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

Percentage Accurate: 99.5% → 99.8%

Time: 16.2s

Alternatives: 15

Speedup: 1.2×

• 20.8% 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, 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 99.5%

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

   1. +-commutative N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right), \color{blue}{x}\right) \]

   3. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right), x\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

   7. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right), x\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

   11. neg-mul-1 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(6 \cdot \left(-1 \cdot z\right)\right)\right)\right), x\right) \]

   12. associate-*r* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\left(6 \cdot -1\right) \cdot z\right)\right)\right), x\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(-6 \cdot z\right)\right)\right), x\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\left(\mathsf{neg}\left(6\right)\right) \cdot z\right)\right)\right), x\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(6\right)\right), z\right)\right)\right), x\right) \]

   16. metadata-eval 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(-6, z\right)\right)\right), x\right) \]

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 50.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.056:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-149}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.056)
   (* -6.0 (* y z))
   (if (<= z -1.6e-150)
     (* x -3.0)
     (if (<= z 5.4e-149)
       (* y 4.0)
       (if (<= z 0.52)
         (* x -3.0)
         (if (<= z 1.5e+247) (* z (* y -6.0)) (* x (* z 6.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.056) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.6e-150) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-149) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else if (z <= 1.5e+247) {
		tmp = z * (y * -6.0);
	} else {
		tmp = x * (z * 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 <= (-0.056d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-1.6d-150)) then
        tmp = x * (-3.0d0)
    else if (z <= 5.4d-149) then
        tmp = y * 4.0d0
    else if (z <= 0.52d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.5d+247) then
        tmp = z * (y * (-6.0d0))
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.056) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.6e-150) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-149) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else if (z <= 1.5e+247) {
		tmp = z * (y * -6.0);
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.056:
		tmp = -6.0 * (y * z)
	elif z <= -1.6e-150:
		tmp = x * -3.0
	elif z <= 5.4e-149:
		tmp = y * 4.0
	elif z <= 0.52:
		tmp = x * -3.0
	elif z <= 1.5e+247:
		tmp = z * (y * -6.0)
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.056)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -1.6e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.4e-149)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.52)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.5e+247)
		tmp = Float64(z * Float64(y * -6.0));
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.056)
		tmp = -6.0 * (y * z);
	elseif (z <= -1.6e-150)
		tmp = x * -3.0;
	elseif (z <= 5.4e-149)
		tmp = y * 4.0;
	elseif (z <= 0.52)
		tmp = x * -3.0;
	elseif (z <= 1.5e+247)
		tmp = z * (y * -6.0);
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.056], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.4e-149], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.5e+247], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.0560000000000000012

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 94.4%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 94.4%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-6 \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-6, z\right), y\right) \]

   8. Simplified 54.7%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot y\right), \color{blue}{-6}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot z\right), -6\right) \]

      5. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), -6\right) \]

   10. Applied egg-rr 54.7%

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

   if -0.0560000000000000012 < z < -1.5999999999999999e-150 or 5.40000000000000028e-149 < 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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 98.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 61.4%

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

   if -1.5999999999999999e-150 < z < 5.40000000000000028e-149

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if 0.52000000000000002 < z < 1.5e247

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 96.5%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 96.5%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-6 \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-6, z\right), y\right) \]

   8. Simplified 56.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot -6\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, -6\right), z\right) \]

   10. Applied egg-rr 56.9%

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

   if 1.5e247 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

         \[\leadsto x \cdot \left(\left(-1 \cdot -6\right) \cdot z\right) \]

      5. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(-6 \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-1 \cdot -6\right) \cdot \color{blue}{z}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(6 \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{6}\right)\right) \]

