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

Percentage Accurate: 99.5% → 99.8%

Time: 15.0s

Alternatives: 15

Speedup: 1.2×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x + y \cdot 4\\ \mathbf{if}\;z \leq -5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4500:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (+ x (* y 4.0))))
   (if (<= z -5e+51)
     (* y (* z -6.0))
     (if (<= z -4500.0)
       (* z (* x 6.0))
       (if (<= z -7.5)
         t_0
         (if (<= z -4.5e-295)
           (* x -3.0)
           (if (<= z 4.6e-101)
             t_1
             (if (<= z 8e-72)
               (* x -3.0)
               (if (<= z 1.05)
                 t_1
                 (if (<= z 6.5e+85) t_0 (* 6.0 (* x z))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x + (y * 4.0);
	double tmp;
	if (z <= -5e+51) {
		tmp = y * (z * -6.0);
	} else if (z <= -4500.0) {
		tmp = z * (x * 6.0);
	} else if (z <= -7.5) {
		tmp = t_0;
	} else if (z <= -4.5e-295) {
		tmp = x * -3.0;
	} else if (z <= 4.6e-101) {
		tmp = t_1;
	} else if (z <= 8e-72) {
		tmp = x * -3.0;
	} else if (z <= 1.05) {
		tmp = t_1;
	} else if (z <= 6.5e+85) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x + (y * 4.0d0)
    if (z <= (-5d+51)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-4500.0d0)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-7.5d0)) then
        tmp = t_0
    else if (z <= (-4.5d-295)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.6d-101) then
        tmp = t_1
    else if (z <= 8d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d0) then
        tmp = t_1
    else if (z <= 6.5d+85) then
        tmp = t_0
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x + (y * 4.0);
	double tmp;
	if (z <= -5e+51) {
		tmp = y * (z * -6.0);
	} else if (z <= -4500.0) {
		tmp = z * (x * 6.0);
	} else if (z <= -7.5) {
		tmp = t_0;
	} else if (z <= -4.5e-295) {
		tmp = x * -3.0;
	} else if (z <= 4.6e-101) {
		tmp = t_1;
	} else if (z <= 8e-72) {
		tmp = x * -3.0;
	} else if (z <= 1.05) {
		tmp = t_1;
	} else if (z <= 6.5e+85) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x + (y * 4.0)
	tmp = 0
	if z <= -5e+51:
		tmp = y * (z * -6.0)
	elif z <= -4500.0:
		tmp = z * (x * 6.0)
	elif z <= -7.5:
		tmp = t_0
	elif z <= -4.5e-295:
		tmp = x * -3.0
	elif z <= 4.6e-101:
		tmp = t_1
	elif z <= 8e-72:
		tmp = x * -3.0
	elif z <= 1.05:
		tmp = t_1
	elif z <= 6.5e+85:
		tmp = t_0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x + Float64(y * 4.0))
	tmp = 0.0
	if (z <= -5e+51)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -4500.0)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -7.5)
		tmp = t_0;
	elseif (z <= -4.5e-295)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.6e-101)
		tmp = t_1;
	elseif (z <= 8e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05)
		tmp = t_1;
	elseif (z <= 6.5e+85)
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x + (y * 4.0);
	tmp = 0.0;
	if (z <= -5e+51)
		tmp = y * (z * -6.0);
	elseif (z <= -4500.0)
		tmp = z * (x * 6.0);
	elseif (z <= -7.5)
		tmp = t_0;
	elseif (z <= -4.5e-295)
		tmp = x * -3.0;
	elseif (z <= 4.6e-101)
		tmp = t_1;
	elseif (z <= 8e-72)
		tmp = x * -3.0;
	elseif (z <= 1.05)
		tmp = t_1;
	elseif (z <= 6.5e+85)
		tmp = t_0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+51], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4500.0], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5], t$95$0, If[LessEqual[z, -4.5e-295], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.6e-101], t$95$1, If[LessEqual[z, 8e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05], t$95$1, If[LessEqual[z, 6.5e+85], t$95$0, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5e51

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 59.2%

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

       1. *-commutative 59.2%

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

       2. associate-*r* 61.1%

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

       3. *-commutative 61.1%

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

   11. Simplified 61.1%

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

   if -5e51 < z < -4500

   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. Taylor expanded in x around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. +-commutative 82.3%

