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

Percentage Accurate: 95.8% → 97.8%

Time: 8.7s

Alternatives: 8

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: 95.8% 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: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 66.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 66.4%

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

   5. Simplified 66.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
   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. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 99.9%

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

   7. Applied egg-rr 99.9%

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

      1. remove-double-div N/A

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

      2. div-inv N/A

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

      3. clear-num N/A

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

      4. div-inv N/A

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

      5. associate-/l/ N/A

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

      6. associate-/r* N/A

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

      7. remove-double-div N/A

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

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

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

      9. associate-/l/ N/A

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

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

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

      11. *-lowering-*.f64 100.0%

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

   9. Applied egg-rr 100.0%

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

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

   1. Initial program 98.3%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. fma-define N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. fmm-undef N/A

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

      7. *-rgt-identity N/A

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

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

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

      9. *-lowering-*.f64 98.4%

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

   4. Applied egg-rr 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+172}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -5e+172)
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -5e+172) {
		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 (((1.0d0 - y) * z) <= (-5d+172)) 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 (((1.0 - y) * z) <= -5e+172) {
		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 ((1.0 - y) * z) <= -5e+172:
		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 (Float64(Float64(1.0 - y) * z) <= -5e+172)
		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 (((1.0 - y) * z) <= -5e+172)
		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[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -5e+172], 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 (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -5.0000000000000001e172

   1. Initial program 89.9%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. fma-define N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. fmm-undef N/A

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

      7. *-rgt-identity N/A

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

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

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

      9. *-lowering-*.f64 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. cancel-sign-sub-inv N/A

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

      6. remove-double-neg N/A

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

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

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

      8. distribute-lft-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. distribute-lft-in N/A

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

      12. +-commutative N/A

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

      13. sub-neg N/A

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

      14. associate-*r* N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

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

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

      18. associate-*r* N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. distribute-lft-in N/A

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

      22. mul-1-neg N/A

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

      23. distribute-lft-neg-in N/A

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

      24. distribute-rgt-neg-out N/A

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

      25. remove-double-neg N/A

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

   7. Simplified 99.9%

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

   if -5.0000000000000001e172 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+172}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e+85)
   (* y (* x z))
   (if (<= y 1.3e+57) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+85) {
		tmp = y * (x * z);
	} else if (y <= 1.3e+57) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.6d+85)) then
        tmp = y * (x * z)
    else if (y <= 1.3d+57) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e+85) {
		tmp = y * (x * z);
	} else if (y <= 1.3e+57) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e+85:
		tmp = y * (x * z)
	elif y <= 1.3e+57:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e+85)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.3e+57)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e+85)
		tmp = y * (x * z);
	elseif (y <= 1.3e+57)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e+85], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+57], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5999999999999998e85

   1. Initial program 95.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 75.9%

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

   5. Simplified 75.9%

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

      1. associate-*r* N/A

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

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

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

      3. *-lowering-*.f64 80.4%

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

   7. Applied egg-rr 80.4%

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

   if -3.5999999999999998e85 < y < 1.3e57

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 93.7%

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

   5. Simplified 93.7%

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

   if 1.3e57 < y

   1. Initial program 90.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 82.0%

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

   5. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
   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. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 88.1%

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

   7. Applied egg-rr 88.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+85)
   (* x (* y z))
   (if (<= y 6.5e+56) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+85) {
		tmp = x * (y * z);
	} else if (y <= 6.5e+56) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.35d+85)) then
        tmp = x * (y * z)
    else if (y <= 6.5d+56) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+85) {
		tmp = x * (y * z);
	} else if (y <= 6.5e+56) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+85:
		tmp = x * (y * z)
	elif y <= 6.5e+56:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+85)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 6.5e+56)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+85)
		tmp = x * (y * z);
	elseif (y <= 6.5e+56)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+85], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+56], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.34999999999999992e85

   1. Initial program 95.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 75.9%

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

   5. Simplified 75.9%

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

   if -1.34999999999999992e85 < y < 6.5000000000000001e56

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 93.7%

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

   5. Simplified 93.7%

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

   if 6.5000000000000001e56 < y

   1. Initial program 90.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 82.0%

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

   5. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
   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. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 88.1%

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

   7. Applied egg-rr 88.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+85}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= y -4.4e+85) t_0 (if (<= y 6.5e+56) (* 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+85) {
		tmp = t_0;
	} else if (y <= 6.5e+56) {
		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+85)) then
        tmp = t_0
    else if (y <= 6.5d+56) 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+85) {
		tmp = t_0;
	} else if (y <= 6.5e+56) {
		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+85:
		tmp = t_0
	elif y <= 6.5e+56:
		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+85)
		tmp = t_0;
	elseif (y <= 6.5e+56)
		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+85)
		tmp = t_0;
	elseif (y <= 6.5e+56)
		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+85], t$95$0, If[LessEqual[y, 6.5e+56], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4000000000000003e85 or 6.5000000000000001e56 < y

   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

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   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 79.6%

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

   5. Simplified 79.6%

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

   if -4.4000000000000003e85 < y < 6.5000000000000001e56

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= y -2.5e+84) t_0 (if (<= y 6.5e+56) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -2.5e+84) {
		tmp = t_0;
	} else if (y <= 6.5e+56) {
		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 (y <= (-2.5d+84)) then
        tmp = t_0
    else if (y <= 6.5d+56) 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 (y <= -2.5e+84) {
		tmp = t_0;
	} else if (y <= 6.5e+56) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if y <= -2.5e+84:
		tmp = t_0
	elif y <= 6.5e+56:
		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 (y <= -2.5e+84)
		tmp = t_0;
	elseif (y <= 6.5e+56)
		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 (y <= -2.5e+84)
		tmp = t_0;
	elseif (y <= 6.5e+56)
		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[y, -2.5e+84], t$95$0, If[LessEqual[y, 6.5e+56], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e84 or 6.5000000000000001e56 < y

   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

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   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 79.6%

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

   5. Simplified 79.6%

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

   if -2.5e84 < y < 6.5000000000000001e56

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 46.3%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 96.6%

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

   1. *-commutative N/A

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

   2. sub-neg N/A

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

   3. distribute-lft-in N/A

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

   4. fma-define N/A

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

   5. distribute-rgt-neg-out N/A

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

   6. fmm-undef N/A

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

   7. *-rgt-identity N/A

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

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

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

   9. *-lowering-*.f64 96.6%

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

4. Applied egg-rr 96.6%

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

   1. *-commutative N/A

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

   2. sub-neg N/A

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

   3. *-lft-identity N/A

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

   4. *-commutative N/A

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

   5. distribute-lft-neg-in N/A

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

   6. distribute-rgt-in N/A

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

   7. sub-neg N/A

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

   8. *-commutative N/A

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

   9. sub-neg N/A

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

   10. +-commutative N/A

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

   11. distribute-rgt1-in N/A

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

   12. cancel-sign-sub-inv N/A

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

   13. --lowering--.f64 N/A

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

   14. associate-*l* N/A

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

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

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

   16. --lowering--.f64 N/A

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

   17. *-commutative N/A

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

   18. *-lowering-*.f64 97.4%

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

6. Applied egg-rr 97.4%

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

7. Final simplification 97.4%

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

Alternative 8: 38.7% 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 96.6%

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

3. Taylor expanded in z around 0

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

5. Simplified 33.1%

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

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024155 
(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))))