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

Percentage Accurate: 99.6% → 99.6%

Time: 26.3s

Alternatives: 14

Speedup: 1.0×

• 21.2% 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: 99.6% 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: 99.6% 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]

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. Add Preprocessing

Alternative 2: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-275}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+187}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -2e+198)
     (* y (* z -6.0))
     (if (<= z -0.5)
       t_0
       (if (<= z 2.55e-275)
         (* x -3.0)
         (if (<= z 0.5)
           (* y 4.0)
           (if (<= z 4.1e+187) t_0 (* z (* y -6.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2e+198) {
		tmp = y * (z * -6.0);
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= 2.55e-275) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 4.1e+187) {
		tmp = t_0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-2d+198)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= 2.55d-275) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else if (z <= 4.1d+187) then
        tmp = t_0
    else
        tmp = z * (y * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2e+198) {
		tmp = y * (z * -6.0);
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= 2.55e-275) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 4.1e+187) {
		tmp = t_0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -2e+198:
		tmp = y * (z * -6.0)
	elif z <= -0.5:
		tmp = t_0
	elif z <= 2.55e-275:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	elif z <= 4.1e+187:
		tmp = t_0
	else:
		tmp = z * (y * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2e+198)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= 2.55e-275)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.1e+187)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2e+198)
		tmp = y * (z * -6.0);
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= 2.55e-275)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	elseif (z <= 4.1e+187)
		tmp = t_0;
	else
		tmp = z * (y * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+198], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, 2.55e-275], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.1e+187], t$95$0, N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.00000000000000004e198

   1. Initial program 99.7%

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

   3. Taylor expanded in 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 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 74.8%

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

   8. Simplified 74.8%

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

   if -2.00000000000000004e198 < z < -0.5 or 0.5 < z < 4.1e187

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 58.4%

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

   10. Simplified 58.4%

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

   if -0.5 < z < 2.54999999999999992e-275

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 97.9%

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

   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 58.0%

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

   10. Simplified 58.0%

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

   if 2.54999999999999992e-275 < z < 0.5

   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 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 59.3%

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

   8. Simplified 59.3%

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

   if 4.1e187 < z

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 66.4%

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

   10. Simplified 66.4%

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

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

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

       4. *-lowering-*.f64 66.5%

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

   12. Applied egg-rr 66.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-275}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+187}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))) (t_1 (* 6.0 (* x z))))
   (if (<= z -8e+195)
     t_0
     (if (<= z -0.5)
       t_1
       (if (<= z 1.15e-288)
         (* x -3.0)
         (if (<= z 0.55) (* y 4.0) (if (<= z 1.12e+193) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8e+195) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= 1.15e-288) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else if (z <= 1.12e+193) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y * (z * (-6.0d0))
    t_1 = 6.0d0 * (x * z)
    if (z <= (-8d+195)) then
        tmp = t_0
    else if (z <= (-0.5d0)) then
        tmp = t_1
    else if (z <= 1.15d-288) then
        tmp = x * (-3.0d0)
    else if (z <= 0.55d0) then
        tmp = y * 4.0d0
    else if (z <= 1.12d+193) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8e+195) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= 1.15e-288) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else if (z <= 1.12e+193) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -8e+195:
		tmp = t_0
	elif z <= -0.5:
		tmp = t_1
	elif z <= 1.15e-288:
		tmp = x * -3.0
	elif z <= 0.55:
		tmp = y * 4.0
	elif z <= 1.12e+193:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8e+195)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= 1.15e-288)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.55)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.12e+193)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8e+195)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= 1.15e-288)
		tmp = x * -3.0;
	elseif (z <= 0.55)
		tmp = y * 4.0;
	elseif (z <= 1.12e+193)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+195], t$95$0, If[LessEqual[z, -0.5], t$95$1, If[LessEqual[z, 1.15e-288], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.12e+193], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.99999999999999982e195 or 1.1199999999999999e193 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 70.6%

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

   8. Simplified 70.6%

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

   if -7.99999999999999982e195 < z < -0.5 or 0.55000000000000004 < z < 1.1199999999999999e193

