Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.8%

Time: 13.6s

Alternatives: 16

Speedup: 1.2×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + \left(y - x\right) \cdot 4\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (+ (* -6.0 (* z (- y x))) (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

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 + (((-6.0d0) * (z * (y - x))) + ((y - x) * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

Python

def code(x, y, z):
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(-6.0 * Float64(z * Float64(y - x))) + Float64(Float64(y - x) * 4.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 99.8%

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]

6. Final simplification 99.8%

   \[\leadsto x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + \left(y - x\right) \cdot 4\right) \]
7. Add Preprocessing

Alternative 2: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-13)
   (+ x (* -6.0 (* x (- 0.6666666666666666 z))))
   (if (<= z 2.2e-5)
     (+ (* y 4.0) (* x -3.0))
     (if (<= z 7.7e+161) (* y (+ 4.0 (* -6.0 z))) (- x (* z (* x -6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x + (-6.0 * (x * (0.6666666666666666 - z)));
	} else if (z <= 2.2e-5) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 7.7e+161) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x - (z * (x * -6.0));
	}
	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 <= (-7.5d-13)) then
        tmp = x + ((-6.0d0) * (x * (0.6666666666666666d0 - z)))
    else if (z <= 2.2d-5) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else if (z <= 7.7d+161) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x - (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x + (-6.0 * (x * (0.6666666666666666 - z)));
	} else if (z <= 2.2e-5) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 7.7e+161) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x - (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-13:
		tmp = x + (-6.0 * (x * (0.6666666666666666 - z)))
	elif z <= 2.2e-5:
		tmp = (y * 4.0) + (x * -3.0)
	elif z <= 7.7e+161:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x - (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-13)
		tmp = Float64(x + Float64(-6.0 * Float64(x * Float64(0.6666666666666666 - z))));
	elseif (z <= 2.2e-5)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	elseif (z <= 7.7e+161)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x - Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-13)
		tmp = x + (-6.0 * (x * (0.6666666666666666 - z)));
	elseif (z <= 2.2e-5)
		tmp = (y * 4.0) + (x * -3.0);
	elseif (z <= 7.7e+161)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x - (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-13], N[(x + N[(-6.0 * N[(x * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-5], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.7e+161], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000004e-13

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.0%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -7.5000000000000004e-13 < z < 2.1999999999999999e-5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 99.7%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

       2. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -6 \cdot \left(0.6666666666666666 - z\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

       3. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       4. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       5. distribute-lft-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\left(-6 \cdot \left(-z\right) + -6 \cdot 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       6. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6 \cdot z\right)} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       7. distribute-lft-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6\right) \cdot z} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       8. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{6} \cdot z + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       9. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(6 \cdot z + \color{blue}{-4}\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       10. fma-define 99.8%

           \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\mathsf{fma}\left(6, z, -4\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       11. associate-*r* 99.6%

           \[\leadsto \mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   11. Simplified 99.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

   12. Taylor expanded in z around 0 99.9%

       \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 2.1999999999999999e-5 < z < 7.70000000000000044e161

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if 7.70000000000000044e161 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 0.0%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 99.9%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in y around 0 62.6%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 62.6%

          \[\leadsto x + \color{blue}{\left(-6 \cdot x\right) \cdot \left(0.6666666666666666 - z\right)} \]

       2. *-commutative 62.6%

          \[\leadsto x + \color{blue}{\left(x \cdot -6\right)} \cdot \left(0.6666666666666666 - z\right) \]

   11. Simplified 62.6%

       \[\leadsto x + \color{blue}{\left(x \cdot -6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   12. Taylor expanded in z around inf 62.6%

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

       1. neg-mul-1 62.6%

          \[\leadsto x + \left(x \cdot -6\right) \cdot \color{blue}{\left(-z\right)} \]

   14. Simplified 62.6%

       \[\leadsto x + \left(x \cdot -6\right) \cdot \color{blue}{\left(-z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-13)
   (* x (+ -3.0 (* z 6.0)))
   (if (<= z 4.4e-7)
     (+ (* y 4.0) (* x -3.0))
     (if (<= z 2.25e+162) (* y (+ 4.0 (* -6.0 z))) (- x (* z (* x -6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.4e-7) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 2.25e+162) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x - (z * (x * -6.0));
	}
	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 <= (-7.5d-13)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 4.4d-7) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else if (z <= 2.25d+162) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x - (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.4e-7) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 2.25e+162) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x - (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-13:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 4.4e-7:
		tmp = (y * 4.0) + (x * -3.0)
	elif z <= 2.25e+162:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x - (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-13)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 4.4e-7)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	elseif (z <= 2.25e+162)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x - Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-13)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 4.4e-7)
		tmp = (y * 4.0) + (x * -3.0);
	elseif (z <= 2.25e+162)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x - (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-13], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-7], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+162], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000004e-13

