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

Percentage Accurate: 99.5% → 99.7%

Time: 10.8s

Alternatives: 16

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. +-commutative 99.3%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-268}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-264}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -3.3e+90)
     (* z (* y -6.0))
     (if (<= z -4.2)
       t_0
       (if (<= z -7.2e-129)
         (* y 4.0)
         (if (<= z -3.4e-268)
           (* x -3.0)
           (if (<= z 3.1e-264)
             (* y 4.0)
             (if (<= z 3.9e-119)
               (* x -3.0)
               (if (<= z 0.56) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.3e+90) {
		tmp = z * (y * -6.0);
	} else if (z <= -4.2) {
		tmp = t_0;
	} else if (z <= -7.2e-129) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-268) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-264) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-119) {
		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 = x * (z * 6.0d0)
    if (z <= (-3.3d+90)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-4.2d0)) then
        tmp = t_0
    else if (z <= (-7.2d-129)) then
        tmp = y * 4.0d0
    else if (z <= (-3.4d-268)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.1d-264) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-119) 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 = x * (z * 6.0);
	double tmp;
	if (z <= -3.3e+90) {
		tmp = z * (y * -6.0);
	} else if (z <= -4.2) {
		tmp = t_0;
	} else if (z <= -7.2e-129) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-268) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-264) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-119) {
		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 = x * (z * 6.0)
	tmp = 0
	if z <= -3.3e+90:
		tmp = z * (y * -6.0)
	elif z <= -4.2:
		tmp = t_0
	elif z <= -7.2e-129:
		tmp = y * 4.0
	elif z <= -3.4e-268:
		tmp = x * -3.0
	elif z <= 3.1e-264:
		tmp = y * 4.0
	elif z <= 3.9e-119:
		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(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.3e+90)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -4.2)
		tmp = t_0;
	elseif (z <= -7.2e-129)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.4e-268)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.1e-264)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-119)
		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 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.3e+90)
		tmp = z * (y * -6.0);
	elseif (z <= -4.2)
		tmp = t_0;
	elseif (z <= -7.2e-129)
		tmp = y * 4.0;
	elseif (z <= -3.4e-268)
		tmp = x * -3.0;
	elseif (z <= 3.1e-264)
		tmp = y * 4.0;
	elseif (z <= 3.9e-119)
		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[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+90], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2], t$95$0, If[LessEqual[z, -7.2e-129], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.4e-268], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.1e-264], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-119], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.30000000000000008e90

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around inf 66.3%

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

       1. *-commutative 66.3%

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

       2. *-commutative 66.3%

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

       3. associate-*r* 66.4%

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

       4. *-commutative 66.4%

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

   11. Simplified 66.4%

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

   if -3.30000000000000008e90 < z < -4.20000000000000018 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. Step-by-step derivation

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. +-commutative 61.4%

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

      3. metadata-eval 61.4%

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

      4. cancel-sign-sub-inv 61.4%

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

      5. *-commutative 61.4%

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

      6. cancel-sign-sub-inv 61.4%

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

      7. distribute-lft-neg-in 61.4%

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

      8. *-commutative 61.4%

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

      9. distribute-lft-neg-in 61.4%

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

      10. metadata-eval 61.4%

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

      11. sub-neg 61.4%

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

      12. distribute-lft-in 61.4%

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

      13. metadata-eval 61.4%

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

      14. neg-mul-1 61.4%

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

      15. *-commutative 61.4%

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

      16. associate-*l* 61.4%

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

      17. associate-+r+ 61.4%

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

      18. metadata-eval 61.4%

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

      19. *-commutative 61.4%

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

      20. associate-*l* 61.4%

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

      21. metadata-eval 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in z around inf 59.8%

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

      1. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if -4.20000000000000018 < z < -7.2e-129 or -3.4e-268 < z < 3.1000000000000002e-264 or 3.8999999999999999e-119 < z < 0.56000000000000005

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in z around 0 66.9%

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

   if -7.2e-129 < z < -3.4e-268 or 3.1000000000000002e-264 < z < 3.8999999999999999e-119

