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

Percentage Accurate: 99.5% → 99.7%

Time: 11.5s

Alternatives: 14

Speedup: 1.2×

• 21.0% 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: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (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) * (4.0d0 + (z * (-6.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

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

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

   2. associate-*l* N/A

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

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

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

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

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

   5. sub-neg N/A

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

   6. distribute-lft-in N/A

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

   7. *-commutative N/A

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

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

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

   9. metadata-eval N/A

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

   10. metadata-eval N/A

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

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

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

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

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

   13. metadata-eval N/A

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

   14. metadata-eval N/A

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

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

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

   16. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{elif}\;z \leq 350000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -210000000000.0)
     t_0
     (if (<= z -1e-65)
       (* x (+ (* z 6.0) -3.0))
       (if (<= z 350000.0) (* y (+ 4.0 (* z -6.0))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_0;
	} else if (z <= -1e-65) {
		tmp = x * ((z * 6.0) + -3.0);
	} else if (z <= 350000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} 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 = z * ((y - x) * (-6.0d0))
    if (z <= (-210000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1d-65)) then
        tmp = x * ((z * 6.0d0) + (-3.0d0))
    else if (z <= 350000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -210000000000.0) {
		tmp = t_0;
	} else if (z <= -1e-65) {
		tmp = x * ((z * 6.0) + -3.0);
	} else if (z <= 350000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -210000000000.0:
		tmp = t_0
	elif z <= -1e-65:
		tmp = x * ((z * 6.0) + -3.0)
	elif z <= 350000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -210000000000.0)
		tmp = t_0;
	elseif (z <= -1e-65)
		tmp = Float64(x * Float64(Float64(z * 6.0) + -3.0));
	elseif (z <= 350000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -210000000000.0)
		tmp = t_0;
	elseif (z <= -1e-65)
		tmp = x * ((z * 6.0) + -3.0);
	elseif (z <= 350000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -210000000000.0], t$95$0, If[LessEqual[z, -1e-65], N[(x * N[(N[(z * 6.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 350000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e11 or 3.5e5 < 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 99.2%

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

   5. Simplified 99.2%

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

   if -2.1e11 < z < -9.99999999999999923e-66

   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. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

      10. associate-+l+ N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

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

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

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

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

      18. metadata-eval 87.6%

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

   5. Simplified 87.6%

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

   if -9.99999999999999923e-66 < z < 3.5e5

   1. Initial program 99.4%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)\right)}}}\right)\right) \]

      5. flip3-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x + \color{blue}{\left(y - x\right) \cdot \left(4 + z \cdot -6\right)}}\right)\right) \]

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

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

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

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

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

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0

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

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

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

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

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

      3. *-lowering-*.f64 63.3%

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

   9. Simplified 63.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -210000000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{elif}\;z \leq 350000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -0.5)
     t_0
     (if (<= z -8.5e-66) (* x -3.0) (if (<= z 0.54) (* y 4.0) 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 <= -8.5e-66) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-8.5d-66)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.54d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -8.5e-66) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} 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 <= -8.5e-66:
		tmp = x * -3.0
	elif z <= 0.54:
		tmp = y * 4.0
	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 <= -8.5e-66)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.54)
		tmp = Float64(y * 4.0);
	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 <= -8.5e-66)
		tmp = x * -3.0;
	elseif (z <= 0.54)
		tmp = y * 4.0;
	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, -8.5e-66], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.54], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.54000000000000004 < 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   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. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 57.9%

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

   8. Simplified 57.9%

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

   if -0.5 < z < -8.49999999999999966e-66

   1. Initial program 99.4%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 94.3%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 82.1%

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

   10. Simplified 82.1%

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

   if -8.49999999999999966e-66 < z < 0.54000000000000004

   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 0

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

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

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

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

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

      3. --lowering--.f64 63.1%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 63.1%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 62.0%