      10. *-lowering-*.f64 72.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   8. Simplified 72.7%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot 6\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.056:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-149}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0055:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-153}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-149}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0055)
   (* y (* -6.0 z))
   (if (<= z -1.95e-153)
     (* x -3.0)
     (if (<= z 1.02e-149)
       (* y 4.0)
       (if (<= z 0.52)
         (* x -3.0)
         (if (<= z 1.25e+248) (* z (* y -6.0)) (* x (* z 6.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0055) {
		tmp = y * (-6.0 * z);
	} else if (z <= -1.95e-153) {
		tmp = x * -3.0;
	} else if (z <= 1.02e-149) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else if (z <= 1.25e+248) {
		tmp = z * (y * -6.0);
	} else {
		tmp = x * (z * 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 <= (-0.0055d0)) then
        tmp = y * ((-6.0d0) * z)
    else if (z <= (-1.95d-153)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.02d-149) then
        tmp = y * 4.0d0
    else if (z <= 0.52d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.25d+248) then
        tmp = z * (y * (-6.0d0))
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0055) {
		tmp = y * (-6.0 * z);
	} else if (z <= -1.95e-153) {
		tmp = x * -3.0;
	} else if (z <= 1.02e-149) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else if (z <= 1.25e+248) {
		tmp = z * (y * -6.0);
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0055:
		tmp = y * (-6.0 * z)
	elif z <= -1.95e-153:
		tmp = x * -3.0
	elif z <= 1.02e-149:
		tmp = y * 4.0
	elif z <= 0.52:
		tmp = x * -3.0
	elif z <= 1.25e+248:
		tmp = z * (y * -6.0)
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0055)
		tmp = Float64(y * Float64(-6.0 * z));
	elseif (z <= -1.95e-153)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.02e-149)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.52)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.25e+248)
		tmp = Float64(z * Float64(y * -6.0));
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0055)
		tmp = y * (-6.0 * z);
	elseif (z <= -1.95e-153)
		tmp = x * -3.0;
	elseif (z <= 1.02e-149)
		tmp = y * 4.0;
	elseif (z <= 0.52)
		tmp = x * -3.0;
	elseif (z <= 1.25e+248)
		tmp = z * (y * -6.0);
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0055], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-153], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.02e-149], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.25e+248], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.0054999999999999997

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 94.4%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 94.4%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-6 \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-6, z\right), y\right) \]

   8. Simplified 54.7%

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

   if -0.0054999999999999997 < z < -1.9500000000000001e-153 or 1.0200000000000001e-149 < 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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 98.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 61.4%

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

   if -1.9500000000000001e-153 < z < 1.0200000000000001e-149

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if 0.52000000000000002 < z < 1.2499999999999999e248

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 96.5%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 96.5%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-6 \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-6, z\right), y\right) \]

   8. Simplified 56.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot -6\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 56.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, -6\right), z\right) \]

   10. Applied egg-rr 56.9%

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

   if 1.2499999999999999e248 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

         \[\leadsto x \cdot \left(\left(-1 \cdot -6\right) \cdot z\right) \]

      5. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(-6 \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-1 \cdot -6\right) \cdot \color{blue}{z}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(6 \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{6}\right)\right) \]

