 87.8%

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

      1. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   if 9.7999999999999994e-36 < z < 0.112000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 77.8%

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

   if 0.112000000000000002 < z

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot \left(y + -1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105000:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-89}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.112:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+186} \lor \neg \left(t\_0 \leq 5 \cdot 10^{+201}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (or (<= t_0 -1e+186) (not (<= t_0 5e+201)))
     (* z (* x (+ y -1.0)))
     (+ x (* x (- (* y z) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if ((t_0 <= -1e+186) || !(t_0 <= 5e+201)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * ((y * z) - 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) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - y) * z
    if ((t_0 <= (-1d+186)) .or. (.not. (t_0 <= 5d+201))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x + (x * ((y * z) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if ((t_0 <= -1e+186) || !(t_0 <= 5e+201)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * ((y * z) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if (t_0 <= -1e+186) or not (t_0 <= 5e+201):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x + (x * ((y * z) - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if ((t_0 <= -1e+186) || !(t_0 <= 5e+201))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x + Float64(x * Float64(Float64(y * z) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if ((t_0 <= -1e+186) || ~((t_0 <= 5e+201)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x + (x * ((y * z) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+186], N[Not[LessEqual[t$95$0, 5e+201]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -9.9999999999999998e185 or 4.9999999999999995e201 < (*.f64 (-.f64 1 y) z)

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   if -9.9999999999999998e185 < (*.f64 (-.f64 1 y) z) < 4.9999999999999995e201

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-commutative 100.0%

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

      4. metadata-eval 100.0%

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

      5. neg-mul-1 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. unsub-neg 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+186} \lor \neg \left(\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+201}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 10^{+77}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e+25)
   (* z (- (* y x) x))
   (if (<= z 1e+77) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+25) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1e+77) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1d+25)) then
        tmp = z * ((y * x) - x)
    else if (z <= 1d+77) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+25) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1e+77) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e+25:
		tmp = z * ((y * x) - x)
	elif z <= 1e+77:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+25)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 1e+77)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e+25)
		tmp = z * ((y * x) - x);
	elseif (z <= 1e+77)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+25], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+77], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000009e25

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. *-commutative 99.9%

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

      3. mul-1-neg 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around 0 99.9%

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

   if -1.00000000000000009e25 < z < 9.99999999999999983e76

   1. Initial program 99.9%

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

   if 9.99999999999999983e76 < z

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 10^{+77}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 10^{+77}:\\ \;\;\;\;x - \left(\left(1 - y\right) \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+29)
   (* z (- (* y x) x))
   (if (<= z 1e+77) (- x (* (* (- 1.0 y) z) x)) (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+29) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1e+77) {
		tmp = x - (((1.0 - y) * z) * x);
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5d+29)) then
        tmp = z * ((y * x) - x)
    else if (z <= 1d+77) then
        tmp = x - (((1.0d0 - y) * z) * x)
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+29) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1e+77) {
		tmp = x - (((1.0 - y) * z) * x);
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+29:
		tmp = z * ((y * x) - x)
	elif z <= 1e+77:
		tmp = x - (((1.0 - y) * z) * x)
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+29)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 1e+77)
		tmp = Float64(x - Float64(Float64(Float64(1.0 - y) * z) * x));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+29)
		tmp = z * ((y * x) - x);
	elseif (z <= 1e+77)
		tmp = x - (((1.0 - y) * z) * x);
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+29], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+77], N[(x - N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000001e29

   1. Initial program 91.9%

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

   3. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. *-commutative 99.9%

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

      3. mul-1-neg 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around 0 99.9%

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

   if -5.0000000000000001e29 < z < 9.99999999999999983e76

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

   if 9.99999999999999983e76 < z

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 10^{+77}:\\ \;\;\;\;x - \left(\left(1 - y\right) \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 7400000:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.98)
   (* z (- (* y x) x))
   (if (<= z 7400000.0) (+ x (* x (* y z))) (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.98) {
		tmp = z * ((y * x) - x);
	} else if (z <= 7400000.0) {
		tmp = x + (x * (y * z));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.98d0)) then
        tmp = z * ((y * x) - x)
    else if (z <= 7400000.0d0) then
        tmp = x + (x * (y * z))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.98) {
		tmp = z * ((y * x) - x);
	} else if (z <= 7400000.0) {
		tmp = x + (x * (y * z));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.98:
		tmp = z * ((y * x) - x)
	elif z <= 7400000.0:
		tmp = x + (x * (y * z))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.98)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 7400000.0)
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.98)
		tmp = z * ((y * x) - x);
	elseif (z <= 7400000.0)
		tmp = x + (x * (y * z));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.98], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7400000.0], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.97999999999999998