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

      3. sub-neg 82.3%

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

      4. distribute-rgt-in 82.0%

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

      5. metadata-eval 82.0%

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

      6. metadata-eval 82.0%

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

      7. neg-mul-1 82.0%

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

      8. associate-*r* 82.0%

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

      9. *-commutative 82.0%

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

      10. distribute-lft-in 82.0%

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

      11. +-commutative 82.0%

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

      12. distribute-lft-in 82.0%

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

      13. associate-+r+ 82.0%

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

      14. metadata-eval 82.0%

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

      15. metadata-eval 82.0%

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

      16. metadata-eval 82.0%

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

      17. distribute-lft-in 82.0%

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

      18. +-commutative 82.0%

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

      19. distribute-rgt-in 82.0%

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

      20. *-commutative 82.0%

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

      21. associate-*l* 82.0%

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

      22. metadata-eval 82.0%

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

      23. metadata-eval 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in z around inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*r* 70.9%

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

   9. Simplified 70.9%

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

   if -4500 < z < -7.5 or 1.05000000000000004 < z < 6.4999999999999994e85

   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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 92.6%

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

   7. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   9. Simplified 69.9%

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

   if -7.5 < z < -4.5000000000000002e-295 or 4.5999999999999999e-101 < z < 7.9999999999999997e-72

   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. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. +-commutative 64.4%

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

      3. sub-neg 64.4%

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

      4. distribute-rgt-in 64.4%

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

      5. metadata-eval 64.4%

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

      6. metadata-eval 64.4%

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

      7. neg-mul-1 64.4%

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

      8. associate-*r* 64.4%

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

      9. *-commutative 64.4%

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

      10. distribute-lft-in 64.4%

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

      11. +-commutative 64.4%

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

      12. distribute-lft-in 64.4%

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

      13. associate-+r+ 64.4%

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

      14. metadata-eval 64.4%

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

      15. metadata-eval 64.4%

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

      16. metadata-eval 64.4%

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

      17. distribute-lft-in 64.4%

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

      18. +-commutative 64.4%

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

      19. distribute-rgt-in 64.4%

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

      20. *-commutative 64.4%

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

      21. associate-*l* 64.4%

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

      22. metadata-eval 64.4%

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

      23. metadata-eval 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -4.5000000000000002e-295 < z < 4.5999999999999999e-101 or 7.9999999999999997e-72 < z < 1.05000000000000004

   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. Taylor expanded in y around inf 65.9%

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

      1. associate-*r* 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in z around 0 65.5%

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

   if 6.4999999999999994e85 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. +-commutative 66.9%