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

   8. Simplified 62.0%

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

Alternative 4: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{-0.16666666666666666}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.66)
   (+ x (* (- y x) (* z -6.0)))
   (if (<= z 0.66)
     (+ x (* (- y x) 4.0))
     (/ (- y x) (/ -0.16666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = (y - x) / (-0.16666666666666666 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.66d0)) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (y - x) / ((-0.16666666666666666d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = (y - x) / (-0.16666666666666666 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.66:
		tmp = x + ((y - x) * (z * -6.0))
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = (y - x) / (-0.16666666666666666 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.66)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(Float64(y - x) / Float64(-0.16666666666666666 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.66)
		tmp = x + ((y - x) * (z * -6.0));
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = (y - x) / (-0.16666666666666666 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.66], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(-0.16666666666666666 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031

   1. Initial program 99.8%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 97.8%

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

   7. Simplified 97.8%

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

   if -0.660000000000000031 < z < 0.660000000000000031

   1. Initial program 99.4%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 97.2%

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

   if 0.660000000000000031 < 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 96.8%

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

   5. Simplified 96.8%

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

      1. associate-*r* N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. clear-num N/A

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

      5. associate-/r/ N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\frac{-1}{6}}{z}}{y - x}}} \]

      6. clear-num N/A

         \[\leadsto \frac{y - x}{\color{blue}{\frac{\frac{-1}{6}}{z}}} \]

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

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

      8. *-rgt-identity N/A

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

      9. rgt-mult-inverse N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. rgt-mult-inverse N/A

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

      16. *-rgt-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\frac{-1}{6}}{z}\right)\right) \]

      17. /-lowering-/.f64 96.8%

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

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{-0.16666666666666666}{z}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{-0.16666666666666666}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* z (* (- y x) -6.0))
   (if (<= z 0.66)
     (+ x (* (- y x) 4.0))
     (/ (- y x) (/ -0.16666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = (y - x) / (-0.16666666666666666 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (y - x) / ((-0.16666666666666666d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = (y - x) / (-0.16666666666666666 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = (y - x) / (-0.16666666666666666 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(Float64(y - x) / Float64(-0.16666666666666666 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = (y - x) / (-0.16666666666666666 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(-0.16666666666666666 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 97.7%

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

   5. Simplified 97.7%

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

   if -0.55000000000000004 < z < 0.660000000000000031

   1. Initial program 99.4%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 97.2%

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

   if 0.660000000000000031 < 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 96.8%

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

   5. Simplified 96.8%

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

      1. associate-*r* N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. clear-num N/A

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

      5. associate-/r/ N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\frac{-1}{6}}{z}}{y - x}}} \]

      6. clear-num N/A

         \[\leadsto \frac{y - x}{\color{blue}{\frac{\frac{-1}{6}}{z}}} \]

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

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

      8. *-rgt-identity N/A

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

      9. rgt-mult-inverse N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. rgt-mult-inverse N/A

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

      16. *-rgt-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\frac{-1}{6}}{z}\right)\right) \]

      17. /-lowering-/.f64 96.8%

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

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{-0.16666666666666666}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{-0.16666666666666666}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.58) t_0 (if (<= z 0.66) (+ x (* (- y x) 4.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.58d0)) then
        tmp = t_0
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.58:
		tmp = t_0
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.58], t$95$0, If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.660000000000000031 < 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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 97.3%