      10. *-lowering-*.f64 72.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   8. Simplified 72.7%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot 6\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0055:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-153}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-149}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-6 \cdot z\right)\\ \mathbf{if}\;z \leq -0.32:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-153}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-146}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+249}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* -6.0 z))))
   (if (<= z -0.32)
     t_0
     (if (<= z -9.2e-153)
       (* x -3.0)
       (if (<= z 6.4e-146)
         (* y 4.0)
         (if (<= z 0.58)
           (* x -3.0)
           (if (<= z 3.8e+249) t_0 (* x (* z 6.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (-6.0 * z);
	double tmp;
	if (z <= -0.32) {
		tmp = t_0;
	} else if (z <= -9.2e-153) {
		tmp = x * -3.0;
	} else if (z <= 6.4e-146) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else if (z <= 3.8e+249) {
		tmp = t_0;
	} else {
		tmp = x * (z * 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) :: t_0
    real(8) :: tmp
    t_0 = y * ((-6.0d0) * z)
    if (z <= (-0.32d0)) then
        tmp = t_0
    else if (z <= (-9.2d-153)) then
        tmp = x * (-3.0d0)
    else if (z <= 6.4d-146) then
        tmp = y * 4.0d0
    else if (z <= 0.58d0) then
        tmp = x * (-3.0d0)
    else if (z <= 3.8d+249) then
        tmp = t_0
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (-6.0 * z);
	double tmp;
	if (z <= -0.32) {
		tmp = t_0;
	} else if (z <= -9.2e-153) {
		tmp = x * -3.0;
	} else if (z <= 6.4e-146) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else if (z <= 3.8e+249) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (-6.0 * z)
	tmp = 0
	if z <= -0.32:
		tmp = t_0
	elif z <= -9.2e-153:
		tmp = x * -3.0
	elif z <= 6.4e-146:
		tmp = y * 4.0
	elif z <= 0.58:
		tmp = x * -3.0
	elif z <= 3.8e+249:
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-6.0 * z))
	tmp = 0.0
	if (z <= -0.32)
		tmp = t_0;
	elseif (z <= -9.2e-153)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.4e-146)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.58)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.8e+249)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (-6.0 * z);
	tmp = 0.0;
	if (z <= -0.32)
		tmp = t_0;
	elseif (z <= -9.2e-153)
		tmp = x * -3.0;
	elseif (z <= 6.4e-146)
		tmp = y * 4.0;
	elseif (z <= 0.58)
		tmp = x * -3.0;
	elseif (z <= 3.8e+249)
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.32], t$95$0, If[LessEqual[z, -9.2e-153], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.4e-146], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.8e+249], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.320000000000000007 or 0.57999999999999996 < z < 3.7999999999999997e249

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 95.4%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 95.4%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(-6 \cdot z\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 55.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(-6, z\right), y\right) \]

   8. Simplified 55.8%

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

   if -0.320000000000000007 < z < -9.19999999999999988e-153 or 6.3999999999999998e-146 < z < 0.57999999999999996

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 98.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 61.4%

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

   if -9.19999999999999988e-153 < z < 6.3999999999999998e-146

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if 3.7999999999999997e249 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

         \[\leadsto x \cdot \left(\left(-1 \cdot -6\right) \cdot z\right) \]

      5. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(-6 \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-1 \cdot -6\right) \cdot \color{blue}{z}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(6 \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{6}\right)\right) \]

      10. *-lowering-*.f64 72.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   8. Simplified 72.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.32:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-153}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-146}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+249}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;z \leq -100000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-148}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= z -100000.0)
     (* 6.0 (* z (- x y)))
     (if (<= z -9e-153)
       t_0
       (if (<= z 2.6e-148)
         (* y 4.0)
         (if (<= z 14.5) t_0 (* z (* 6.0 (- x y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -100000.0) {
		tmp = 6.0 * (z * (x - y));
	} else if (z <= -9e-153) {
		tmp = t_0;
	} else if (z <= 2.6e-148) {
		tmp = y * 4.0;
	} else if (z <= 14.5) {
		tmp = t_0;
	} else {
		tmp = z * (6.0 * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (z <= (-100000.0d0)) then
        tmp = 6.0d0 * (z * (x - y))
    else if (z <= (-9d-153)) then
        tmp = t_0
    else if (z <= 2.6d-148) then
        tmp = y * 4.0d0
    else if (z <= 14.5d0) then
        tmp = t_0
    else
        tmp = z * (6.0d0 * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -100000.0) {
		tmp = 6.0 * (z * (x - y));
	} else if (z <= -9e-153) {
		tmp = t_0;
	} else if (z <= 2.6e-148) {
		tmp = y * 4.0;
	} else if (z <= 14.5) {
		tmp = t_0;
	} else {
		tmp = z * (6.0 * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if z <= -100000.0:
		tmp = 6.0 * (z * (x - y))
	elif z <= -9e-153:
		tmp = t_0
	elif z <= 2.6e-148:
		tmp = y * 4.0
	elif z <= 14.5:
		tmp = t_0
	else:
		tmp = z * (6.0 * (x - y))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (z <= -100000.0)
		tmp = Float64(6.0 * Float64(z * Float64(x - y)));
	elseif (z <= -9e-153)
		tmp = t_0;
	elseif (z <= 2.6e-148)
		tmp = Float64(y * 4.0);
	elseif (z <= 14.5)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (z <= -100000.0)
		tmp = 6.0 * (z * (x - y));
	elseif (z <= -9e-153)
		tmp = t_0;
	elseif (z <= 2.6e-148)
		tmp = y * 4.0;
	elseif (z <= 14.5)
		tmp = t_0;
	else
		tmp = z * (6.0 * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -100000.0], N[(6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-153], t$95$0, If[LessEqual[z, 2.6e-148], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 14.5], t$95$0, N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1e5