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. cancel-sign-sub-inv 77.7%

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

      5. *-commutative 77.7%

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

      6. cancel-sign-sub-inv 77.7%

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

      7. distribute-lft-neg-in 77.7%

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

      8. *-commutative 77.7%

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

      9. distribute-lft-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

      11. sub-neg 77.7%

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

      12. distribute-lft-in 77.7%

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

      13. metadata-eval 77.7%

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

      14. neg-mul-1 77.7%

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

      15. *-commutative 77.7%

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

      16. associate-*l* 77.7%

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

      17. associate-+r+ 77.7%

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

      18. metadata-eval 77.7%

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

      19. *-commutative 77.7%

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

      20. associate-*l* 77.7%

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

      21. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around 0 77.7%

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

      1. *-commutative 77.7%

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

   10. Simplified 77.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.2:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-268}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-264}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-137}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-267}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -3.6e+90)
     (* y (* z -6.0))
     (if (<= z -5.0)
       t_0
       (if (<= z -3.6e-137)
         (* y 4.0)
         (if (<= z -5.8e-260)
           (* x -3.0)
           (if (<= z 1.25e-267)
             (* y 4.0)
             (if (<= z 1.6e-120)
               (* x -3.0)
               (if (<= z 0.5) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.6e+90) {
		tmp = y * (z * -6.0);
	} else if (z <= -5.0) {
		tmp = t_0;
	} else if (z <= -3.6e-137) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-260) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-267) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-120) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-3.6d+90)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-5.0d0)) then
        tmp = t_0
    else if (z <= (-3.6d-137)) then
        tmp = y * 4.0d0
    else if (z <= (-5.8d-260)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.25d-267) then
        tmp = y * 4.0d0
    else if (z <= 1.6d-120) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.6e+90) {
		tmp = y * (z * -6.0);
	} else if (z <= -5.0) {
		tmp = t_0;
	} else if (z <= -3.6e-137) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-260) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-267) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-120) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -3.6e+90:
		tmp = y * (z * -6.0)
	elif z <= -5.0:
		tmp = t_0
	elif z <= -3.6e-137:
		tmp = y * 4.0
	elif z <= -5.8e-260:
		tmp = x * -3.0
	elif z <= 1.25e-267:
		tmp = y * 4.0
	elif z <= 1.6e-120:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.6e+90)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -5.0)
		tmp = t_0;
	elseif (z <= -3.6e-137)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.8e-260)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.25e-267)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.6e-120)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.6e+90)
		tmp = y * (z * -6.0);
	elseif (z <= -5.0)
		tmp = t_0;
	elseif (z <= -3.6e-137)
		tmp = y * 4.0;
	elseif (z <= -5.8e-260)
		tmp = x * -3.0;
	elseif (z <= 1.25e-267)
		tmp = y * 4.0;
	elseif (z <= 1.6e-120)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+90], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.0], t$95$0, If[LessEqual[z, -3.6e-137], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.8e-260], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.25e-267], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.6e-120], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e90

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 66.4%

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

   6. Taylor expanded in z around inf 66.4%

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

   if -3.6e90 < z < -5 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. +-commutative 61.4%

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

      3. metadata-eval 61.4%

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

      4. cancel-sign-sub-inv 61.4%

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

      5. *-commutative 61.4%

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

      6. cancel-sign-sub-inv 61.4%

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

      7. distribute-lft-neg-in 61.4%

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

      8. *-commutative 61.4%

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

      9. distribute-lft-neg-in 61.4%

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

      10. metadata-eval 61.4%

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

      11. sub-neg 61.4%

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

      12. distribute-lft-in 61.4%

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

      13. metadata-eval 61.4%

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

      14. neg-mul-1 61.4%

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

      15. *-commutative 61.4%

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

      16. associate-*l* 61.4%

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

      17. associate-+r+ 61.4%

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

      18. metadata-eval 61.4%

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

      19. *-commutative 61.4%

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

      20. associate-*l* 61.4%

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

      21. metadata-eval 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in z around inf 59.8%

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

      1. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if -5 < z < -3.60000000000000006e-137 or -5.7999999999999999e-260 < z < 1.25e-267 or 1.6e-120 < z < 0.5

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in z around 0 66.9%

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

   if -3.60000000000000006e-137 < z < -5.7999999999999999e-260 or 1.25e-267 < z < 1.6e-120

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. cancel-sign-sub-inv 77.7%

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

      5. *-commutative 77.7%

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

      6. cancel-sign-sub-inv 77.7%

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

      7. distribute-lft-neg-in 77.7%

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

      8. *-commutative 77.7%

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

      9. distribute-lft-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

      11. sub-neg 77.7%

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

      12. distribute-lft-in 77.7%

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

      13. metadata-eval 77.7%

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

      14. neg-mul-1 77.7%

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

      15. *-commutative 77.7%

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

      16. associate-*l* 77.7%

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

      17. associate-+r+ 77.7%

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

      18. metadata-eval 77.7%

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

      19. *-commutative 77.7%

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

      20. associate-*l* 77.7%

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

      21. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around 0 77.7%

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

      1. *-commutative 77.7%

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

   10. Simplified 77.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-137}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-267}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+90}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.39:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-137}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-261}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-115}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -3.5e+90)
     (* -6.0 (* y z))
     (if (<= z -0.39)
       t_0
       (if (<= z -5e-137)
         (* y 4.0)
         (if (<= z -9.2e-261)
           (* x -3.0)
           (if (<= z 3e-266)
             (* y 4.0)
             (if (<= z 1.15e-115)
               (* x -3.0)
               (if (<= z 0.65) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.5e+90) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.39) {
		tmp = t_0;
	} else if (z <= -5e-137) {
		tmp = y * 4.0;
	} else if (z <= -9.2e-261) {
		tmp = x * -3.0;
	} else if (z <= 3e-266) {
		tmp = y * 4.0;
	} else if (z <= 1.15e-115) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-3.5d+90)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-0.39d0)) then
        tmp = t_0
    else if (z <= (-5d-137)) then
        tmp = y * 4.0d0
    else if (z <= (-9.2d-261)) then
        tmp = x * (-3.0d0)
    else if (z <= 3d-266) then
        tmp = y * 4.0d0
    else if (z <= 1.15d-115) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.5e+90) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.39) {
		tmp = t_0;
	} else if (z <= -5e-137) {
		tmp = y * 4.0;
	} else if (z <= -9.2e-261) {
		tmp = x * -3.0;
	} else if (z <= 3e-266) {
		tmp = y * 4.0;
	} else if (z <= 1.15e-115) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -3.5e+90:
		tmp = -6.0 * (y * z)
	elif z <= -0.39:
		tmp = t_0
	elif z <= -5e-137:
		tmp = y * 4.0
	elif z <= -9.2e-261:
		tmp = x * -3.0
	elif z <= 3e-266:
		tmp = y * 4.0
	elif z <= 1.15e-115:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.5e+90)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -0.39)
		tmp = t_0;
	elseif (z <= -5e-137)
		tmp = Float64(y * 4.0);
	elseif (z <= -9.2e-261)
		tmp = Float64(x * -3.0);
	elseif (z <= 3e-266)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.15e-115)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.5e+90)
		tmp = -6.0 * (y * z);
	elseif (z <= -0.39)
		tmp = t_0;
	elseif (z <= -5e-137)
		tmp = y * 4.0;
	elseif (z <= -9.2e-261)
		tmp = x * -3.0;
	elseif (z <= 3e-266)
		tmp = y * 4.0;
	elseif (z <= 1.15e-115)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+90], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.39], t$95$0, If[LessEqual[z, -5e-137], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -9.2e-261], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3e-266], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.15e-115], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999998e90