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

      3. sub-neg 66.9%

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

      4. distribute-rgt-in 66.9%

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

      5. metadata-eval 66.9%

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

      6. metadata-eval 66.9%

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

      7. neg-mul-1 66.9%

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

      8. associate-*r* 66.9%

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

      9. *-commutative 66.9%

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

      10. distribute-lft-in 66.9%

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

      11. +-commutative 66.9%

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

      12. distribute-lft-in 66.9%

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

      13. associate-+r+ 66.9%

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

      14. metadata-eval 66.9%

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

      15. metadata-eval 66.9%

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

      16. metadata-eval 66.9%

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

      17. distribute-lft-in 66.9%

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

      18. +-commutative 66.9%

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

      19. distribute-rgt-in 66.9%

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

      20. *-commutative 66.9%

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

      21. associate-*l* 66.9%

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

      22. metadata-eval 66.9%

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

      23. metadata-eval 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around inf 66.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4500:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.5:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-101}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+85}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1150000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -8.2e+192)
     t_0
     (if (<= z -3.4e+53)
       t_1
       (if (<= z -1150000.0)
         t_0
         (if (<= z -0.8)
           t_1
           (if (<= z 0.6) (* x -3.0) (if (<= z 7e+89) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -8.2e+192) {
		tmp = t_0;
	} else if (z <= -3.4e+53) {
		tmp = t_1;
	} else if (z <= -1150000.0) {
		tmp = t_0;
	} else if (z <= -0.8) {
		tmp = t_1;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else if (z <= 7e+89) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-8.2d+192)) then
        tmp = t_0
    else if (z <= (-3.4d+53)) then
        tmp = t_1
    else if (z <= (-1150000.0d0)) then
        tmp = t_0
    else if (z <= (-0.8d0)) then
        tmp = t_1
    else if (z <= 0.6d0) then
        tmp = x * (-3.0d0)
    else if (z <= 7d+89) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -8.2e+192) {
		tmp = t_0;
	} else if (z <= -3.4e+53) {
		tmp = t_1;
	} else if (z <= -1150000.0) {
		tmp = t_0;
	} else if (z <= -0.8) {
		tmp = t_1;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else if (z <= 7e+89) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -8.2e+192:
		tmp = t_0
	elif z <= -3.4e+53:
		tmp = t_1
	elif z <= -1150000.0:
		tmp = t_0
	elif z <= -0.8:
		tmp = t_1
	elif z <= 0.6:
		tmp = x * -3.0
	elif z <= 7e+89:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -8.2e+192)
		tmp = t_0;
	elseif (z <= -3.4e+53)
		tmp = t_1;
	elseif (z <= -1150000.0)
		tmp = t_0;
	elseif (z <= -0.8)
		tmp = t_1;
	elseif (z <= 0.6)
		tmp = Float64(x * -3.0);
	elseif (z <= 7e+89)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -8.2e+192)
		tmp = t_0;
	elseif (z <= -3.4e+53)
		tmp = t_1;
	elseif (z <= -1150000.0)
		tmp = t_0;
	elseif (z <= -0.8)
		tmp = t_1;
	elseif (z <= 0.6)
		tmp = x * -3.0;
	elseif (z <= 7e+89)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+192], t$95$0, If[LessEqual[z, -3.4e+53], t$95$1, If[LessEqual[z, -1150000.0], t$95$0, If[LessEqual[z, -0.8], t$95$1, If[LessEqual[z, 0.6], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7e+89], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.20000000000000006e192 or -3.39999999999999998e53 < z < -1.15e6 or 7.0000000000000001e89 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 68.0%

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

      1. *-commutative 68.0%

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

      2. +-commutative 68.0%

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

      3. sub-neg 68.0%

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

      4. distribute-rgt-in 68.0%

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

      5. metadata-eval 68.0%

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

      6. metadata-eval 68.0%

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

      7. neg-mul-1 68.0%

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

      8. associate-*r* 68.0%

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

      9. *-commutative 68.0%

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

      10. distribute-lft-in 68.0%

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

      11. +-commutative 68.0%

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

      12. distribute-lft-in 68.0%

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

      13. associate-+r+ 68.0%

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

      14. metadata-eval 68.0%

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

      15. metadata-eval 68.0%

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

      16. metadata-eval 68.0%

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

      17. distribute-lft-in 68.0%

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

      18. +-commutative 68.0%

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

      19. distribute-rgt-in 68.0%

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

      20. *-commutative 68.0%

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

      21. associate-*l* 68.0%

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

      22. metadata-eval 68.0%

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

      23. metadata-eval 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in z around inf 66.9%

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

   if -8.20000000000000006e192 < z < -3.39999999999999998e53 or -1.15e6 < z < -0.80000000000000004 or 0.599999999999999978 < z < 7.0000000000000001e89

   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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around inf 97.7%

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

   7. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

   9. Simplified 69.4%

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

   if -0.80000000000000004 < z < 0.599999999999999978

   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. Taylor expanded in x around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. +-commutative 52.7%

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

      3. sub-neg 52.7%

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

      4. distribute-rgt-in 52.7%

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

      5. metadata-eval 52.7%

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

      6. metadata-eval 52.7%

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

      7. neg-mul-1 52.7%

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

      8. associate-*r* 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-in 52.7%

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

      11. +-commutative 52.7%

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

      12. distribute-lft-in 52.7%

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

      13. associate-+r+ 52.7%

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

      14. metadata-eval 52.7%

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

      15. metadata-eval 52.7%

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

      16. metadata-eval 52.7%

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

      17. distribute-lft-in 52.7%

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

      18. +-commutative 52.7%

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

      19. distribute-rgt-in 52.7%

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

      20. *-commutative 52.7%

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

      21. associate-*l* 52.7%

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

      22. metadata-eval 52.7%

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

      23. metadata-eval 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in z around 0 51.8%