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 97.3%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 97.3%

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

   if -1e5 < z < -9e-153 or 2.60000000000000008e-148 < z < 14.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \left(\color{blue}{1} + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \left(\mathsf{neg}\left(-1 \cdot x\right)\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot x\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right)\right)} \]

      5. distribute-neg-in N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-6 \cdot \left(\frac{2}{3} - z\right)\right)\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-6 \cdot \left(\frac{2}{3} - z\right)}\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(-6\right)\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + 6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{-1}\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - \color{blue}{1}\right) \]

      12. associate-*r* N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)} \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right) \]

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

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + -1\right)\right)\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6\right)\right) \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right)\right) \]

   5. Simplified 63.4%

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

   if -9e-153 < z < 2.60000000000000008e-148

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if 14.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 98.2%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 98.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(6 \cdot \left(x - y\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(6, \left(x - y\right)\right), z\right) \]

      5. --lowering--.f64 98.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(6, \mathsf{\_.f64}\left(x, y\right)\right), z\right) \]

   7. Applied egg-rr 98.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -100000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-148}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := 6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{if}\;z \leq -215000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-148}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-152}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* 6.0 (* z (- x y)))))
   (if (<= z -215000.0)
     t_1
     (if (<= z -3.8e-148)
       t_0
       (if (<= z 4.2e-152) (* y 4.0) (if (<= z 14.5) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = 6.0 * (z * (x - y));
	double tmp;
	if (z <= -215000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-148) {
		tmp = t_0;
	} else if (z <= 4.2e-152) {
		tmp = y * 4.0;
	} else if (z <= 14.5) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = 6.0d0 * (z * (x - y))
    if (z <= (-215000.0d0)) then
        tmp = t_1
    else if (z <= (-3.8d-148)) then
        tmp = t_0
    else if (z <= 4.2d-152) then
        tmp = y * 4.0d0
    else if (z <= 14.5d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = 6.0 * (z * (x - y));
	double tmp;
	if (z <= -215000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-148) {
		tmp = t_0;
	} else if (z <= 4.2e-152) {
		tmp = y * 4.0;
	} else if (z <= 14.5) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = 6.0 * (z * (x - y))
	tmp = 0
	if z <= -215000.0:
		tmp = t_1
	elif z <= -3.8e-148:
		tmp = t_0
	elif z <= 4.2e-152:
		tmp = y * 4.0
	elif z <= 14.5:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(6.0 * Float64(z * Float64(x - y)))
	tmp = 0.0
	if (z <= -215000.0)
		tmp = t_1;
	elseif (z <= -3.8e-148)
		tmp = t_0;
	elseif (z <= 4.2e-152)
		tmp = Float64(y * 4.0);
	elseif (z <= 14.5)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = 6.0 * (z * (x - y));
	tmp = 0.0;
	if (z <= -215000.0)
		tmp = t_1;
	elseif (z <= -3.8e-148)
		tmp = t_0;
	elseif (z <= 4.2e-152)
		tmp = y * 4.0;
	elseif (z <= 14.5)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -215000.0], t$95$1, If[LessEqual[z, -3.8e-148], t$95$0, If[LessEqual[z, 4.2e-152], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 14.5], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -215000 or 14.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 97.8%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 97.8%