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 66.4%

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

   6. Taylor expanded in z around inf 66.3%

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

   if -3.4999999999999998e90 < z < -0.39000000000000001 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. +-commutative 61.4%

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

      3. metadata-eval 61.4%

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

      4. cancel-sign-sub-inv 61.4%

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

      5. *-commutative 61.4%

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

      6. cancel-sign-sub-inv 61.4%

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

      7. distribute-lft-neg-in 61.4%

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

      8. *-commutative 61.4%

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

      9. distribute-lft-neg-in 61.4%

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

      10. metadata-eval 61.4%

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

      11. sub-neg 61.4%

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

      12. distribute-lft-in 61.4%

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

      13. metadata-eval 61.4%

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

      14. neg-mul-1 61.4%

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

      15. *-commutative 61.4%

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

      16. associate-*l* 61.4%

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

      17. associate-+r+ 61.4%

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

      18. metadata-eval 61.4%

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

      19. *-commutative 61.4%

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

      20. associate-*l* 61.4%

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

      21. metadata-eval 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in z around inf 59.8%

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

      1. *-commutative 59.8%

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

   10. Simplified 59.8%

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

   if -0.39000000000000001 < z < -5.00000000000000001e-137 or -9.2e-261 < z < 3e-266 or 1.14999999999999992e-115 < z < 0.650000000000000022

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in z around 0 66.9%

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

   if -5.00000000000000001e-137 < z < -9.2e-261 or 3e-266 < z < 1.14999999999999992e-115

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. cancel-sign-sub-inv 77.7%

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

      5. *-commutative 77.7%

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

      6. cancel-sign-sub-inv 77.7%

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

      7. distribute-lft-neg-in 77.7%

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

      8. *-commutative 77.7%

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

      9. distribute-lft-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

      11. sub-neg 77.7%

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

      12. distribute-lft-in 77.7%

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

      13. metadata-eval 77.7%

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

      14. neg-mul-1 77.7%

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

      15. *-commutative 77.7%

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

      16. associate-*l* 77.7%

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

      17. associate-+r+ 77.7%

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

      18. metadata-eval 77.7%

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

      19. *-commutative 77.7%

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

      20. associate-*l* 77.7%

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

      21. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around 0 77.7%

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

      1. *-commutative 77.7%

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

   10. Simplified 77.7%

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

Alternative 5: 50.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-258}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-267}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-118}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -3.6e+90)
     (* -6.0 (* y z))
     (if (<= z -5.8)
       t_0
       (if (<= z -4e-127)
         (* y 4.0)
         (if (<= z -1e-258)
           (* x -3.0)
           (if (<= z 7.8e-267)
             (* y 4.0)
             (if (<= z 9.5e-118)
               (* x -3.0)
               (if (<= z 0.65) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -3.6e+90) {
		tmp = -6.0 * (y * z);
	} else if (z <= -5.8) {
		tmp = t_0;
	} else if (z <= -4e-127) {
		tmp = y * 4.0;
	} else if (z <= -1e-258) {
		tmp = x * -3.0;
	} else if (z <= 7.8e-267) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-118) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		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 * (x * z)
    if (z <= (-3.6d+90)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-5.8d0)) then
        tmp = t_0
    else if (z <= (-4d-127)) then
        tmp = y * 4.0d0
    else if (z <= (-1d-258)) then
        tmp = x * (-3.0d0)
    else if (z <= 7.8d-267) then
        tmp = y * 4.0d0
    else if (z <= 9.5d-118) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) 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 * (x * z);
	double tmp;
	if (z <= -3.6e+90) {
		tmp = -6.0 * (y * z);
	} else if (z <= -5.8) {
		tmp = t_0;
	} else if (z <= -4e-127) {
		tmp = y * 4.0;
	} else if (z <= -1e-258) {
		tmp = x * -3.0;
	} else if (z <= 7.8e-267) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-118) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -3.6e+90:
		tmp = -6.0 * (y * z)
	elif z <= -5.8:
		tmp = t_0
	elif z <= -4e-127:
		tmp = y * 4.0
	elif z <= -1e-258:
		tmp = x * -3.0
	elif z <= 7.8e-267:
		tmp = y * 4.0
	elif z <= 9.5e-118:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.6e+90)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -5.8)
		tmp = t_0;
	elseif (z <= -4e-127)
		tmp = Float64(y * 4.0);
	elseif (z <= -1e-258)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.8e-267)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e-118)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		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 * (x * z);
	tmp = 0.0;
	if (z <= -3.6e+90)
		tmp = -6.0 * (y * z);
	elseif (z <= -5.8)
		tmp = t_0;
	elseif (z <= -4e-127)
		tmp = y * 4.0;
	elseif (z <= -1e-258)
		tmp = x * -3.0;
	elseif (z <= 7.8e-267)
		tmp = y * 4.0;
	elseif (z <= 9.5e-118)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		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[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+90], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8], t$95$0, If[LessEqual[z, -4e-127], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1e-258], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.8e-267], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e-118], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e90

