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

Percentage Accurate: 96.1% → 98.8%

Time: 9.1s

Alternatives: 10

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x (+ y -1.0)))))
   (if (<= z -1.1) t_0 (if (<= z 1.0) (* x (+ 1.0 (* y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * (y + -1.0));
	double tmp;
	if (z <= -1.1) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * 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 <= (-1.1d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (y * 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 <= -1.1) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * (y + -1.0))
	tmp = 0
	if z <= -1.1:
		tmp = t_0
	elif z <= 1.0:
		tmp = x * (1.0 + (y * 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 <= -1.1)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(y * 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 <= -1.1)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x * (1.0 + (y * 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, -1.1], t$95$0, If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 1 < z

   1. Initial program 90.7%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 90.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 90.7%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(x \cdot \left(1 - y\right)\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(x \cdot \left(1 - y\right)\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \left(-1 \cdot \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(1 - y\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      12. associate--r- N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(\left(0 - 1\right) + \color{blue}{y}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(-1 + y\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right)\right) \]

      15. +-lowering-+.f64 98.9%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   7. Simplified 98.9%

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

   if -1.1000000000000001 < z < 1

   1. Initial program 99.9%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 99.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(z \cdot \left(1 - y\right)\right) \cdot x\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(z \cdot \frac{1 \cdot 1 - y \cdot y}{1 + y}\right) \cdot x\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(z \cdot \frac{1 - y \cdot y}{1 + y}\right) \cdot x\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y} \cdot x\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \color{blue}{\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \frac{1}{\color{blue}{\frac{1 + y}{z \cdot \left(1 - y \cdot y\right)}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{x}{\color{blue}{\frac{1 + y}{z \cdot \left(1 - y \cdot y\right)}}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 + y}{z \cdot \left(1 - y \cdot y\right)}\right)}\right)\right) \]

      9. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y}}}\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y}\right)}\right)\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(z \cdot \color{blue}{\frac{1 - y \cdot y}{1 + y}}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(z \cdot \frac{1 \cdot 1 - y \cdot y}{1 + y}\right)\right)\right)\right) \]

      13. flip-- N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(z \cdot \left(1 - \color{blue}{y}\right)\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(1 - y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\left(1 - y\right), \color{blue}{z}\right)\right)\right)\right) \]

      16. --lowering--.f64 100.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right)\right)\right)\right) \]

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{-1}{y \cdot z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\frac{-1}{z}}{\color{blue}{y}}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\frac{\mathsf{neg}\left(1\right)}{z}}{y}\right)\right)\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(\frac{1}{z}\right)}{y}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{1}{z}\right)\right), \color{blue}{y}\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(1\right)}{z}\right), y\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-1}{z}\right), y\right)\right)\right) \]

      7. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(-1, z\right), y\right)\right)\right) \]

   9. Simplified 99.8%

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

       1. sub-neg N/A

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

       2. +-commutative N/A

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

       3. distribute-neg-frac N/A

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

       4. associate-/l/ N/A

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

       5. associate-/r/ N/A

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

       6. metadata-eval N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(1\right)} \cdot \left(y \cdot z\right) + x \]

       7. frac-2neg N/A

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

       8. /-rgt-identity N/A

          \[\leadsto x \cdot \left(y \cdot z\right) + x \]

       9. *-rgt-identity N/A

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

       10. distribute-lft-out N/A

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

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z + 1\right)}\right) \]

       12. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{1}\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot y\right), 1\right)\right) \]

       14. *-lowering-*.f64 99.8%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, y\right), 1\right)\right) \]

   11. Applied egg-rr 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + y \cdot z\right)\\ \mathbf{if}\;y \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* y z)))))
   (if (<= y -1000000.0) t_0 (if (<= y 2e-22) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (y * z));
	double tmp;
	if (y <= -1000000.0) {
		tmp = t_0;
	} else if (y <= 2e-22) {
		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 = x * (1.0d0 + (y * z))
    if (y <= (-1000000.0d0)) then
        tmp = t_0
    else if (y <= 2d-22) 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 = x * (1.0 + (y * z));
	double tmp;
	if (y <= -1000000.0) {
		tmp = t_0;
	} else if (y <= 2e-22) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (y * z))
	tmp = 0
	if y <= -1000000.0:
		tmp = t_0
	elif y <= 2e-22:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(y * z)))
	tmp = 0.0
	if (y <= -1000000.0)
		tmp = t_0;
	elseif (y <= 2e-22)
		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 = x * (1.0 + (y * z));
	tmp = 0.0;
	if (y <= -1000000.0)
		tmp = t_0;
	elseif (y <= 2e-22)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1000000.0], t$95$0, If[LessEqual[y, 2e-22], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1e6 or 2.0000000000000001e-22 < y