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

   if -215000 < z < -3.80000000000000014e-148 or 4.19999999999999998e-152 < z < 14.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \left(\color{blue}{1} + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \left(\mathsf{neg}\left(-1 \cdot x\right)\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot x\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right)\right)} \]

      5. distribute-neg-in N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-6 \cdot \left(\frac{2}{3} - z\right)\right)\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-6 \cdot \left(\frac{2}{3} - z\right)}\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(-6\right)\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + 6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{-1}\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - \color{blue}{1}\right) \]

      12. associate-*r* N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)} \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right) \]

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

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + -1\right)\right)\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6\right)\right) \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right)\right) \]

   5. Simplified 63.4%

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

   if -3.80000000000000014e-148 < z < 4.19999999999999998e-152

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -215000:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-152}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 14.5:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{if}\;z \leq -0.0145:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-146}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z (- x y)))))
   (if (<= z -0.0145)
     t_0
     (if (<= z -1.52e-149)
       (* x -3.0)
       (if (<= z 9.6e-146) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * (x - y));
	double tmp;
	if (z <= -0.0145) {
		tmp = t_0;
	} else if (z <= -1.52e-149) {
		tmp = x * -3.0;
	} else if (z <= 9.6e-146) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 * (z * (x - y))
    if (z <= (-0.0145d0)) then
        tmp = t_0
    else if (z <= (-1.52d-149)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.6d-146) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 * (z * (x - y));
	double tmp;
	if (z <= -0.0145) {
		tmp = t_0;
	} else if (z <= -1.52e-149) {
		tmp = x * -3.0;
	} else if (z <= 9.6e-146) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * (x - y))
	tmp = 0
	if z <= -0.0145:
		tmp = t_0
	elif z <= -1.52e-149:
		tmp = x * -3.0
	elif z <= 9.6e-146:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * Float64(x - y)))
	tmp = 0.0
	if (z <= -0.0145)
		tmp = t_0;
	elseif (z <= -1.52e-149)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.6e-146)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * (x - y));
	tmp = 0.0;
	if (z <= -0.0145)
		tmp = t_0;
	elseif (z <= -1.52e-149)
		tmp = x * -3.0;
	elseif (z <= 9.6e-146)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0145], t$95$0, If[LessEqual[z, -1.52e-149], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.6e-146], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0145000000000000007 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 95.9%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 95.9%

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

   if -0.0145000000000000007 < z < -1.5199999999999999e-149 or 9.6000000000000006e-146 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 98.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 61.4%

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

   if -1.5199999999999999e-149 < z < 9.6000000000000006e-146

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0145:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-146}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-146}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -0.5)
     t_0
     (if (<= z -1.6e-148)
       (* x -3.0)
       (if (<= z 3.3e-146) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -1.6e-148) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-146) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 = x * (z * 6.0d0)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-1.6d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.3d-146) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -1.6e-148) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-146) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -1.6e-148:
		tmp = x * -3.0
	elif z <= 3.3e-146:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -1.6e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.3e-146)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -1.6e-148)
		tmp = x * -3.0;
	elseif (z <= 3.3e-146)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -1.6e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.3e-146], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 95.9%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 95.9%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

         \[\leadsto x \cdot \left(\left(-1 \cdot -6\right) \cdot z\right) \]

      5. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(-6 \cdot z\right)\right)}\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-1 \cdot -6\right) \cdot \color{blue}{z}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(6 \cdot z\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{6}\right)\right) \]

      10. *-lowering-*.f64 45.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   8. Simplified 45.5%

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

   if -0.5 < z < -1.59999999999999997e-148 or 3.3e-146 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 98.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 61.4%