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 66.4%

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

   6. Taylor expanded in z around inf 66.3%

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

   if -3.6e90 < z < -5.79999999999999982 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 97.3%

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

      1. *-commutative 97.3%

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

   8. Simplified 97.3%

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

   9. Taylor expanded in y around 0 58.8%

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

       1. *-commutative 58.8%

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

   11. Simplified 58.8%

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

   if -5.79999999999999982 < z < -4.0000000000000001e-127 or -9.99999999999999954e-259 < z < 7.79999999999999954e-267 or 9.49999999999999931e-118 < z < 0.650000000000000022

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in z around 0 66.9%

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

   if -4.0000000000000001e-127 < z < -9.99999999999999954e-259 or 7.79999999999999954e-267 < z < 9.49999999999999931e-118

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. cancel-sign-sub-inv 77.7%

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

      5. *-commutative 77.7%

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

      6. cancel-sign-sub-inv 77.7%

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

      7. distribute-lft-neg-in 77.7%

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

      8. *-commutative 77.7%

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

      9. distribute-lft-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

      11. sub-neg 77.7%

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

      12. distribute-lft-in 77.7%

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

      13. metadata-eval 77.7%

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

      14. neg-mul-1 77.7%

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

      15. *-commutative 77.7%

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

      16. associate-*l* 77.7%

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

      17. associate-+r+ 77.7%

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

      18. metadata-eval 77.7%

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

      19. *-commutative 77.7%

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

      20. associate-*l* 77.7%

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

      21. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around 0 77.7%

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

      1. *-commutative 77.7%

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

   10. Simplified 77.7%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-258}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-267}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-118}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ t_1 := \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-264}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 27500:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))) (t_1 (* (- y x) (* z -6.0))))
   (if (<= z -470.0)
     t_1
     (if (<= z -6.5e-129)
       t_0
       (if (<= z -2.1e-267)
         (* x (+ -3.0 (* z 6.0)))
         (if (<= z 4.8e-264)
           t_0
           (if (<= z 4.3e-120) (* x -3.0) (if (<= z 27500.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -6.5e-129) {
		tmp = t_0;
	} else if (z <= -2.1e-267) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.8e-264) {
		tmp = t_0;
	} else if (z <= 4.3e-120) {
		tmp = x * -3.0;
	} else if (z <= 27500.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    t_1 = (y - x) * (z * (-6.0d0))
    if (z <= (-470.0d0)) then
        tmp = t_1
    else if (z <= (-6.5d-129)) then
        tmp = t_0
    else if (z <= (-2.1d-267)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 4.8d-264) then
        tmp = t_0
    else if (z <= 4.3d-120) then
        tmp = x * (-3.0d0)
    else if (z <= 27500.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -6.5e-129) {
		tmp = t_0;
	} else if (z <= -2.1e-267) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.8e-264) {
		tmp = t_0;
	} else if (z <= 4.3e-120) {
		tmp = x * -3.0;
	} else if (z <= 27500.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	t_1 = (y - x) * (z * -6.0)
	tmp = 0
	if z <= -470.0:
		tmp = t_1
	elif z <= -6.5e-129:
		tmp = t_0
	elif z <= -2.1e-267:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 4.8e-264:
		tmp = t_0
	elif z <= 4.3e-120:
		tmp = x * -3.0
	elif z <= 27500.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	t_1 = Float64(Float64(y - x) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -470.0)
		tmp = t_1;
	elseif (z <= -6.5e-129)
		tmp = t_0;
	elseif (z <= -2.1e-267)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 4.8e-264)
		tmp = t_0;
	elseif (z <= 4.3e-120)
		tmp = Float64(x * -3.0);
	elseif (z <= 27500.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	t_1 = (y - x) * (z * -6.0);
	tmp = 0.0;
	if (z <= -470.0)
		tmp = t_1;
	elseif (z <= -6.5e-129)
		tmp = t_0;
	elseif (z <= -2.1e-267)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 4.8e-264)
		tmp = t_0;
	elseif (z <= 4.3e-120)
		tmp = x * -3.0;
	elseif (z <= 27500.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -470.0], t$95$1, If[LessEqual[z, -6.5e-129], t$95$0, If[LessEqual[z, -2.1e-267], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-264], t$95$0, If[LessEqual[z, 4.3e-120], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 27500.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -470 or 27500 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. *-commutative 98.6%