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 58.4%

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

   10. Simplified 58.4%

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

   if -0.5 < z < 1.15e-288

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 97.9%

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

   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 58.0%

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

   10. Simplified 58.0%

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

   if 1.15e-288 < z < 0.55000000000000004

   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 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+195}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+193}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -6e+195)
     t_0
     (if (<= z -0.5)
       t_1
       (if (<= z 1.75e-288)
         (* x -3.0)
         (if (<= z 0.68) (* y 4.0) (if (<= z 6.4e+193) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -6e+195) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= 1.75e-288) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 6.4e+193) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-6d+195)) then
        tmp = t_0
    else if (z <= (-0.5d0)) then
        tmp = t_1
    else if (z <= 1.75d-288) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else if (z <= 6.4d+193) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -6e+195) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= 1.75e-288) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 6.4e+193) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -6e+195:
		tmp = t_0
	elif z <= -0.5:
		tmp = t_1
	elif z <= 1.75e-288:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	elif z <= 6.4e+193:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -6e+195)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= 1.75e-288)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.4e+193)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -6e+195)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= 1.75e-288)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	elseif (z <= 6.4e+193)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+195], t$95$0, If[LessEqual[z, -0.5], t$95$1, If[LessEqual[z, 1.75e-288], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.4e+193], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000001e195 or 6.40000000000000026e193 < z

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 70.5%

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

   10. Simplified 70.5%

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

   if -6.0000000000000001e195 < z < -0.5 or 0.680000000000000049 < z < 6.40000000000000026e193

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 58.4%

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

   10. Simplified 58.4%

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

   if -0.5 < z < 1.7500000000000001e-288

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 97.9%

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

   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 58.0%

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

   10. Simplified 58.0%

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

   if 1.7500000000000001e-288 < z < 0.680000000000000049

   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 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+195}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+193}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.00033:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-283}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 660000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.00033)
     t_0
     (if (<= z 3.9e-283)
       (* x -3.0)
       (if (<= z 660000.0) (* 6.0 (* y (- 0.6666666666666666 z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.00033) {
		tmp = t_0;
	} else if (z <= 3.9e-283) {
		tmp = x * -3.0;
	} else if (z <= 660000.0) {
		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 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.00033d0)) then
        tmp = t_0
    else if (z <= 3.9d-283) then
        tmp = x * (-3.0d0)
    else if (z <= 660000.0d0) 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 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.00033) {
		tmp = t_0;
	} else if (z <= 3.9e-283) {
		tmp = x * -3.0;
	} else if (z <= 660000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.00033:
		tmp = t_0
	elif z <= 3.9e-283:
		tmp = x * -3.0
	elif z <= 660000.0:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.00033)
		tmp = t_0;
	elseif (z <= 3.9e-283)
		tmp = Float64(x * -3.0);
	elseif (z <= 660000.0)
		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 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.00033)
		tmp = t_0;
	elseif (z <= 3.9e-283)
		tmp = x * -3.0;
	elseif (z <= 660000.0)
		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[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00033], t$95$0, If[LessEqual[z, 3.9e-283], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 660000.0], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e-4 or 6.6e5 < z

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 96.4%

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

   7. Simplified 96.4%

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

   if -3.3e-4 < z < 3.9000000000000002e-283

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 99.9%

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

   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 59.3%

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

   10. Simplified 59.3%

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

   if 3.9000000000000002e-283 < z < 6.6e5

   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 60.6%

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

   5. Simplified 60.6%

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

Alternative 6: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.000115:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.000115)
     t_0
     (if (<= z 1.42e-288) (* x -3.0) (if (<= z 0.56) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.000115) {
		tmp = t_0;
	} else if (z <= 1.42e-288) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		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 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.000115d0)) then
        tmp = t_0
    else if (z <= 1.42d-288) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) 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 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.000115) {
		tmp = t_0;
	} else if (z <= 1.42e-288) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.000115:
		tmp = t_0
	elif z <= 1.42e-288:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.000115)
		tmp = t_0;
	elseif (z <= 1.42e-288)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.000115)
		tmp = t_0;
	elseif (z <= 1.42e-288)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.000115], t$95$0, If[LessEqual[z, 1.42e-288], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-4 or 0.56000000000000005 < z