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-*l* 98.1%

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

      3. *-commutative 98.1%

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

      4. sub-neg 98.1%

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

      5. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

      1. distribute-lft-in 98.2%

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

      2. *-commutative 98.2%

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

      3. mul-1-neg 98.2%

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

   7. Applied egg-rr 98.2%

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

   8. Taylor expanded in z around 0 98.2%

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

   if -0.97999999999999998 < z < 7.4e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around inf 97.3%

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

      1. *-commutative 97.3%

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

   6. Simplified 97.3%

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

   if 7.4e6 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 7400000:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.45 \cdot 10^{+42} \lor \neg \left(y \leq 1550000\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.45e+42) (not (<= y 1550000.0)))
   (* x (* y z))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.45e+42) || !(y <= 1550000.0)) {
		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 <= (-4.45d+42)) .or. (.not. (y <= 1550000.0d0))) 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 <= -4.45e+42) || !(y <= 1550000.0)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.45e+42) or not (y <= 1550000.0):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.45e+42) || !(y <= 1550000.0))
		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 <= -4.45e+42) || ~((y <= 1550000.0)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.45e+42], N[Not[LessEqual[y, 1550000.0]], $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 < -4.44999999999999988e42 or 1.55e6 < y

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   if -4.44999999999999988e42 < y < 1.55e6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.45 \cdot 10^{+42} \lor \neg \left(y \leq 1550000\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+42} \lor \neg \left(y \leq 4300\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.12e+42) (not (<= y 4300.0))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.12e+42) || !(y <= 4300.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.12d+42)) .or. (.not. (y <= 4300.0d0))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.12e+42) || !(y <= 4300.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.12e+42) or not (y <= 4300.0):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.12e+42) || !(y <= 4300.0))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.12e+42) || ~((y <= 4300.0)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.12e+42], N[Not[LessEqual[y, 4300.0]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.12e42 or 4300 < y

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*l* 76.4%

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

      3. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if -1.12e42 < y < 4300

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+42} \lor \neg \left(y \leq 4300\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+42} \lor \neg \left(y \leq 31500\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.2e+42) (not (<= y 31500.0))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e+42) || !(y <= 31500.0)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.2d+42)) .or. (.not. (y <= 31500.0d0))) then
        tmp = z * (y * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e+42) || !(y <= 31500.0)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.2e+42) or not (y <= 31500.0):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.2e+42) || !(y <= 31500.0))
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.2e+42) || ~((y <= 31500.0)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.2e+42], N[Not[LessEqual[y, 31500.0]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1999999999999999e42 or 31500 < y

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. associate-*r* 79.2%

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

      2. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -1.1999999999999999e42 < y < 31500

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+42} \lor \neg \left(y \leq 31500\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+41} \lor \neg \left(y \leq 3850\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e+41) (not (<= y 3850.0))) (* z (* y x)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+41) || !(y <= 3850.0)) {
		tmp = z * (y * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9.5d+41)) .or. (.not. (y <= 3850.0d0))) then
        tmp = z * (y * x)
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+41) || !(y <= 3850.0)) {
		tmp = z * (y * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e+41) or not (y <= 3850.0):
		tmp = z * (y * x)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e+41) || !(y <= 3850.0))
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.5e+41) || ~((y <= 3850.0)))
		tmp = z * (y * x);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.5e+41], N[Not[LessEqual[y, 3850.0]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999996e41 or 3850 < y

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. associate-*r* 79.2%

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

      2. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -9.4999999999999996e41 < y < 3850

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.5%

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

      1. sub-neg 94.5%

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

      2. distribute-rgt-in 94.5%

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

      3. *-un-lft-identity 94.5%

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

   5. Applied egg-rr 94.5%

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

      1. distribute-lft-neg-out 94.5%

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

      2. *-commutative 94.5%

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

      3. unsub-neg 94.5%

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

   7. Applied egg-rr 94.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+41} \lor \neg \left(y \leq 3850\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 7.6\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 7.6))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 7.6)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 7.6d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 7.6)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 7.6):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 7.6))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 7.6)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 7.6]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 7.5999999999999996 < z

   1. Initial program 89.7%

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

   3. Taylor expanded in z around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*l* 98.9%

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

      3. *-commutative 98.9%

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

      4. sub-neg 98.9%

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

      5. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 46.7%

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

      1. neg-mul-1 46.7%

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

   8. Simplified 46.7%

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

   if -1 < z < 7.5999999999999996

   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 72.1%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 7.6\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.5% 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 94.4%

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

3. Taylor expanded in z around 0 34.9%

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

4. Final simplification 34.9%

   \[\leadsto x \]
5. Add Preprocessing

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 2024029 
(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))))