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

   8. Simplified 98.6%

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

   9. Taylor expanded in z around 0 98.6%

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

       1. associate-*r* 98.7%

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

       2. *-commutative 98.7%

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

   11. Simplified 98.7%

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

   if -470 < z < -6.49999999999999952e-129 or -2.1000000000000001e-267 < z < 4.7999999999999997e-264 or 4.29999999999999982e-120 < z < 27500

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -6.49999999999999952e-129 < z < -2.1000000000000001e-267

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 79.3%

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

      1. +-commutative 79.3%

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

      2. +-commutative 79.3%

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

      3. metadata-eval 79.3%

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

      4. cancel-sign-sub-inv 79.3%

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

      5. *-commutative 79.3%

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

      6. cancel-sign-sub-inv 79.3%

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

      7. distribute-lft-neg-in 79.3%

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

      8. *-commutative 79.3%

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

      9. distribute-lft-neg-in 79.3%

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

      10. metadata-eval 79.3%

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

      11. sub-neg 79.3%

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

      12. distribute-lft-in 79.3%

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

      13. metadata-eval 79.3%

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

      14. neg-mul-1 79.3%

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

      15. *-commutative 79.3%

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

      16. associate-*l* 79.3%

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

      17. associate-+r+ 79.3%

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

      18. metadata-eval 79.3%

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

      19. *-commutative 79.3%

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

      20. associate-*l* 79.3%

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

      21. metadata-eval 79.3%

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

   7. Simplified 79.3%

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

   if 4.7999999999999997e-264 < z < 4.29999999999999982e-120

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. +-commutative 75.9%

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

      3. metadata-eval 75.9%

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

      4. cancel-sign-sub-inv 75.9%

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

      5. *-commutative 75.9%

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

      6. cancel-sign-sub-inv 75.9%

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

      7. distribute-lft-neg-in 75.9%

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

      8. *-commutative 75.9%

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

      9. distribute-lft-neg-in 75.9%

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

      10. metadata-eval 75.9%

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

      11. sub-neg 75.9%

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

      12. distribute-lft-in 75.9%

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

      13. metadata-eval 75.9%

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

      14. neg-mul-1 75.9%

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

      15. *-commutative 75.9%

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

      16. associate-*l* 75.9%

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

      17. associate-+r+ 75.9%

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

      18. metadata-eval 75.9%

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

      19. *-commutative 75.9%

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

      20. associate-*l* 75.9%

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

      21. metadata-eval 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in z around 0 75.9%

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

      1. *-commutative 75.9%

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

   10. Simplified 75.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -470:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 27500:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ t_1 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-137}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-264}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-115}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))) (t_1 (* z (* (- y x) -6.0))))
   (if (<= z -470.0)
     t_1
     (if (<= z -1.8e-137)
       t_0
       (if (<= z -3.3e-255)
         (* x (+ -3.0 (* z 6.0)))
         (if (<= z 4.2e-264)
           t_0
           (if (<= z 6.2e-115) (* x -3.0) (if (<= z 170000.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -1.8e-137) {
		tmp = t_0;
	} else if (z <= -3.3e-255) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.2e-264) {
		tmp = t_0;
	} else if (z <= 6.2e-115) {
		tmp = x * -3.0;
	} else if (z <= 170000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    t_1 = z * ((y - x) * (-6.0d0))
    if (z <= (-470.0d0)) then
        tmp = t_1
    else if (z <= (-1.8d-137)) then
        tmp = t_0
    else if (z <= (-3.3d-255)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 4.2d-264) then
        tmp = t_0
    else if (z <= 6.2d-115) then
        tmp = x * (-3.0d0)
    else if (z <= 170000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -1.8e-137) {
		tmp = t_0;
	} else if (z <= -3.3e-255) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 4.2e-264) {
		tmp = t_0;
	} else if (z <= 6.2e-115) {
		tmp = x * -3.0;
	} else if (z <= 170000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	t_1 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -470.0:
		tmp = t_1
	elif z <= -1.8e-137:
		tmp = t_0
	elif z <= -3.3e-255:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 4.2e-264:
		tmp = t_0
	elif z <= 6.2e-115:
		tmp = x * -3.0
	elif z <= 170000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	t_1 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -470.0)
		tmp = t_1;
	elseif (z <= -1.8e-137)
		tmp = t_0;
	elseif (z <= -3.3e-255)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 4.2e-264)
		tmp = t_0;
	elseif (z <= 6.2e-115)
		tmp = Float64(x * -3.0);
	elseif (z <= 170000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	t_1 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -470.0)
		tmp = t_1;
	elseif (z <= -1.8e-137)
		tmp = t_0;
	elseif (z <= -3.3e-255)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 4.2e-264)
		tmp = t_0;
	elseif (z <= 6.2e-115)
		tmp = x * -3.0;
	elseif (z <= 170000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -470.0], t$95$1, If[LessEqual[z, -1.8e-137], t$95$0, If[LessEqual[z, -3.3e-255], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-264], t$95$0, If[LessEqual[z, 6.2e-115], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 170000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -470 or 1.7e5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. *-commutative 98.6%

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

   8. Simplified 98.6%

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

   if -470 < z < -1.80000000000000003e-137 or -3.29999999999999988e-255 < z < 4.2000000000000004e-264 or 6.20000000000000013e-115 < z < 1.7e5

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -1.80000000000000003e-137 < z < -3.29999999999999988e-255