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

      1. *-commutative 51.8%

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

   9. Simplified 51.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+192}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+53}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1150000:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.8:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+89}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(6 \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.65:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* 6.0 z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -5e+193)
     t_0
     (if (<= z -2.5e+51)
       t_1
       (if (<= z -135.0)
         t_0
         (if (<= z -1.65)
           t_1
           (if (<= z 0.68)
             (* x -3.0)
             (if (<= z 2.25e+85) t_1 (* 6.0 (* x z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (6.0 * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -5e+193) {
		tmp = t_0;
	} else if (z <= -2.5e+51) {
		tmp = t_1;
	} else if (z <= -135.0) {
		tmp = t_0;
	} else if (z <= -1.65) {
		tmp = t_1;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else if (z <= 2.25e+85) {
		tmp = t_1;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (6.0d0 * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-5d+193)) then
        tmp = t_0
    else if (z <= (-2.5d+51)) then
        tmp = t_1
    else if (z <= (-135.0d0)) then
        tmp = t_0
    else if (z <= (-1.65d0)) then
        tmp = t_1
    else if (z <= 0.68d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.25d+85) then
        tmp = t_1
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (6.0 * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -5e+193) {
		tmp = t_0;
	} else if (z <= -2.5e+51) {
		tmp = t_1;
	} else if (z <= -135.0) {
		tmp = t_0;
	} else if (z <= -1.65) {
		tmp = t_1;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else if (z <= 2.25e+85) {
		tmp = t_1;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (6.0 * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -5e+193:
		tmp = t_0
	elif z <= -2.5e+51:
		tmp = t_1
	elif z <= -135.0:
		tmp = t_0
	elif z <= -1.65:
		tmp = t_1
	elif z <= 0.68:
		tmp = x * -3.0
	elif z <= 2.25e+85:
		tmp = t_1
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(6.0 * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5e+193)
		tmp = t_0;
	elseif (z <= -2.5e+51)
		tmp = t_1;
	elseif (z <= -135.0)
		tmp = t_0;
	elseif (z <= -1.65)
		tmp = t_1;
	elseif (z <= 0.68)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.25e+85)
		tmp = t_1;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (6.0 * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5e+193)
		tmp = t_0;
	elseif (z <= -2.5e+51)
		tmp = t_1;
	elseif (z <= -135.0)
		tmp = t_0;
	elseif (z <= -1.65)
		tmp = t_1;
	elseif (z <= 0.68)
		tmp = x * -3.0;
	elseif (z <= 2.25e+85)
		tmp = t_1;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+193], t$95$0, If[LessEqual[z, -2.5e+51], t$95$1, If[LessEqual[z, -135.0], t$95$0, If[LessEqual[z, -1.65], t$95$1, If[LessEqual[z, 0.68], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.25e+85], t$95$1, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999972e193 or -2.5e51 < z < -135

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. +-commutative 70.3%

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

      3. sub-neg 70.3%

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

      4. distribute-rgt-in 70.2%

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

      5. metadata-eval 70.2%

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

      6. metadata-eval 70.2%

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

      7. neg-mul-1 70.2%

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

      8. associate-*r* 70.2%

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

      9. *-commutative 70.2%

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

      10. distribute-lft-in 70.2%

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

      11. +-commutative 70.2%

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

      12. distribute-lft-in 70.2%

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

      13. associate-+r+ 70.2%

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

      14. metadata-eval 70.2%

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

      15. metadata-eval 70.2%

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

      16. metadata-eval 70.2%

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

      17. distribute-lft-in 70.2%

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

      18. +-commutative 70.2%

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

      19. distribute-rgt-in 70.2%

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

      20. *-commutative 70.2%

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

      21. associate-*l* 70.2%

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

      22. metadata-eval 70.2%

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

      23. metadata-eval 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

   if -4.99999999999999972e193 < z < -2.5e51 or -135 < z < -1.6499999999999999 or 0.680000000000000049 < z < 2.25000000000000003e85

   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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around inf 97.7%