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

   if -1.59999999999999997e-148 < z < 3.3e-146

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-146}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-155}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -0.5)
     t_0
     (if (<= z -2.45e-151)
       (* x -3.0)
       (if (<= z 2.5e-155) (* y 4.0) (if (<= z 0.5) (* x -3.0) 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 <= -2.45e-151) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-155) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 <= (-2.45d-151)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-155) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 <= -2.45e-151) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-155) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 <= -2.45e-151:
		tmp = x * -3.0
	elif z <= 2.5e-155:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	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 <= -2.45e-151)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-155)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	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 <= -2.45e-151)
		tmp = x * -3.0;
	elseif (z <= 2.5e-155)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	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, -2.45e-151], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-155], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 95.9%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 95.9%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 45.4%

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

   if -0.5 < z < -2.44999999999999983e-151 or 2.4999999999999999e-155 < z < 0.5

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 98.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 98.3%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 61.4%

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

   if -2.44999999999999983e-151 < z < 2.4999999999999999e-155

   1. Initial program 99.2%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 61.3%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-155}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* 6.0 (* z (- x y)))
   (if (<= z 0.65) (+ (* x -3.0) (* y 4.0)) (* z (* 6.0 (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = 6.0 * (z * (x - y));
	} else if (z <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (6.0 * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = 6.0d0 * (z * (x - y))
    else if (z <= 0.65d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * (6.0d0 * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = 6.0 * (z * (x - y));
	} else if (z <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (6.0 * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = 6.0 * (z * (x - y))
	elif z <= 0.65:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * (6.0 * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(6.0 * Float64(z * Float64(x - y)));
	elseif (z <= 0.65)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = 6.0 * (z * (x - y));
	elseif (z <= 0.65)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * (6.0 * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 94.4%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 94.4%

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

   if -0.57999999999999996 < 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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 99.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 99.1%

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

   if 0.650000000000000022 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. metadata-eval N/A

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

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

         \[\leadsto \mathsf{neg}\left(6 \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

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

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

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - x\right)\right)}\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right)\right)\right) \]

      9. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(y + -1 \cdot \color{blue}{x}\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x + \color{blue}{y}\right)\right)\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(-1 \cdot \left(-1 \cdot x\right) + \color{blue}{-1 \cdot y}\right)\right)\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(\left(-1 \cdot -1\right) \cdot x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(1 \cdot x + -1 \cdot y\right)\right)\right) \]

      14. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \color{blue}{-1} \cdot y\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \left(x - \color{blue}{y}\right)\right)\right) \]

      17. --lowering--.f64 97.2%

          \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 97.2%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(6 \cdot \left(x - y\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(6, \left(x - y\right)\right), z\right) \]

      5. --lowering--.f64 97.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(6, \mathsf{\_.f64}\left(x, y\right)\right), z\right) \]

   7. Applied egg-rr 97.3%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -6.2e+41) t_0 (if (<= x 6.8e+84) (* y (+ 4.0 (* -6.0 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -6.2e+41) {
		tmp = t_0;
	} else if (x <= 6.8e+84) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-6.2d+41)) then
        tmp = t_0
    else if (x <= 6.8d+84) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -6.2e+41) {
		tmp = t_0;
	} else if (x <= 6.8e+84) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -6.2e+41:
		tmp = t_0
	elif x <= 6.8e+84:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -6.2e+41)
		tmp = t_0;
	elseif (x <= 6.8e+84)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -6.2e+41)
		tmp = t_0;
	elseif (x <= 6.8e+84)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+41], t$95$0, If[LessEqual[x, 6.8e+84], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e41 or 6.7999999999999996e84 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \left(\color{blue}{1} + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \left(\mathsf{neg}\left(-1 \cdot x\right)\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot x\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right)\right)} \]

      5. distribute-neg-in N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-6 \cdot \left(\frac{2}{3} - z\right)\right)\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-6 \cdot \left(\frac{2}{3} - z\right)}\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(-6\right)\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + 6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{-1}\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - \color{blue}{1}\right) \]