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 62.0%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 62.0%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 62.0%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 62.0%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 62.0%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 62.0%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 62.0%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 62.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 62.0%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 62.0%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 62.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 62.0%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -7.5000000000000004e-13 < z < 4.4000000000000002e-7

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 99.7%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

       2. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -6 \cdot \left(0.6666666666666666 - z\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

       3. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       4. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       5. distribute-lft-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\left(-6 \cdot \left(-z\right) + -6 \cdot 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       6. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6 \cdot z\right)} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       7. distribute-lft-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6\right) \cdot z} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       8. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{6} \cdot z + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       9. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(6 \cdot z + \color{blue}{-4}\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       10. fma-define 99.8%

           \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\mathsf{fma}\left(6, z, -4\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       11. associate-*r* 99.6%

           \[\leadsto \mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   11. Simplified 99.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

   12. Taylor expanded in z around 0 99.9%

       \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 4.4000000000000002e-7 < z < 2.24999999999999986e162

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if 2.24999999999999986e162 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 0.0%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 0.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 99.9%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in y around 0 62.6%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 62.6%

          \[\leadsto x + \color{blue}{\left(-6 \cdot x\right) \cdot \left(0.6666666666666666 - z\right)} \]

       2. *-commutative 62.6%

          \[\leadsto x + \color{blue}{\left(x \cdot -6\right)} \cdot \left(0.6666666666666666 - z\right) \]

   11. Simplified 62.6%

       \[\leadsto x + \color{blue}{\left(x \cdot -6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   12. Taylor expanded in z around inf 62.6%

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

       1. neg-mul-1 62.6%

          \[\leadsto x + \left(x \cdot -6\right) \cdot \color{blue}{\left(-z\right)} \]

   14. Simplified 62.6%

       \[\leadsto x + \left(x \cdot -6\right) \cdot \color{blue}{\left(-z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-13)
   (* x (+ -3.0 (* z 6.0)))
   (if (<= z 2.1e-9)
     (+ (* y 4.0) (* x -3.0))
     (if (<= z 3.6e+163) (* y (+ 4.0 (* -6.0 z))) (+ x (* 6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 2.1e-9) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 3.6e+163) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x + (6.0 * (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 (z <= (-7.5d-13)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 2.1d-9) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else if (z <= 3.6d+163) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x + (6.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 2.1e-9) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 3.6e+163) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x + (6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-13:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 2.1e-9:
		tmp = (y * 4.0) + (x * -3.0)
	elif z <= 3.6e+163:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x + (6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-13)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 2.1e-9)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	elseif (z <= 3.6e+163)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-13)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 2.1e-9)
		tmp = (y * 4.0) + (x * -3.0);
	elseif (z <= 3.6e+163)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x + (6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-13], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-9], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+163], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000004e-13

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 62.0%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 62.0%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 62.0%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 62.0%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 62.0%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 62.0%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 62.0%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 62.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 62.0%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 62.0%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 62.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 62.0%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -7.5000000000000004e-13 < z < 2.10000000000000019e-9

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 99.7%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

       2. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -6 \cdot \left(0.6666666666666666 - z\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

       3. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       4. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       5. distribute-lft-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\left(-6 \cdot \left(-z\right) + -6 \cdot 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       6. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6 \cdot z\right)} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       7. distribute-lft-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6\right) \cdot z} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       8. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{6} \cdot z + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       9. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(6 \cdot z + \color{blue}{-4}\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       10. fma-define 99.8%

           \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\mathsf{fma}\left(6, z, -4\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       11. associate-*r* 99.6%

           \[\leadsto \mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   11. Simplified 99.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

   12. Taylor expanded in z around 0 99.9%

       \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 2.10000000000000019e-9 < z < 3.59999999999999978e163