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 95.4%

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

   7. Simplified 95.4%

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

   if -1.15e-4 < z < 1.42e-288

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 99.9%

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

   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 59.3%

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

   10. Simplified 59.3%

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

   if 1.42e-288 < z < 0.56000000000000005

   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 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000115:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.45:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-271}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.00145:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.45)
     t_0
     (if (<= z 1.7e-271) (* x -3.0) (if (<= z 0.00145) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.45) {
		tmp = t_0;
	} else if (z <= 1.7e-271) {
		tmp = x * -3.0;
	} else if (z <= 0.00145) {
		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 = (-6.0d0) * (y * z)
    if (z <= (-2.45d0)) then
        tmp = t_0
    else if (z <= 1.7d-271) then
        tmp = x * (-3.0d0)
    else if (z <= 0.00145d0) 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 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.45) {
		tmp = t_0;
	} else if (z <= 1.7e-271) {
		tmp = x * -3.0;
	} else if (z <= 0.00145) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.45:
		tmp = t_0
	elif z <= 1.7e-271:
		tmp = x * -3.0
	elif z <= 0.00145:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.45)
		tmp = t_0;
	elseif (z <= 1.7e-271)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.00145)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.45)
		tmp = t_0;
	elseif (z <= 1.7e-271)
		tmp = x * -3.0;
	elseif (z <= 0.00145)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45], t$95$0, If[LessEqual[z, 1.7e-271], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.00145], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4500000000000002 or 0.00145 < z

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. fma-define N/A

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

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

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

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

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

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

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

      8. metadata-eval N/A

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

      9. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

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

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

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

      2. *-commutative N/A

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

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

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

      4. --lowering--.f64 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 50.7%

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

   10. Simplified 50.7%

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

   if -2.4500000000000002 < z < 1.7e-271

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 96.9%

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

   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 57.5%

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

   10. Simplified 57.5%

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

   if 1.7e-271 < z < 0.00145

   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 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 60.4%

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

   8. Simplified 60.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-271}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.00145:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.56) t_0 (if (<= z 0.56) (+ (* y 4.0) (* x -3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.56) {
		tmp = t_0;
	} else if (z <= 0.56) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.56d0)) then
        tmp = t_0
    else if (z <= 0.56d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.56) {
		tmp = t_0;
	} else if (z <= 0.56) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.56:
		tmp = t_0
	elif z <= 0.56:
		tmp = (y * 4.0) + (x * -3.0)
	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 <= -0.56)
		tmp = t_0;
	elseif (z <= 0.56)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	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 <= -0.56)
		tmp = t_0;
	elseif (z <= 0.56)
		tmp = (y * 4.0) + (x * -3.0);
	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, -0.56], t$95$0, If[LessEqual[z, 0.56], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.56000000000000005 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. 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%

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

   if -0.56000000000000005 < z < 0.56000000000000005

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 97.7%

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

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]
   9. Step-by-step derivation

      1. metadata-eval N/A

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

      2. distribute-rgt1-in N/A

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

      3. +-commutative N/A

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

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

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

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

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

      6. distribute-rgt1-in N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 97.8%

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

   10. Simplified 97.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.6) t_0 (if (<= z 0.62) (+ 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 <= -0.6) {
		tmp = t_0;
	} else if (z <= 0.62) {
		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 <= (-0.6d0)) then
        tmp = t_0
    else if (z <= 0.62d0) 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 <= -0.6) {
		tmp = t_0;
	} else if (z <= 0.62) {
		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 <= -0.6:
		tmp = t_0
	elif z <= 0.62:
		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 <= -0.6)
		tmp = t_0;
	elseif (z <= 0.62)
		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 <= -0.6)
		tmp = t_0;
	elseif (z <= 0.62)
		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, -0.6], t$95$0, If[LessEqual[z, 0.62], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.619999999999999996 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. 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%