   1. Initial program 90.7%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 90.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 90.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(z \cdot \left(1 - y\right)\right) \cdot x\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(z \cdot \frac{1 \cdot 1 - y \cdot y}{1 + y}\right) \cdot x\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(z \cdot \frac{1 - y \cdot y}{1 + y}\right) \cdot x\right)\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y} \cdot x\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \color{blue}{\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y}}\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \frac{1}{\color{blue}{\frac{1 + y}{z \cdot \left(1 - y \cdot y\right)}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{x}{\color{blue}{\frac{1 + y}{z \cdot \left(1 - y \cdot y\right)}}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 + y}{z \cdot \left(1 - y \cdot y\right)}\right)}\right)\right) \]

      9. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y}}}\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{z \cdot \left(1 - y \cdot y\right)}{1 + y}\right)}\right)\right)\right) \]

      11. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(z \cdot \color{blue}{\frac{1 - y \cdot y}{1 + y}}\right)\right)\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(z \cdot \frac{1 \cdot 1 - y \cdot y}{1 + y}\right)\right)\right)\right) \]

      13. flip-- N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(z \cdot \left(1 - \color{blue}{y}\right)\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(1 - y\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\left(1 - y\right), \color{blue}{z}\right)\right)\right)\right) \]

      16. --lowering--.f64 90.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right)\right)\right)\right) \]

   6. Applied egg-rr 90.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{-1}{y \cdot z}\right)}\right)\right) \]
   8. Step-by-step derivation

      1. associate-/l/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\frac{-1}{z}}{\color{blue}{y}}\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\frac{\mathsf{neg}\left(1\right)}{z}}{y}\right)\right)\right) \]

      3. distribute-neg-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \left(\frac{\mathsf{neg}\left(\frac{1}{z}\right)}{y}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{1}{z}\right)\right), \color{blue}{y}\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{\mathsf{neg}\left(1\right)}{z}\right), y\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-1}{z}\right), y\right)\right)\right) \]

      7. /-lowering-/.f64 91.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(-1, z\right), y\right)\right)\right) \]

   9. Simplified 91.6%

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

       1. sub-neg N/A

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

       2. +-commutative N/A

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

       3. distribute-neg-frac N/A

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

       4. associate-/l/ N/A

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

       5. associate-/r/ N/A

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

       6. metadata-eval N/A

          \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\mathsf{neg}\left(1\right)} \cdot \left(y \cdot z\right) + x \]

       7. frac-2neg N/A

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

       8. /-rgt-identity N/A

          \[\leadsto x \cdot \left(y \cdot z\right) + x \]

       9. *-rgt-identity N/A

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

       10. distribute-lft-out N/A

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

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z + 1\right)}\right) \]

       12. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{1}\right)\right) \]

       13. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(z \cdot y\right), 1\right)\right) \]

       14. *-lowering-*.f64 89.7%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, y\right), 1\right)\right) \]

   11. Applied egg-rr 89.7%

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

   if -1e6 < y < 2.0000000000000001e-22

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 100.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1000000:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e+146)
   (* z (* x y))
   (if (<= y 1.1e+14) (* x (- 1.0 z)) (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+146) {
		tmp = z * (x * y);
	} else if (y <= 1.1e+14) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (x * 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 <= (-6.8d+146)) then
        tmp = z * (x * y)
    else if (y <= 1.1d+14) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+146) {
		tmp = z * (x * y);
	} else if (y <= 1.1e+14) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e+146:
		tmp = z * (x * y)
	elif y <= 1.1e+14:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e+146)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1.1e+14)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e+146)
		tmp = z * (x * y);
	elseif (y <= 1.1e+14)
		tmp = x * (1.0 - z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e+146], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+14], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999981e146

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 68.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 68.4%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot x\right), \color{blue}{z}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), z\right) \]

      6. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 85.9%

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

   if -6.79999999999999981e146 < y < 1.1e14

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 93.2%

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

   if 1.1e14 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 75.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(z \cdot x\right) \cdot y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot x\right), \color{blue}{y}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot z\right), y\right) \]

      5. *-lowering-*.f64 79.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Applied egg-rr 79.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1600000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))))
   (if (<= y -4.5e+146) t_0 (if (<= y 1600000000000.0) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -4.5e+146) {
		tmp = t_0;
	} else if (y <= 1600000000000.0) {
		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)
    if (y <= (-4.5d+146)) then
        tmp = t_0
    else if (y <= 1600000000000.0d0) 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);
	double tmp;
	if (y <= -4.5e+146) {
		tmp = t_0;
	} else if (y <= 1600000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * y)
	tmp = 0
	if y <= -4.5e+146:
		tmp = t_0
	elif y <= 1600000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -4.5e+146)
		tmp = t_0;
	elseif (y <= 1600000000000.0)
		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);
	tmp = 0.0;
	if (y <= -4.5e+146)
		tmp = t_0;
	elseif (y <= 1600000000000.0)
		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 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+146], t$95$0, If[LessEqual[y, 1600000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000026e146 or 1.6e12 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 73.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot x\right), \color{blue}{z}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot y\right), z\right) \]