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if 3.59999999999999978e163 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 62.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(x \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-13)
   (* x (+ -3.0 (* z 6.0)))
   (if (<= z 3e-9)
     (+ x (* (- y x) 4.0))
     (if (<= z 6.5e+161) (* y (+ 4.0 (* -6.0 z))) (+ x (* 6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 3e-9) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 6.5e+161) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x + (6.0 * (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 (z <= (-7.5d-13)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 3d-9) then
        tmp = x + ((y - x) * 4.0d0)
    else if (z <= 6.5d+161) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x + (6.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 3e-9) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 6.5e+161) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x + (6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-13:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 3e-9:
		tmp = x + ((y - x) * 4.0)
	elif z <= 6.5e+161:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x + (6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-13)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 3e-9)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	elseif (z <= 6.5e+161)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-13)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 3e-9)
		tmp = x + ((y - x) * 4.0);
	elseif (z <= 6.5e+161)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x + (6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-13], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-9], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+161], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000004e-13

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 62.0%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 62.0%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 62.0%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 62.0%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 62.0%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 62.0%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 62.0%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 62.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 62.0%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 62.0%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 62.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 62.0%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -7.5000000000000004e-13 < z < 2.99999999999999998e-9

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 2.99999999999999998e-9 < z < 6.5e161

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if 6.5e161 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 62.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(x \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-13)
   (* x (+ -3.0 (* z 6.0)))
   (if (<= z 3.2e-5)
     (+ x (* (- y x) 4.0))
     (if (<= z 2.5e+162) (* y (+ 4.0 (* -6.0 z))) (* 6.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 3.2e-5) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 2.5e+162) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = 6.0 * (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 (z <= (-7.5d-13)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 3.2d-5) then
        tmp = x + ((y - x) * 4.0d0)
    else if (z <= 2.5d+162) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-13) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 3.2e-5) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 2.5e+162) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-13:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 3.2e-5:
		tmp = x + ((y - x) * 4.0)
	elif z <= 2.5e+162:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-13)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 3.2e-5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	elseif (z <= 2.5e+162)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-13)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 3.2e-5)
		tmp = x + ((y - x) * 4.0);
	elseif (z <= 2.5e+162)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-13], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+162], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000004e-13

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 62.0%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 62.0%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 62.0%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 62.0%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 62.0%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 62.0%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 62.0%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 62.0%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 62.0%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 62.0%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 62.0%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 62.0%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 62.0%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 62.0%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 62.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 62.0%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -7.5000000000000004e-13 < z < 3.19999999999999986e-5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.8%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 3.19999999999999986e-5 < z < 2.4999999999999998e162

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.5%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if 2.4999999999999998e162 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 62.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   7. Taylor expanded in z around inf 62.6%

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

      1. *-commutative 62.6%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   9. Simplified 62.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-163}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.8:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -0.5)
     t_0
     (if (<= z 3.8e-163) (* x -3.0) (if (<= z 0.8) (+ x (* y 4.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= 3.8e-163) {
		tmp = x * -3.0;
	} else if (z <= 0.8) {
		tmp = x + (y * 4.0);
	} 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 = 6.0d0 * (x * z)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= 3.8d-163) then
        tmp = x * (-3.0d0)
    else if (z <= 0.8d0) then
        tmp = x + (y * 4.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= 3.8e-163) {
		tmp = x * -3.0;
	} else if (z <= 0.8) {
		tmp = x + (y * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= 3.8e-163:
		tmp = x * -3.0
	elif z <= 0.8:
		tmp = x + (y * 4.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= 3.8e-163)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.8)
		tmp = Float64(x + Float64(y * 4.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= 3.8e-163)
		tmp = x * -3.0;
	elseif (z <= 0.8)
		tmp = x + (y * 4.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, 3.8e-163], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.8], N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.80000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 97.2%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 54.2%

      \[\leadsto x + \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   7. Taylor expanded in z around inf 54.2%

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

      1. *-commutative 54.2%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   9. Simplified 54.2%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]

   if -0.5 < z < 3.8e-163

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.4%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 62.5%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 62.5%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 62.5%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 62.5%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 62.5%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 62.5%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 62.5%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 62.5%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 62.5%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 62.5%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 62.5%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 62.5%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 62.5%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 62.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 62.5%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 62.5%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 62.5%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 62.5%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 62.5%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 62.5%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 62.5%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 62.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 62.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 62.3%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 3.8e-163 < z < 0.80000000000000004