      12. associate-*r* N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)} \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right) \]

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

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + -1\right)\right)\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6\right)\right) \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right)\right) \]

   5. Simplified 83.8%

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

   if -6.2e41 < x < 6.7999999999999996e84

   1. Initial program 99.5%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right), \color{blue}{x}\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right), x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(6 \cdot \left(-1 \cdot z\right)\right)\right)\right), x\right) \]

      12. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\left(6 \cdot -1\right) \cdot z\right)\right)\right), x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(-6 \cdot z\right)\right)\right), x\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\left(\mathsf{neg}\left(6\right)\right) \cdot z\right)\right)\right), x\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(6\right)\right), z\right)\right)\right), x\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(-6, z\right)\right)\right), x\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(4 + -6 \cdot z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(4, \left(-6 \cdot z\right)\right), y\right) \]

      4. *-lowering-*.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(4, \mathsf{*.f64}\left(-6, z\right)\right), y\right) \]

   7. Simplified 74.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+85}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -8e+40)
     t_0
     (if (<= x 1.35e+85) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -8e+40) {
		tmp = t_0;
	} else if (x <= 1.35e+85) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-8d+40)) then
        tmp = t_0
    else if (x <= 1.35d+85) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -8e+40) {
		tmp = t_0;
	} else if (x <= 1.35e+85) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -8e+40:
		tmp = t_0
	elif x <= 1.35e+85:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -8e+40)
		tmp = t_0;
	elseif (x <= 1.35e+85)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -8e+40)
		tmp = t_0;
	elseif (x <= 1.35e+85)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+40], t$95$0, If[LessEqual[x, 1.35e+85], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000024e40 or 1.34999999999999992e85 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. remove-double-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) \cdot \left(\color{blue}{1} + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. neg-mul-1 N/A

         \[\leadsto \left(\mathsf{neg}\left(-1 \cdot x\right)\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right) \]

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

         \[\leadsto \mathsf{neg}\left(\left(-1 \cdot x\right) \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)\right)\right)} \]

      5. distribute-neg-in N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-6 \cdot \left(\frac{2}{3} - z\right)\right)\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-6 \cdot \left(\frac{2}{3} - z\right)}\right)\right)\right) \]

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

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + \left(\mathsf{neg}\left(-6\right)\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      8. metadata-eval N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(-1 + 6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{-1}\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \left(-1 \cdot x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - \color{blue}{1}\right) \]

      12. associate-*r* N/A

          \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)} \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right) \]

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

          \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right) + -1\right)\right)\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(6\right)\right) \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(\color{blue}{-1}\right)\right)\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + 1\right)\right) \]

   5. Simplified 83.8%

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

   if -8.00000000000000024e40 < x < 1.34999999999999992e85

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{2}{3} - z\right), \color{blue}{\left(6 \cdot y\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), \left(\color{blue}{6} \cdot y\right)\right) \]

      5. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), \mathsf{*.f64}\left(6, \color{blue}{y}\right)\right) \]

   5. Simplified 74.3%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(\frac{2}{3} - z\right) \cdot y\right), \color{blue}{6}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{3} - z\right), y\right), 6\right) \]

      5. --lowering--.f64 74.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), y\right), 6\right) \]

   7. Applied egg-rr 74.4%

      \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot y\right) \cdot 6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+85}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+52}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e-36) (* x -3.0) (if (<= x 1.85e+52) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-36) {
		tmp = x * -3.0;
	} else if (x <= 1.85e+52) {
		tmp = y * 4.0;
	} 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 (x <= (-1.3d-36)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.85d+52) then
        tmp = y * 4.0d0
    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 (x <= -1.3e-36) {
		tmp = x * -3.0;
	} else if (x <= 1.85e+52) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e-36:
		tmp = x * -3.0
	elif x <= 1.85e+52:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e-36)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.85e+52)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e-36)
		tmp = x * -3.0;
	elseif (x <= 1.85e+52)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e-36], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.85e+52], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e-36 or 1.85e52 < x