      6. *-lowering-*.f64 81.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 81.3%

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

   if -4.50000000000000026e146 < y < 1.6e12

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 93.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1600000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2000000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= y -4.4e+146) t_0 (if (<= y 2000000000000.0) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -4.4e+146) {
		tmp = t_0;
	} else if (y <= 2000000000000.0) {
		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 = x * (y * z)
    if (y <= (-4.4d+146)) then
        tmp = t_0
    else if (y <= 2000000000000.0d0) 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 = x * (y * z);
	double tmp;
	if (y <= -4.4e+146) {
		tmp = t_0;
	} else if (y <= 2000000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if y <= -4.4e+146:
		tmp = t_0
	elif y <= 2000000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -4.4e+146)
		tmp = t_0;
	elseif (y <= 2000000000000.0)
		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 = x * (y * z);
	tmp = 0.0;
	if (y <= -4.4e+146)
		tmp = t_0;
	elseif (y <= 2000000000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+146], t$95$0, If[LessEqual[y, 2000000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999996e146 or 2e12 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 73.2%

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

   if -4.3999999999999996e146 < y < 2e12

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 93.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 2000000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= z -1.4e-16) t_0 (if (<= z 1.8e-7) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (z <= -1.4e-16) {
		tmp = t_0;
	} else if (z <= 1.8e-7) {
		tmp = x;
	} 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 = x * (y * z)
    if (z <= (-1.4d-16)) then
        tmp = t_0
    else if (z <= 1.8d-7) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (z <= -1.4e-16) {
		tmp = t_0;
	} else if (z <= 1.8e-7) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if z <= -1.4e-16:
		tmp = t_0
	elif z <= 1.8e-7:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.4e-16)
		tmp = t_0;
	elseif (z <= 1.8e-7)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.4e-16)
		tmp = t_0;
	elseif (z <= 1.8e-7)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-16], t$95$0, If[LessEqual[z, 1.8e-7], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e-16 or 1.79999999999999997e-7 < z

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 47.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 47.5%

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

   if -1.4000000000000001e-16 < z < 1.79999999999999997e-7

   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

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 82.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -106:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -106.0) (* z (* x (+ y -1.0))) (+ x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -106.0) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * (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 <= (-106.0d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x + (x * (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -106.0) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -106.0:
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x + (x * (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -106.0)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -106.0)
		tmp = z * (x * (y + -1.0));
	else
		tmp = x + (x * (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -106.0], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -106

   1. Initial program 87.6%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 87.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(x \cdot \left(1 - y\right)\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(x \cdot \left(1 - y\right)\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \left(-1 \cdot \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(1 - y\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      12. associate--r- N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(\left(0 - 1\right) + \color{blue}{y}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(-1 + y\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right)\right) \]

      15. +-lowering-+.f64 99.0%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   7. Simplified 99.0%

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

   if -106 < z

   1. Initial program 98.4%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 98.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 98.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -106:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -106:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -106.0) (* z (* x (+ y -1.0))) (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -106.0) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * (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 <= (-106.0d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -106.0) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -106.0:
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -106.0)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -106.0)
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -106.0], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $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 z < -106

   1. Initial program 87.6%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

         \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

      10. --lowering--.f64 87.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(x \cdot \left(1 - y\right)\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(x \cdot \left(1 - y\right)\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \left(-1 \cdot \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(1 - y\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\left(1 - y\right)}\right)\right)\right) \]

      12. associate--r- N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(\left(0 - 1\right) + \color{blue}{y}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(-1 + y\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(y + \color{blue}{-1}\right)\right)\right) \]

      15. +-lowering-+.f64 99.0%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   7. Simplified 99.0%

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

   if -106 < z

   1. Initial program 98.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -106:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((x * z) * (y + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. fma-define N/A

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

   4. distribute-lft-neg-out N/A

      \[\leadsto \mathsf{fma}\left(1, x, \mathsf{neg}\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)\right) \]

   5. fmm-undef N/A

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

   6. *-lft-identity N/A

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

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\left(1 - y\right) \cdot z\right), \color{blue}{x}\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(1 - y\right), z\right), x\right)\right) \]

   10. --lowering--.f64 95.6%

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), z\right), x\right)\right) \]

4. Applied egg-rr 95.6%

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

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(\left(1 - y\right) \cdot z\right) \cdot x\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(1 - y\right) \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(1 - y\right), \color{blue}{\left(z \cdot x\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), \left(\color{blue}{z} \cdot x\right)\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), \left(x \cdot \color{blue}{z}\right)\right)\right) \]

   6. *-lowering-*.f64 98.7%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, y\right), \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

6. Applied egg-rr 98.7%

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

7. Final simplification 98.7%

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

Alternative 10: 38.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 44.3%

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

Developer Target 1: 99.8% 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 2024138 
(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))))