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.2%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.8%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

      2. *-commutative 58.5%

         \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot \left(0.6666666666666666 - z\right) \]

      3. associate-*r* 58.9%

         \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      4. sub-neg 58.9%

         \[\leadsto x + y \cdot \left(6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      5. +-commutative 58.9%

         \[\leadsto x + y \cdot \left(6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}\right) \]

      6. distribute-lft-in 58.9%

         \[\leadsto x + y \cdot \color{blue}{\left(6 \cdot \left(-z\right) + 6 \cdot 0.6666666666666666\right)} \]

      7. neg-mul-1 58.9%

         \[\leadsto x + y \cdot \left(6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot 0.6666666666666666\right) \]

      8. associate-*r* 58.9%

         \[\leadsto x + y \cdot \left(\color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot 0.6666666666666666\right) \]

      9. metadata-eval 58.9%

         \[\leadsto x + y \cdot \left(\color{blue}{-6} \cdot z + 6 \cdot 0.6666666666666666\right) \]

      10. metadata-eval 58.9%

          \[\leadsto x + y \cdot \left(-6 \cdot z + \color{blue}{4}\right) \]

      11. fma-undefine 58.9%

          \[\leadsto x + y \cdot \color{blue}{\mathsf{fma}\left(-6, z, 4\right)} \]

   7. Simplified 58.9%

      \[\leadsto x + \color{blue}{y \cdot \mathsf{fma}\left(-6, z, 4\right)} \]

   8. Taylor expanded in z around 0 56.1%

      \[\leadsto x + y \cdot \color{blue}{4} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-163}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.8:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;x + -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.65) (not (<= z 0.65)))
   (+ x (* -6.0 (* z (- y x))))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.65) || !(z <= 0.65)) {
		tmp = x + (-6.0 * (z * (y - x)));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.65d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = x + ((-6.0d0) * (z * (y - x)))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.65) || !(z <= 0.65)) {
		tmp = x + (-6.0 * (z * (y - x)));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.65) or not (z <= 0.65):
		tmp = x + (-6.0 * (z * (y - x)))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.65) || !(z <= 0.65))
		tmp = Float64(x + Float64(-6.0 * Float64(z * Float64(y - x))));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.65) || ~((z <= 0.65)))
		tmp = x + (-6.0 * (z * (y - x)));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.65], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(x + N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.650000000000000022 or 0.650000000000000022 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 97.2%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.650000000000000022 < z < 0.650000000000000022

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 99.7%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

       2. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -6 \cdot \left(0.6666666666666666 - z\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

       3. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       4. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       5. distribute-lft-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\left(-6 \cdot \left(-z\right) + -6 \cdot 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       6. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6 \cdot z\right)} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       7. distribute-lft-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6\right) \cdot z} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       8. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{6} \cdot z + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       9. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(6 \cdot z + \color{blue}{-4}\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       10. fma-define 99.8%

           \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\mathsf{fma}\left(6, z, -4\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       11. associate-*r* 99.6%

           \[\leadsto \mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   11. Simplified 99.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

   12. Taylor expanded in z around 0 99.0%

       \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;x + -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.65)
   (+ x (* (- y x) (* -6.0 z)))
   (if (<= z 0.52) (+ (* y 4.0) (* x -3.0)) (+ x (* -6.0 (* z (- y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + ((y - x) * (-6.0 * z));
	} else if (z <= 0.52) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + (-6.0 * (z * (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.65d0)) then
        tmp = x + ((y - x) * ((-6.0d0) * z))
    else if (z <= 0.52d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = x + ((-6.0d0) * (z * (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + ((y - x) * (-6.0 * z));
	} else if (z <= 0.52) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = x + (-6.0 * (z * (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.65:
		tmp = x + ((y - x) * (-6.0 * z))
	elif z <= 0.52:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = x + (-6.0 * (z * (y - x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.65)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(-6.0 * z)));
	elseif (z <= 0.52)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(z * Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.65)
		tmp = x + ((y - x) * (-6.0 * z));
	elseif (z <= 0.52)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = x + (-6.0 * (z * (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.65], N[(x + N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 98.2%

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

      1. *-commutative 98.2%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot -6} \]

      2. *-commutative 98.2%

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot z\right)} \cdot -6 \]

      3. associate-*l* 98.2%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z \cdot -6\right)} \]