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

   7. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

   9. Simplified 69.4%

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

   if -1.6499999999999999 < z < 0.680000000000000049

   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. Taylor expanded in x around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. +-commutative 52.7%

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

      3. sub-neg 52.7%

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

      4. distribute-rgt-in 52.7%

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

      5. metadata-eval 52.7%

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

      6. metadata-eval 52.7%

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

      7. neg-mul-1 52.7%

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

      8. associate-*r* 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-in 52.7%

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

      11. +-commutative 52.7%

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

      12. distribute-lft-in 52.7%

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

      13. associate-+r+ 52.7%

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

      14. metadata-eval 52.7%

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

      15. metadata-eval 52.7%

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

      16. metadata-eval 52.7%

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

      17. distribute-lft-in 52.7%

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

      18. +-commutative 52.7%

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

      19. distribute-rgt-in 52.7%

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

      20. *-commutative 52.7%

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

      21. associate-*l* 52.7%

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

      22. metadata-eval 52.7%

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

      23. metadata-eval 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in z around 0 51.8%

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

      1. *-commutative 51.8%

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

   9. Simplified 51.8%

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

   if 2.25000000000000003e85 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. +-commutative 66.9%

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

      3. sub-neg 66.9%

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

      4. distribute-rgt-in 66.9%

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

      5. metadata-eval 66.9%

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

      6. metadata-eval 66.9%

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

      7. neg-mul-1 66.9%

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

      8. associate-*r* 66.9%

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

      9. *-commutative 66.9%

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

      10. distribute-lft-in 66.9%

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

      11. +-commutative 66.9%

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

      12. distribute-lft-in 66.9%

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

      13. associate-+r+ 66.9%

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

      14. metadata-eval 66.9%

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

      15. metadata-eval 66.9%

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

      16. metadata-eval 66.9%

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

      17. distribute-lft-in 66.9%

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

      18. +-commutative 66.9%

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

      19. distribute-rgt-in 66.9%

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

      20. *-commutative 66.9%

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

      21. associate-*l* 66.9%

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

      22. metadata-eval 66.9%

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

      23. metadata-eval 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around inf 66.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+51}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -135:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.65:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+85}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.115:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.115)
     t_1
     (if (<= z -3.8e-294)
       (* x -3.0)
       (if (<= z 2.55e-101)
         t_0
         (if (<= z 8.4e-72) (* x -3.0) (if (<= z 0.68) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.115) {
		tmp = t_1;
	} else if (z <= -3.8e-294) {
		tmp = x * -3.0;
	} else if (z <= 2.55e-101) {
		tmp = t_0;
	} else if (z <= 8.4e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.115d0)) then
        tmp = t_1
    else if (z <= (-3.8d-294)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.55d-101) then
        tmp = t_0
    else if (z <= 8.4d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.115) {
		tmp = t_1;
	} else if (z <= -3.8e-294) {
		tmp = x * -3.0;
	} else if (z <= 2.55e-101) {
		tmp = t_0;
	} else if (z <= 8.4e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.115:
		tmp = t_1
	elif z <= -3.8e-294:
		tmp = x * -3.0
	elif z <= 2.55e-101:
		tmp = t_0
	elif z <= 8.4e-72:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.115)
		tmp = t_1;
	elseif (z <= -3.8e-294)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.55e-101)
		tmp = t_0;
	elseif (z <= 8.4e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.115)
		tmp = t_1;
	elseif (z <= -3.8e-294)
		tmp = x * -3.0;
	elseif (z <= 2.55e-101)
		tmp = t_0;
	elseif (z <= 8.4e-72)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.115], t$95$1, If[LessEqual[z, -3.8e-294], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.55e-101], t$95$0, If[LessEqual[z, 8.4e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.115000000000000005 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 98.2%

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

   if -0.115000000000000005 < z < -3.8e-294 or 2.5500000000000001e-101 < z < 8.4e-72

   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. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. +-commutative 64.4%