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 79.3%

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

      1. +-commutative 79.3%

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

      2. +-commutative 79.3%

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

      3. metadata-eval 79.3%

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

      4. cancel-sign-sub-inv 79.3%

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

      5. *-commutative 79.3%

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

      6. cancel-sign-sub-inv 79.3%

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

      7. distribute-lft-neg-in 79.3%

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

      8. *-commutative 79.3%

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

      9. distribute-lft-neg-in 79.3%

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

      10. metadata-eval 79.3%

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

      11. sub-neg 79.3%

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

      12. distribute-lft-in 79.3%

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

      13. metadata-eval 79.3%

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

      14. neg-mul-1 79.3%

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

      15. *-commutative 79.3%

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

      16. associate-*l* 79.3%

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

      17. associate-+r+ 79.3%

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

      18. metadata-eval 79.3%

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

      19. *-commutative 79.3%

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

      20. associate-*l* 79.3%

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

      21. metadata-eval 79.3%

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

   7. Simplified 79.3%

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

   if 4.2000000000000004e-264 < z < 6.20000000000000013e-115

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. +-commutative 75.9%

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

      3. metadata-eval 75.9%

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

      4. cancel-sign-sub-inv 75.9%

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

      5. *-commutative 75.9%

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

      6. cancel-sign-sub-inv 75.9%

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

      7. distribute-lft-neg-in 75.9%

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

      8. *-commutative 75.9%

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

      9. distribute-lft-neg-in 75.9%

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

      10. metadata-eval 75.9%

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

      11. sub-neg 75.9%

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

      12. distribute-lft-in 75.9%

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

      13. metadata-eval 75.9%

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

      14. neg-mul-1 75.9%

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

      15. *-commutative 75.9%

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

      16. associate-*l* 75.9%

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

      17. associate-+r+ 75.9%

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

      18. metadata-eval 75.9%

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

      19. *-commutative 75.9%

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

      20. associate-*l* 75.9%

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

      21. metadata-eval 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in z around 0 75.9%

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

      1. *-commutative 75.9%

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

   10. Simplified 75.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -470:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-115}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-128}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-261}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-265}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-7}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.65)
     t_0
     (if (<= z -1.75e-128)
       (* y 4.0)
       (if (<= z -2.8e-261)
         (* x -3.0)
         (if (<= z 5.8e-265)
           (* y 4.0)
           (if (<= z 2.15e-122)
             (* x -3.0)
             (if (<= z 7e-7) (* 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 <= -0.65) {
		tmp = t_0;
	} else if (z <= -1.75e-128) {
		tmp = y * 4.0;
	} else if (z <= -2.8e-261) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-265) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-122) {
		tmp = x * -3.0;
	} else if (z <= 7e-7) {
		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 <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-1.75d-128)) then
        tmp = y * 4.0d0
    else if (z <= (-2.8d-261)) then
        tmp = x * (-3.0d0)
    else if (z <= 5.8d-265) then
        tmp = y * 4.0d0
    else if (z <= 2.15d-122) then
        tmp = x * (-3.0d0)
    else if (z <= 7d-7) 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 <= -0.65) {
		tmp = t_0;
	} else if (z <= -1.75e-128) {
		tmp = y * 4.0;
	} else if (z <= -2.8e-261) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-265) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-122) {
		tmp = x * -3.0;
	} else if (z <= 7e-7) {
		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 <= -0.65:
		tmp = t_0
	elif z <= -1.75e-128:
		tmp = y * 4.0
	elif z <= -2.8e-261:
		tmp = x * -3.0
	elif z <= 5.8e-265:
		tmp = y * 4.0
	elif z <= 2.15e-122:
		tmp = x * -3.0
	elif z <= 7e-7:
		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 <= -0.65)
		tmp = t_0;
	elseif (z <= -1.75e-128)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.8e-261)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.8e-265)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.15e-122)
		tmp = Float64(x * -3.0);
	elseif (z <= 7e-7)
		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 <= -0.65)
		tmp = t_0;
	elseif (z <= -1.75e-128)
		tmp = y * 4.0;
	elseif (z <= -2.8e-261)
		tmp = x * -3.0;
	elseif (z <= 5.8e-265)
		tmp = y * 4.0;
	elseif (z <= 2.15e-122)
		tmp = x * -3.0;
	elseif (z <= 7e-7)
		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, -0.65], t$95$0, If[LessEqual[z, -1.75e-128], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.8e-261], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.8e-265], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.15e-122], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7e-7], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022 or 6.99999999999999968e-7 < z

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 51.2%

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

   6. Taylor expanded in z around inf 50.6%

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

   if -0.650000000000000022 < z < -1.75e-128 or -2.80000000000000009e-261 < z < 5.7999999999999995e-265 or 2.15000000000000009e-122 < z < 6.99999999999999968e-7

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 69.2%

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

   6. Taylor expanded in z around 0 68.9%

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

   if -1.75e-128 < z < -2.80000000000000009e-261 or 5.7999999999999995e-265 < z < 2.15000000000000009e-122

   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. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. cancel-sign-sub-inv 77.7%