      4. *-commutative 98.2%

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(-6 \cdot z\right)} \]

   7. Simplified 98.2%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(-6 \cdot z\right)} \]

   if -0.650000000000000022 < z < 0.52000000000000002

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. expm1-log1p-u 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.6666666666666666 - z\right)\right)} \]
   7. Step-by-step derivation

      1. expm1-undefine 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} - 1\right)} \]

      2. sub-neg 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(0.6666666666666666 - z\right)} + \left(-1\right)\right)} \]

      3. log1p-undefine 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(e^{\color{blue}{\log \left(1 + \left(0.6666666666666666 - z\right)\right)}} + \left(-1\right)\right) \]

      4. rem-exp-log 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(1 + \left(0.6666666666666666 - z\right)\right)} + \left(-1\right)\right) \]

      5. associate-+r- 97.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{\left(\left(1 + 0.6666666666666666\right) - z\right)} + \left(-1\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(\color{blue}{1.6666666666666667} - z\right) + \left(-1\right)\right) \]

      7. metadata-eval 98.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\left(1.6666666666666667 - z\right) + \color{blue}{-1}\right) \]

   8. Simplified 98.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\left(1.6666666666666667 - z\right) + -1\right)} \]

   9. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative 99.7%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

       2. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -6 \cdot \left(0.6666666666666666 - z\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

       3. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       4. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + -6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       5. distribute-lft-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\left(-6 \cdot \left(-z\right) + -6 \cdot 0.6666666666666666\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       6. distribute-rgt-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6 \cdot z\right)} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       7. distribute-lft-neg-in 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{\left(--6\right) \cdot z} + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       8. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(\color{blue}{6} \cdot z + -6 \cdot 0.6666666666666666\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       9. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(x, 1 + \left(6 \cdot z + \color{blue}{-4}\right), 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       10. fma-define 99.8%

           \[\leadsto \mathsf{fma}\left(x, 1 + \color{blue}{\mathsf{fma}\left(6, z, -4\right)}, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

       11. associate-*r* 99.6%

           \[\leadsto \mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   11. Simplified 99.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + \mathsf{fma}\left(6, z, -4\right), \left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

   12. Taylor expanded in z around 0 99.0%

       \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.52000000000000002 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 96.1%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-64} \lor \neg \left(x \leq 1.2 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.5e-64) (not (<= x 1.2e-76)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e-64) || !(x <= 1.2e-76)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (-6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7.5d-64)) .or. (.not. (x <= 1.2d-76))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.5e-64) || !(x <= 1.2e-76)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (-6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.5e-64) or not (x <= 1.2e-76):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (-6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.5e-64) || !(x <= 1.2e-76))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.5e-64) || ~((x <= 1.2e-76)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (-6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.5e-64], N[Not[LessEqual[x, 1.2e-76]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999949e-64 or 1.20000000000000007e-76 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 75.2%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 75.2%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 75.2%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 75.2%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 75.2%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 75.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 75.2%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 75.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 75.2%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 75.2%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 75.2%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 75.2%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 75.2%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 75.2%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 75.2%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 75.2%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 75.2%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 75.2%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 75.2%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 75.2%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 75.2%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 75.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -7.49999999999999949e-64 < x < 1.20000000000000007e-76

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.3%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-64} \lor \neg \left(x \leq 1.2 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-70} \lor \neg \left(x \leq 3.7 \cdot 10^{-154}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-70) (not (<= x 3.7e-154)))
   (* x (+ -3.0 (* z 6.0)))
   (+ x (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-70) || !(x <= 3.7e-154)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = x + (y * 4.0);
	}
	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 ((x <= (-6d-70)) .or. (.not. (x <= 3.7d-154))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = x + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-70) || !(x <= 3.7e-154)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = x + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-70) or not (x <= 3.7e-154):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = x + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-70) || !(x <= 3.7e-154))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(x + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6e-70) || ~((x <= 3.7e-154)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = x + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-70], N[Not[LessEqual[x, 3.7e-154]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000003e-70 or 3.69999999999999987e-154 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.8%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 70.8%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 70.8%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 70.8%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 70.8%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 70.8%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 70.8%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 70.8%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 70.8%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 70.8%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 70.8%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 70.8%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 70.8%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 70.8%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 70.8%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 70.8%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 70.8%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 70.8%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 70.8%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 70.8%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 70.8%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 70.8%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 70.8%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   if -6.0000000000000003e-70 < x < 3.69999999999999987e-154