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

      3. sub-neg 64.4%

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

      4. distribute-rgt-in 64.4%

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

      5. metadata-eval 64.4%

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

      6. metadata-eval 64.4%

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

      7. neg-mul-1 64.4%

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

      8. associate-*r* 64.4%

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

      9. *-commutative 64.4%

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

      10. distribute-lft-in 64.4%

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

      11. +-commutative 64.4%

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

      12. distribute-lft-in 64.4%

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

      13. associate-+r+ 64.4%

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

      14. metadata-eval 64.4%

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

      15. metadata-eval 64.4%

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

      16. metadata-eval 64.4%

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

      17. distribute-lft-in 64.4%

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

      18. +-commutative 64.4%

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

      19. distribute-rgt-in 64.4%

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

      20. *-commutative 64.4%

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

      21. associate-*l* 64.4%

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

      22. metadata-eval 64.4%

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

      23. metadata-eval 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -3.8e-294 < z < 2.5500000000000001e-101 or 8.4e-72 < z < 0.680000000000000049

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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. Taylor expanded in y around inf 65.9%

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

      1. associate-*r* 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in z around 0 65.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.115:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-101}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ t_1 := x + y \cdot 4\\ \mathbf{if}\;z \leq -1400000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))) (t_1 (+ x (* y 4.0))))
   (if (<= z -1400000000.0)
     t_0
     (if (<= z -2.4e-294)
       (* x (+ -3.0 (* 6.0 z)))
       (if (<= z 2.6e-104)
         t_1
         (if (<= z 6.8e-72) (* x -3.0) (if (<= z 0.68) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double t_1 = x + (y * 4.0);
	double tmp;
	if (z <= -1400000000.0) {
		tmp = t_0;
	} else if (z <= -2.4e-294) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.6e-104) {
		tmp = t_1;
	} else if (z <= 6.8e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    t_1 = x + (y * 4.0d0)
    if (z <= (-1400000000.0d0)) then
        tmp = t_0
    else if (z <= (-2.4d-294)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 2.6d-104) then
        tmp = t_1
    else if (z <= 6.8d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double t_1 = x + (y * 4.0);
	double tmp;
	if (z <= -1400000000.0) {
		tmp = t_0;
	} else if (z <= -2.4e-294) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.6e-104) {
		tmp = t_1;
	} else if (z <= 6.8e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	t_1 = x + (y * 4.0)
	tmp = 0
	if z <= -1400000000.0:
		tmp = t_0
	elif z <= -2.4e-294:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 2.6e-104:
		tmp = t_1
	elif z <= 6.8e-72:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	t_1 = Float64(x + Float64(y * 4.0))
	tmp = 0.0
	if (z <= -1400000000.0)
		tmp = t_0;
	elseif (z <= -2.4e-294)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 2.6e-104)
		tmp = t_1;
	elseif (z <= 6.8e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	t_1 = x + (y * 4.0);
	tmp = 0.0;
	if (z <= -1400000000.0)
		tmp = t_0;
	elseif (z <= -2.4e-294)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 2.6e-104)
		tmp = t_1;
	elseif (z <= 6.8e-72)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1400000000.0], t$95$0, If[LessEqual[z, -2.4e-294], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-104], t$95$1, If[LessEqual[z, 6.8e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4e9 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 99.5%

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

   if -1.4e9 < z < -2.39999999999999997e-294

   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. Taylor expanded in x around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. +-commutative 62.9%

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

      3. sub-neg 62.9%

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

      4. distribute-rgt-in 62.9%

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

      5. metadata-eval 62.9%

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

      6. metadata-eval 62.9%

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

      7. neg-mul-1 62.9%

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

      8. associate-*r* 62.9%

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

      9. *-commutative 62.9%

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

      10. distribute-lft-in 62.9%

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

      11. +-commutative 62.9%

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

      12. distribute-lft-in 62.9%

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

      13. associate-+r+ 62.9%

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

      14. metadata-eval 62.9%

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

      15. metadata-eval 62.9%

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

      16. metadata-eval 62.9%

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

      17. distribute-lft-in 62.9%

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

      18. +-commutative 62.9%

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

      19. distribute-rgt-in 62.9%

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

      20. *-commutative 62.9%

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

      21. associate-*l* 62.9%

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

      22. metadata-eval 62.9%

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

      23. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   if -2.39999999999999997e-294 < z < 2.60000000000000003e-104 or 6.7999999999999997e-72 < z < 0.680000000000000049

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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. Taylor expanded in y around inf 65.9%