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

      5. *-commutative 77.7%

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

      6. cancel-sign-sub-inv 77.7%

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

      7. distribute-lft-neg-in 77.7%

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

      8. *-commutative 77.7%

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

      9. distribute-lft-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

      11. sub-neg 77.7%

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

      12. distribute-lft-in 77.7%

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

      13. metadata-eval 77.7%

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

      14. neg-mul-1 77.7%

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

      15. *-commutative 77.7%

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

      16. associate-*l* 77.7%

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

      17. associate-+r+ 77.7%

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

      18. metadata-eval 77.7%

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

      19. *-commutative 77.7%

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

      20. associate-*l* 77.7%

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

      21. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around 0 77.7%

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

      1. *-commutative 77.7%

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

   10. Simplified 77.7%

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

Alternative 9: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+44} \lor \neg \left(y \leq 4.8 \cdot 10^{-58} \lor \neg \left(y \leq 4.2 \cdot 10^{+107}\right) \land y \leq 9.2 \cdot 10^{+128}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e+44)
         (not (or (<= y 4.8e-58) (and (not (<= y 4.2e+107)) (<= y 9.2e+128)))))
   (* y (+ 4.0 (* z -6.0)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+44) || !((y <= 4.8e-58) || (!(y <= 4.2e+107) && (y <= 9.2e+128)))) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7d+44)) .or. (.not. (y <= 4.8d-58) .or. (.not. (y <= 4.2d+107)) .and. (y <= 9.2d+128))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+44) || !((y <= 4.8e-58) || (!(y <= 4.2e+107) && (y <= 9.2e+128)))) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e+44) or not ((y <= 4.8e-58) or (not (y <= 4.2e+107) and (y <= 9.2e+128))):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e+44) || !((y <= 4.8e-58) || (!(y <= 4.2e+107) && (y <= 9.2e+128))))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e+44) || ~(((y <= 4.8e-58) || (~((y <= 4.2e+107)) && (y <= 9.2e+128)))))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e+44], N[Not[Or[LessEqual[y, 4.8e-58], And[N[Not[LessEqual[y, 4.2e+107]], $MachinePrecision], LessEqual[y, 9.2e+128]]]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999998e44 or 4.8000000000000001e-58 < y < 4.1999999999999999e107 or 9.19999999999999992e128 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 84.3%

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

   if -6.9999999999999998e44 < y < 4.8000000000000001e-58 or 4.1999999999999999e107 < y < 9.19999999999999992e128

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. +-commutative 77.1%

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

      3. metadata-eval 77.1%

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

      4. cancel-sign-sub-inv 77.1%

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

      5. *-commutative 77.1%

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

      6. cancel-sign-sub-inv 77.1%

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

      7. distribute-lft-neg-in 77.1%

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

      8. *-commutative 77.1%

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

      9. distribute-lft-neg-in 77.1%

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

      10. metadata-eval 77.1%

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

      11. sub-neg 77.1%

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

      12. distribute-lft-in 77.1%

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

      13. metadata-eval 77.1%

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

      14. neg-mul-1 77.1%

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

      15. *-commutative 77.1%

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

      16. associate-*l* 77.1%

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

      17. associate-+r+ 77.1%

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

      18. metadata-eval 77.1%

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

      19. *-commutative 77.1%

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

      20. associate-*l* 77.1%

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

      21. metadata-eval 77.1%

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

   7. Simplified 77.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+44} \lor \neg \left(y \leq 4.8 \cdot 10^{-58} \lor \neg \left(y \leq 4.2 \cdot 10^{+107}\right) \land y \leq 9.2 \cdot 10^{+128}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot -6\right)\\ t_1 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-304}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-235}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-122}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y -6.0))) (t_1 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -1.4e-59)
     t_1
     (if (<= x -2.6e-304)
       t_0
       (if (<= x 1.65e-235) (* y 4.0) (if (<= x 8e-122) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * -6.0);
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.4e-59) {
		tmp = t_1;
	} else if (x <= -2.6e-304) {
		tmp = t_0;
	} else if (x <= 1.65e-235) {
		tmp = y * 4.0;
	} else if (x <= 8e-122) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * (y * (-6.0d0))
    t_1 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-1.4d-59)) then
        tmp = t_1
    else if (x <= (-2.6d-304)) then
        tmp = t_0
    else if (x <= 1.65d-235) then
        tmp = y * 4.0d0
    else if (x <= 8d-122) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * -6.0);
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.4e-59) {
		tmp = t_1;
	} else if (x <= -2.6e-304) {
		tmp = t_0;
	} else if (x <= 1.65e-235) {
		tmp = y * 4.0;
	} else if (x <= 8e-122) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * -6.0)
	t_1 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -1.4e-59:
		tmp = t_1
	elif x <= -2.6e-304:
		tmp = t_0
	elif x <= 1.65e-235:
		tmp = y * 4.0
	elif x <= 8e-122:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * -6.0))
	t_1 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -1.4e-59)
		tmp = t_1;
	elseif (x <= -2.6e-304)
		tmp = t_0;
	elseif (x <= 1.65e-235)
		tmp = Float64(y * 4.0);
	elseif (x <= 8e-122)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * -6.0);
	t_1 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -1.4e-59)
		tmp = t_1;
	elseif (x <= -2.6e-304)
		tmp = t_0;
	elseif (x <= 1.65e-235)
		tmp = y * 4.0;
	elseif (x <= 8e-122)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e-59], t$95$1, If[LessEqual[x, -2.6e-304], t$95$0, If[LessEqual[x, 1.65e-235], N[(y * 4.0), $MachinePrecision], If[LessEqual[x, 8e-122], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999e-59 or 8.00000000000000047e-122 < x