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.1%

      \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 82.0%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

      2. *-commutative 82.0%

         \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot \left(0.6666666666666666 - z\right) \]

      3. associate-*r* 82.1%

         \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      4. sub-neg 82.1%

         \[\leadsto x + y \cdot \left(6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      5. +-commutative 82.1%

         \[\leadsto x + y \cdot \left(6 \cdot \color{blue}{\left(\left(-z\right) + 0.6666666666666666\right)}\right) \]

      6. distribute-lft-in 82.2%

         \[\leadsto x + y \cdot \color{blue}{\left(6 \cdot \left(-z\right) + 6 \cdot 0.6666666666666666\right)} \]

      7. neg-mul-1 82.2%

         \[\leadsto x + y \cdot \left(6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot 0.6666666666666666\right) \]

      8. associate-*r* 82.2%

         \[\leadsto x + y \cdot \left(\color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot 0.6666666666666666\right) \]

      9. metadata-eval 82.2%

         \[\leadsto x + y \cdot \left(\color{blue}{-6} \cdot z + 6 \cdot 0.6666666666666666\right) \]

      10. metadata-eval 82.2%

          \[\leadsto x + y \cdot \left(-6 \cdot z + \color{blue}{4}\right) \]

      11. fma-undefine 82.2%

          \[\leadsto x + y \cdot \color{blue}{\mathsf{fma}\left(-6, z, 4\right)} \]

   7. Simplified 82.2%

      \[\leadsto x + \color{blue}{y \cdot \mathsf{fma}\left(-6, z, 4\right)} \]

   8. Taylor expanded in z around 0 41.6%

      \[\leadsto x + y \cdot \color{blue}{4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-70} \lor \neg \left(x \leq 3.7 \cdot 10^{-154}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5 \lor \neg \left(z \leq 1.8 \cdot 10^{-16}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.5) (not (<= z 1.8e-16))) (* 6.0 (* x z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.5) || !(z <= 1.8e-16)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.5d0)) .or. (.not. (z <= 1.8d-16))) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.5) || !(z <= 1.8e-16)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.5) or not (z <= 1.8e-16):
		tmp = 6.0 * (x * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.5) || !(z <= 1.8e-16))
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.5) || ~((z <= 1.8e-16)))
		tmp = 6.0 * (x * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.5], N[Not[LessEqual[z, 1.8e-16]], $MachinePrecision]], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.5 or 1.79999999999999991e-16 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 95.9%

      \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   6. Taylor expanded in y around 0 53.6%

      \[\leadsto x + \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   7. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

         \[\leadsto 6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   9. Simplified 53.6%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]

   if -0.5 < z < 1.79999999999999991e-16

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.3%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 57.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-lft-identity 57.2%

         \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

      2. *-commutative 57.2%

         \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

      3. +-commutative 57.2%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

      4. *-commutative 57.2%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

      5. fma-define 57.2%

         \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

      6. associate-*r* 57.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

      7. fma-define 57.2%

         \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

      8. distribute-lft-in 57.2%

         \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

      9. neg-mul-1 57.2%

         \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

      10. distribute-lft-neg-in 57.2%

          \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

      11. metadata-eval 57.2%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

      12. metadata-eval 57.2%

          \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

      13. distribute-rgt-in 57.2%

          \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

      14. +-commutative 57.2%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

      15. sub-neg 57.2%

          \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

      16. distribute-rgt-in 57.2%

          \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      17. sub-neg 57.2%

          \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      18. distribute-rgt-in 57.2%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      19. metadata-eval 57.2%

          \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      20. distribute-lft-neg-in 57.2%

          \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

      21. associate-+r+ 57.2%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

   7. Simplified 57.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

   8. Taylor expanded in z around 0 57.0%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto \color{blue}{x \cdot -3} \]

   10. Simplified 57.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5 \lor \neg \left(z \leq 1.8 \cdot 10^{-16}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(4 + -6 \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) (+ 4.0 (* -6.0 z)))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (-6.0 * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * (4.0d0 + ((-6.0d0) * z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (-6.0 * z)));
}