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 54.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 41.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   8. Simplified 41.4%

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

   if -1.3e-36 < x < 1.85e52

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. neg-mul-1 N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. associate-+l+ N/A

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

      7. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

      8. associate-*r* N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

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

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

      19. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

      21. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

      22. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

      24. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

      26. metadata-eval 40.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

   5. Simplified 40.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 35.5%

         \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

   8. Simplified 35.5%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+52}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6 \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) (- 0.6666666666666666 z)) 6.0)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
}

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 + (((y - x) * (0.6666666666666666d0 - z)) * 6.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
}

Python

def code(x, y, z):
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(0.6666666666666666 - z)) * 6.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{6}\right)\right)\right) \]

   3. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{6}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(y - x\right) \cdot \left(\frac{2}{3} - z\right)\right), \color{blue}{6}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), \left(\frac{2}{3} - z\right)\right), 6\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{2}{3} - z\right)\right), 6\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{2}{3}\right), z\right)\right), 6\right)\right) \]

   8. metadata-eval 99.5%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(\frac{2}{3}, z\right)\right), 6\right)\right) \]

4. Applied egg-rr 99.5%

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

Alternative 15: 26.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 4.0))

C

double code(double x, double y, double z) {
	return y * 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 = y * 4.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * 4.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. sub-neg N/A

      \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

   3. neg-mul-1 N/A

      \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

   4. distribute-lft-in N/A

      \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

   5. associate-+l+ N/A

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

   6. metadata-eval N/A

      \[\leadsto \left(\frac{2}{3} \cdot 6\right) \cdot y + \left(\color{blue}{4} \cdot \left(-1 \cdot x\right) + x\right) \]

   7. associate-*r* N/A

      \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\color{blue}{4 \cdot \left(-1 \cdot x\right)} + x\right) \]

   8. associate-*r* N/A

      \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(\left(4 \cdot -1\right) \cdot x + x\right) \]

   9. metadata-eval N/A

      \[\leadsto \frac{2}{3} \cdot \left(6 \cdot y\right) + \left(-4 \cdot x + x\right) \]

   10. metadata-eval N/A

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

   11. associate-*r* N/A

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

   12. *-commutative N/A

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

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

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{3} \cdot \left(6 \cdot y\right)\right), \color{blue}{\left(\left(-6 \cdot x\right) \cdot \frac{2}{3} + x\right)}\right) \]

   14. associate-*r* N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\left(\frac{2}{3} \cdot 6\right) \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \left(\color{blue}{\left(-6 \cdot x\right)} \cdot \frac{2}{3} + x\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{\left(-6 \cdot x\right) \cdot \frac{2}{3}} + x\right)\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\left(x \cdot -6\right) \cdot \frac{2}{3} + x\right)\right) \]

   19. associate-*l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(-6 \cdot \frac{2}{3}\right) + x\right)\right) \]

   20. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x\right)\right) \]

   21. *-rgt-identity N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -4 + x \cdot \color{blue}{1}\right)\right) \]

   22. distribute-lft-out N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{\left(-4 + 1\right)}\right)\right) \]

   23. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot -3\right)\right) \]

   24. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -4\right)}\right)\right) \]

   26. metadata-eval 47.6%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, -3\right)\right) \]

5. Simplified 47.6%

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

6. Taylor expanded in y around inf

   \[\leadsto \color{blue}{4 \cdot y} \]
7. Step-by-step derivation

   1. *-lowering-*.f64 24.4%

      \[\leadsto \mathsf{*.f64}\left(4, \color{blue}{y}\right) \]

8. Simplified 24.4%

   \[\leadsto \color{blue}{4 \cdot y} \]

9. Final simplification 24.4%

   \[\leadsto y \cdot 4 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024191 
(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))))