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

   if -0.599999999999999978 < z < 0.619999999999999996

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 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 97.7%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;\left(0.6666666666666666 - z\right) \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* 6.0 z)))))
   (if (<= x -9.5e-39)
     t_0
     (if (<= x 1.12e+55) (* (- 0.6666666666666666 z) (* y 6.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (6.0 * z));
	double tmp;
	if (x <= -9.5e-39) {
		tmp = t_0;
	} else if (x <= 1.12e+55) {
		tmp = (0.6666666666666666 - z) * (y * 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 * ((-3.0d0) + (6.0d0 * z))
    if (x <= (-9.5d-39)) then
        tmp = t_0
    else if (x <= 1.12d+55) then
        tmp = (0.6666666666666666d0 - z) * (y * 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 * (-3.0 + (6.0 * z));
	double tmp;
	if (x <= -9.5e-39) {
		tmp = t_0;
	} else if (x <= 1.12e+55) {
		tmp = (0.6666666666666666 - z) * (y * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (6.0 * z))
	tmp = 0
	if x <= -9.5e-39:
		tmp = t_0
	elif x <= 1.12e+55:
		tmp = (0.6666666666666666 - z) * (y * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(6.0 * z)))
	tmp = 0.0
	if (x <= -9.5e-39)
		tmp = t_0;
	elseif (x <= 1.12e+55)
		tmp = Float64(Float64(0.6666666666666666 - z) * Float64(y * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (6.0 * z));
	tmp = 0.0;
	if (x <= -9.5e-39)
		tmp = t_0;
	elseif (x <= 1.12e+55)
		tmp = (0.6666666666666666 - z) * (y * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e-39], t$95$0, If[LessEqual[x, 1.12e+55], N[(N[(0.6666666666666666 - z), $MachinePrecision] * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999999e-39 or 1.12000000000000006e55 < 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 83.6%

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

   5. Simplified 83.6%

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

   if -9.4999999999999999e-39 < x < 1.12000000000000006e55

   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 77.9%

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

   5. Simplified 77.9%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 78.0%

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

   7. Applied egg-rr 78.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;\left(0.6666666666666666 - z\right) \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{-38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* 6.0 z)))))
   (if (<= x -2e-38)
     t_0
     (if (<= x 1.12e+55) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (6.0 * z));
	double tmp;
	if (x <= -2e-38) {
		tmp = t_0;
	} else if (x <= 1.12e+55) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (6.0d0 * z))
    if (x <= (-2d-38)) then
        tmp = t_0
    else if (x <= 1.12d+55) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (6.0 * z));
	double tmp;
	if (x <= -2e-38) {
		tmp = t_0;
	} else if (x <= 1.12e+55) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (6.0 * z))
	tmp = 0
	if x <= -2e-38:
		tmp = t_0
	elif x <= 1.12e+55:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(6.0 * z)))
	tmp = 0.0
	if (x <= -2e-38)
		tmp = t_0;
	elseif (x <= 1.12e+55)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (6.0 * z));
	tmp = 0.0;
	if (x <= -2e-38)
		tmp = t_0;
	elseif (x <= 1.12e+55)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e-38], t$95$0, If[LessEqual[x, 1.12e+55], 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 < -1.9999999999999999e-38 or 1.12000000000000006e55 < 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 83.6%

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

   5. Simplified 83.6%

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

   if -1.9999999999999999e-38 < x < 1.12000000000000006e55

   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 77.9%

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

   5. Simplified 77.9%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-17}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.7e-17) (* x -3.0) (if (<= x 5.8e-64) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e-17) {
		tmp = x * -3.0;
	} else if (x <= 5.8e-64) {
		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 <= (-3.7d-17)) then
        tmp = x * (-3.0d0)
    else if (x <= 5.8d-64) 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 <= -3.7e-17) {
		tmp = x * -3.0;
	} else if (x <= 5.8e-64) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.7e-17:
		tmp = x * -3.0
	elif x <= 5.8e-64:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.7e-17)
		tmp = Float64(x * -3.0);
	elseif (x <= 5.8e-64)
		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 <= -3.7e-17)
		tmp = x * -3.0;
	elseif (x <= 5.8e-64)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.7e-17], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 5.8e-64], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999997e-17 or 5.7999999999999998e-64 < 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 50.2%

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

   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 40.0%

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

   10. Simplified 40.0%

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

   if -3.6999999999999997e-17 < x < 5.7999999999999998e-64

   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 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 42.6%

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

   8. Simplified 42.6%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-17}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 99.5%

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

4. Applied egg-rr 99.5%

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

5. Final simplification 99.5%

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

Alternative 14: 27.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 4.0))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * 4.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 50.9%

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

5. Simplified 50.9%

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

6. Taylor expanded in z around 0

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

   1. *-lowering-*.f64 25.6%

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

8. Simplified 25.6%

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

9. Final simplification 25.6%

   \[\leadsto y \cdot 4 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024141 
(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))))