Python

def code(x, y, z):
	return x + ((y - x) * (4.0 + (-6.0 * z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(4.0 + Float64(-6.0 * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (4.0 + (-6.0 * z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 99.8%

   \[\leadsto x + \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 4 \cdot \left(y - x\right)\right)} \]
6. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto x + \color{blue}{\left(4 \cdot \left(y - x\right) + -6 \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]

   2. associate-*r* 99.8%

      \[\leadsto x + \left(4 \cdot \left(y - x\right) + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)}\right) \]

   3. distribute-rgt-out 99.8%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(4 + -6 \cdot z\right)} \]

7. Applied egg-rr 99.8%

   \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(4 + -6 \cdot z\right)} \]
8. Add Preprocessing

Alternative 14: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- 0.6666666666666666 z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - 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 + (((y - x) * 6.0d0) * (0.6666666666666666d0 - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(0.6666666666666666 - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * (0.6666666666666666 - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 15: 25.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

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 * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. distribute-rgt-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

   8. distribute-lft-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 55.6%

   \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right)} \]
6. Step-by-step derivation

   1. *-lft-identity 55.6%

      \[\leadsto \color{blue}{1 \cdot x} + -1 \cdot \left(x \cdot \left(4 + -6 \cdot z\right)\right) \]

   2. *-commutative 55.6%

      \[\leadsto 1 \cdot x + -1 \cdot \color{blue}{\left(\left(4 + -6 \cdot z\right) \cdot x\right)} \]

   3. +-commutative 55.6%

      \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\left(-6 \cdot z + 4\right)} \cdot x\right) \]

   4. *-commutative 55.6%

      \[\leadsto 1 \cdot x + -1 \cdot \left(\left(\color{blue}{z \cdot -6} + 4\right) \cdot x\right) \]

   5. fma-define 55.5%

      \[\leadsto 1 \cdot x + -1 \cdot \left(\color{blue}{\mathsf{fma}\left(z, -6, 4\right)} \cdot x\right) \]

   6. associate-*r* 55.5%

      \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \mathsf{fma}\left(z, -6, 4\right)\right) \cdot x} \]

   7. fma-define 55.6%

      \[\leadsto 1 \cdot x + \left(-1 \cdot \color{blue}{\left(z \cdot -6 + 4\right)}\right) \cdot x \]

   8. distribute-lft-in 55.6%

      \[\leadsto 1 \cdot x + \color{blue}{\left(-1 \cdot \left(z \cdot -6\right) + -1 \cdot 4\right)} \cdot x \]

   9. neg-mul-1 55.6%

      \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z \cdot -6\right)} + -1 \cdot 4\right) \cdot x \]

   10. distribute-lft-neg-in 55.6%

       \[\leadsto 1 \cdot x + \left(\color{blue}{\left(-z\right) \cdot -6} + -1 \cdot 4\right) \cdot x \]

   11. metadata-eval 55.6%

       \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{-4}\right) \cdot x \]

   12. metadata-eval 55.6%

       \[\leadsto 1 \cdot x + \left(\left(-z\right) \cdot -6 + \color{blue}{0.6666666666666666 \cdot -6}\right) \cdot x \]

   13. distribute-rgt-in 55.6%

       \[\leadsto 1 \cdot x + \color{blue}{\left(-6 \cdot \left(\left(-z\right) + 0.6666666666666666\right)\right)} \cdot x \]

   14. +-commutative 55.6%

       \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \cdot x \]

   15. sub-neg 55.6%

       \[\leadsto 1 \cdot x + \left(-6 \cdot \color{blue}{\left(0.6666666666666666 - z\right)}\right) \cdot x \]

   16. distribute-rgt-in 55.6%

       \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   17. sub-neg 55.6%

       \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

   18. distribute-rgt-in 55.6%

       \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

   19. metadata-eval 55.6%

       \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

   20. distribute-lft-neg-in 55.6%

       \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-z \cdot -6\right)}\right)\right) \]

   21. associate-+r+ 55.6%

       \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + \left(-z \cdot -6\right)\right)} \]

7. Simplified 55.6%

   \[\leadsto \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)} \]

8. Taylor expanded in z around 0 27.6%

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 27.6%

      \[\leadsto \color{blue}{x \cdot -3} \]

10. Simplified 27.6%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 16: 2.6% accurate, 13.0× 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 53.4%

   \[\leadsto x + \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

6. Taylor expanded in z around 0 2.5%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))