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

   5. Simplified 97.3%

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

   if -0.57999999999999996 < z < 0.660000000000000031

   1. Initial program 99.4%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 97.2%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (* z 6.0) -3.0))))
   (if (<= x -1.25e-73) t_0 (if (<= x 4.8e+39) (* y (+ 4.0 (* z -6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * 6.0) + -3.0);
	double tmp;
	if (x <= -1.25e-73) {
		tmp = t_0;
	} else if (x <= 4.8e+39) {
		tmp = y * (4.0 + (z * -6.0));
	} 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) + (-3.0d0))
    if (x <= (-1.25d-73)) then
        tmp = t_0
    else if (x <= 4.8d+39) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    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) + -3.0);
	double tmp;
	if (x <= -1.25e-73) {
		tmp = t_0;
	} else if (x <= 4.8e+39) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * 6.0) + -3.0)
	tmp = 0
	if x <= -1.25e-73:
		tmp = t_0
	elif x <= 4.8e+39:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * 6.0) + -3.0))
	tmp = 0.0
	if (x <= -1.25e-73)
		tmp = t_0;
	elseif (x <= 4.8e+39)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * 6.0) + -3.0);
	tmp = 0.0;
	if (x <= -1.25e-73)
		tmp = t_0;
	elseif (x <= 4.8e+39)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * 6.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e-73], t$95$0, If[LessEqual[x, 4.8e+39], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-73 or 4.8000000000000002e39 < x

   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 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. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

      10. associate-+l+ N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

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

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

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

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

      18. metadata-eval 83.2%

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

   5. Simplified 83.2%

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

   if -1.25e-73 < x < 4.8000000000000002e39

   1. Initial program 99.6%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)\right)}{{x}^{3} + {\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{x}^{3} + {\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)}^{3}}{x \cdot x + \left(\left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right) - x \cdot \left(\left(y - x\right) \cdot \left(4 + z \cdot -6\right)\right)\right)}}}\right)\right) \]

      5. flip3-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x + \color{blue}{\left(y - x\right) \cdot \left(4 + z \cdot -6\right)}}\right)\right) \]

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

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

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

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

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

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0

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

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

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

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

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

      3. *-lowering-*.f64 78.9%

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

   9. Simplified 78.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (* z 6.0) -3.0))))
   (if (<= x -9.6e-74)
     t_0
     (if (<= x 2.2e+40) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * 6.0) + -3.0);
	double tmp;
	if (x <= -9.6e-74) {
		tmp = t_0;
	} else if (x <= 2.2e+40) {
		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 * ((z * 6.0d0) + (-3.0d0))
    if (x <= (-9.6d-74)) then
        tmp = t_0
    else if (x <= 2.2d+40) 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 * ((z * 6.0) + -3.0);
	double tmp;
	if (x <= -9.6e-74) {
		tmp = t_0;
	} else if (x <= 2.2e+40) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * 6.0) + -3.0)
	tmp = 0
	if x <= -9.6e-74:
		tmp = t_0
	elif x <= 2.2e+40:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * 6.0) + -3.0))
	tmp = 0.0
	if (x <= -9.6e-74)
		tmp = t_0;
	elseif (x <= 2.2e+40)
		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 * ((z * 6.0) + -3.0);
	tmp = 0.0;
	if (x <= -9.6e-74)
		tmp = t_0;
	elseif (x <= 2.2e+40)
		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[(N[(z * 6.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e-74], t$95$0, If[LessEqual[x, 2.2e+40], 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 < -9.5999999999999996e-74 or 2.1999999999999999e40 < x

   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 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. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. metadata-eval N/A

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

      10. associate-+l+ N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

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

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

      14. *-commutative N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

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

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

      18. metadata-eval 83.2%

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

   5. Simplified 83.2%

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

   if -9.5999999999999996e-74 < x < 2.1999999999999999e40

   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 x around 0

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

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

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

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

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

      3. --lowering--.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+40}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= x -1.25e-73)
     t_0
     (if (<= x 8.4e+40) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (x <= -1.25e-73) {
		tmp = t_0;
	} else if (x <= 8.4e+40) {
		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 * (z * 6.0d0)
    if (x <= (-1.25d-73)) then
        tmp = t_0
    else if (x <= 8.4d+40) 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 * (z * 6.0);
	double tmp;
	if (x <= -1.25e-73) {
		tmp = t_0;
	} else if (x <= 8.4e+40) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if x <= -1.25e-73:
		tmp = t_0
	elif x <= 8.4e+40:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (x <= -1.25e-73)
		tmp = t_0;
	elseif (x <= 8.4e+40)
		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 * (z * 6.0);
	tmp = 0.0;
	if (x <= -1.25e-73)
		tmp = t_0;
	elseif (x <= 8.4e+40)
		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[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e-73], t$95$0, If[LessEqual[x, 8.4e+40], 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 < -1.25e-73 or 8.4000000000000004e40 < x