   1. Initial program 99.1%

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

      1. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. +-commutative 70.7%

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

      3. metadata-eval 70.7%

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

      4. cancel-sign-sub-inv 70.7%

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

      5. *-commutative 70.7%

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

      6. cancel-sign-sub-inv 70.7%

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

      7. distribute-lft-neg-in 70.7%

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

      8. *-commutative 70.7%

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

      9. distribute-lft-neg-in 70.7%

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

      10. metadata-eval 70.7%

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

      11. sub-neg 70.7%

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

      12. distribute-lft-in 70.7%

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

      13. metadata-eval 70.7%

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

      14. neg-mul-1 70.7%

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

      15. *-commutative 70.7%

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

      16. associate-*l* 70.7%

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

      17. associate-+r+ 70.7%

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

      18. metadata-eval 70.7%

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

      19. *-commutative 70.7%

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

      20. associate-*l* 70.7%

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

      21. metadata-eval 70.7%

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

   7. Simplified 70.7%

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

   if -1.3999999999999999e-59 < x < -2.59999999999999997e-304 or 1.65000000000000014e-235 < x < 8.00000000000000047e-122

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 92.4%

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

   6. Taylor expanded in z around inf 65.9%

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

      1. *-commutative 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in y around inf 57.5%

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

       1. *-commutative 57.5%

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

       2. *-commutative 57.5%

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

       3. associate-*r* 57.6%

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

       4. *-commutative 57.6%

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

   11. Simplified 57.6%

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

   if -2.59999999999999997e-304 < x < 1.65000000000000014e-235

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 100.0%

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

      3. fma-define 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in z around 0 73.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-235}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.5)))
   (* (- y x) (* z -6.0))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.5)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.58d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.5)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.5):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.5))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.5)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 98.2%

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

      1. *-commutative 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in z around 0 98.1%

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

       1. associate-*r* 98.2%

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

       2. *-commutative 98.2%

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

   11. Simplified 98.2%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 98.7%

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

      1. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in z around 0 99.4%

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

6. Final simplification 99.4%

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

Alternative 13: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-120} \lor \neg \left(y \leq 1.1 \cdot 10^{-57}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e-120) (not (<= y 1.1e-57))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e-120) || !(y <= 1.1e-57)) {
		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 ((y <= (-5.9d-120)) .or. (.not. (y <= 1.1d-57))) 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 ((y <= -5.9e-120) || !(y <= 1.1e-57)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e-120) or not (y <= 1.1e-57):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e-120) || !(y <= 1.1e-57))
		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 ((y <= -5.9e-120) || ~((y <= 1.1e-57)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e-120], N[Not[LessEqual[y, 1.1e-57]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.89999999999999979e-120 or 1.09999999999999999e-57 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 73.1%

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

   6. Taylor expanded in z around 0 33.2%

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

   if -5.89999999999999979e-120 < y < 1.09999999999999999e-57

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. +-commutative 83.5%

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

      3. metadata-eval 83.5%

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

      4. cancel-sign-sub-inv 83.5%

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

      5. *-commutative 83.5%

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

      6. cancel-sign-sub-inv 83.5%

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

      7. distribute-lft-neg-in 83.5%

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

      8. *-commutative 83.5%

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

      9. distribute-lft-neg-in 83.5%

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

      10. metadata-eval 83.5%

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

      11. sub-neg 83.5%

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

      12. distribute-lft-in 83.6%

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

      13. metadata-eval 83.6%

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

      14. neg-mul-1 83.6%

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

      15. *-commutative 83.6%

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

      16. associate-*l* 83.6%

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

      17. associate-+r+ 83.6%

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

      18. metadata-eval 83.6%

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

      19. *-commutative 83.6%

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

      20. associate-*l* 83.6%

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

      21. metadata-eval 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in z around 0 34.1%

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

      1. *-commutative 34.1%

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

   10. Simplified 34.1%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-120} \lor \neg \left(y \leq 1.1 \cdot 10^{-57}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

Alternative 15: 26.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in x around inf 52.2%

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

   1. +-commutative 52.2%

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

   2. +-commutative 52.2%

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

   3. metadata-eval 52.2%

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

   4. cancel-sign-sub-inv 52.2%

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

   5. *-commutative 52.2%

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

   6. cancel-sign-sub-inv 52.2%

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

   7. distribute-lft-neg-in 52.2%

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

   8. *-commutative 52.2%

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

   9. distribute-lft-neg-in 52.2%

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

   10. metadata-eval 52.2%

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

   11. sub-neg 52.2%

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

   12. distribute-lft-in 52.2%

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

   13. metadata-eval 52.2%

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

   14. neg-mul-1 52.2%

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

   15. *-commutative 52.2%

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

   16. associate-*l* 52.2%

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

   17. associate-+r+ 52.2%

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

   18. metadata-eval 52.2%

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

   19. *-commutative 52.2%

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

   20. associate-*l* 52.2%

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

   21. metadata-eval 52.2%

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

7. Simplified 52.2%

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

8. Taylor expanded in z around 0 22.3%

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

   1. *-commutative 22.3%

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

10. Simplified 22.3%

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

Alternative 16: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in z around inf 57.4%

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

6. Taylor expanded in z around 0 2.9%

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

Reproduce

herbie shell --seed 2024085 
(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))))