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. --lowering--.f64 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   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. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 52.4%

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

   8. Simplified 52.4%

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

   if -1.25e-73 < x < 8.4000000000000004e40

   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 x around 0

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

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

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

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

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

      3. --lowering--.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+17}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-82) (* x -3.0) (if (<= x 1.25e+17) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-82) {
		tmp = x * -3.0;
	} else if (x <= 1.25e+17) {
		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 <= (-1.4d-82)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.25d+17) 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 <= -1.4e-82) {
		tmp = x * -3.0;
	} else if (x <= 1.25e+17) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-82:
		tmp = x * -3.0
	elif x <= 1.25e+17:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-82)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.25e+17)
		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 <= -1.4e-82)
		tmp = x * -3.0;
	elseif (x <= 1.25e+17)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-82], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.25e+17], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000012e-82 or 1.25e17 < x

   1. Initial program 99.6%

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

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

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

      2. associate-*l* N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

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

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

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

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 39.0%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 31.7%

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

   10. Simplified 31.7%

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

   if -1.40000000000000012e-82 < x < 1.25e17

   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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 79.6%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 79.6%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.9%

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

   8. Simplified 49.9%

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

Alternative 11: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- 0.6666666666666666 z) (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 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 + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(0.6666666666666666 - z) * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(0.6666666666666666 - z), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. *-commutative N/A

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

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

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

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

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

   4. metadata-eval N/A

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

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

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

   6. --lowering--.f64 99.6%

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

4. Applied egg-rr 99.6%

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

Alternative 12: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + 6 \cdot \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* 6.0 (* (- y x) (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	return x + (6.0 * ((y - x) * (0.6666666666666666 - z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (6.0d0 * ((y - x) * (0.6666666666666666d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (6.0 * ((y - x) * (0.6666666666666666 - z)));
}

Python

def code(x, y, z):
	return x + (6.0 * ((y - x) * (0.6666666666666666 - z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(6.0 * Float64(Float64(y - x) * Float64(0.6666666666666666 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (6.0 * ((y - x) * (0.6666666666666666 - z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 * N[(N[(y - x), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. *-commutative N/A

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

   2. associate-*r* N/A

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

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

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

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

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

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

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

   6. metadata-eval N/A

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

   7. --lowering--.f64 99.4%

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

4. Applied egg-rr 99.4%

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

5. Final simplification 99.4%

   \[\leadsto x + 6 \cdot \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \]
6. Add Preprocessing

Alternative 13: 26.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

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

Java

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

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

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

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

   2. associate-*l* N/A

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

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

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

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

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

   5. sub-neg N/A

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

   6. distribute-lft-in N/A

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

   7. *-commutative N/A

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

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

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

   9. metadata-eval N/A

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

   10. metadata-eval N/A

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

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

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

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

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

   13. metadata-eval N/A

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

   14. metadata-eval N/A

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

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

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

   16. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around 0

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
6. Step-by-step derivation

7. Simplified 49.6%

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

8. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 22.9%

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

10. Simplified 22.9%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 14: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

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

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

   2. associate-*l* N/A

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

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

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

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

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

   5. sub-neg N/A

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

   6. distribute-lft-in N/A

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

   7. *-commutative N/A

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

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

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

   9. metadata-eval N/A

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

   10. metadata-eval N/A

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

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

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

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

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

   13. metadata-eval N/A

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

   14. metadata-eval N/A

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

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

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

   16. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 50.6%

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

7. Simplified 50.6%

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

8. Taylor expanded in z around 0

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

10. Simplified 2.8%

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

Reproduce

herbie shell --seed 2024145 
(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))))