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

      1. associate-*r* 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in z around 0 65.5%

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

   if 2.60000000000000003e-104 < z < 6.7999999999999997e-72

   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. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

      2. +-commutative 78.3%

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

      3. sub-neg 78.3%

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

      4. distribute-rgt-in 78.3%

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

      5. metadata-eval 78.3%

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

      6. metadata-eval 78.3%

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

      7. neg-mul-1 78.3%

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

      8. associate-*r* 78.3%

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

      9. *-commutative 78.3%

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

      10. distribute-lft-in 78.3%

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

      11. +-commutative 78.3%

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

      12. distribute-lft-in 78.3%

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

      13. associate-+r+ 78.3%

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

      14. metadata-eval 78.3%

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

      15. metadata-eval 78.3%

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

      16. metadata-eval 78.3%

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

      17. distribute-lft-in 78.3%

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

      18. +-commutative 78.3%

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

      19. distribute-rgt-in 78.3%

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

      20. *-commutative 78.3%

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

      21. associate-*l* 78.3%

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

      22. metadata-eval 78.3%

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

      23. metadata-eval 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-104}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ \mathbf{if}\;z \leq -410000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))))
   (if (<= z -410000000.0)
     (* z (* (- y x) -6.0))
     (if (<= z -1.16e-294)
       (* x (+ -3.0 (* 6.0 z)))
       (if (<= z 2.45e-104)
         t_0
         (if (<= z 5e-73)
           (* x -3.0)
           (if (<= z 0.68) t_0 (* -6.0 (* (- y x) z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double tmp;
	if (z <= -410000000.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -1.16e-294) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.45e-104) {
		tmp = t_0;
	} else if (z <= 5e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = t_0;
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    if (z <= (-410000000.0d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= (-1.16d-294)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 2.45d-104) then
        tmp = t_0
    else if (z <= 5d-73) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = t_0
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double tmp;
	if (z <= -410000000.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -1.16e-294) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.45e-104) {
		tmp = t_0;
	} else if (z <= 5e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = t_0;
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	tmp = 0
	if z <= -410000000.0:
		tmp = z * ((y - x) * -6.0)
	elif z <= -1.16e-294:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 2.45e-104:
		tmp = t_0
	elif z <= 5e-73:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = t_0
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	tmp = 0.0
	if (z <= -410000000.0)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= -1.16e-294)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 2.45e-104)
		tmp = t_0;
	elseif (z <= 5e-73)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	tmp = 0.0;
	if (z <= -410000000.0)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= -1.16e-294)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 2.45e-104)
		tmp = t_0;
	elseif (z <= 5e-73)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = t_0;
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -410000000.0], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.16e-294], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-104], t$95$0, If[LessEqual[z, 5e-73], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], t$95$0, N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.1e8

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.6%

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

      5. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r* 99.8%

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

      3. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   if -4.1e8 < z < -1.16000000000000006e-294

   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. Taylor expanded in x around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. +-commutative 62.9%

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

      3. sub-neg 62.9%

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

      4. distribute-rgt-in 62.9%

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

      5. metadata-eval 62.9%

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

      6. metadata-eval 62.9%

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

      7. neg-mul-1 62.9%

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

      8. associate-*r* 62.9%

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

      9. *-commutative 62.9%

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

      10. distribute-lft-in 62.9%

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

      11. +-commutative 62.9%

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

      12. distribute-lft-in 62.9%

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

      13. associate-+r+ 62.9%

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

      14. metadata-eval 62.9%

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

      15. metadata-eval 62.9%

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

      16. metadata-eval 62.9%

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

      17. distribute-lft-in 62.9%

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

      18. +-commutative 62.9%

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

      19. distribute-rgt-in 62.9%

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

      20. *-commutative 62.9%

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

      21. associate-*l* 62.9%

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

      22. metadata-eval 62.9%

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

      23. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   if -1.16000000000000006e-294 < z < 2.4500000000000001e-104 or 4.9999999999999998e-73 < z < 0.680000000000000049

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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. Taylor expanded in y around inf 65.9%

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

      1. associate-*r* 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in z around 0 65.5%

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

   if 2.4500000000000001e-104 < z < 4.9999999999999998e-73

   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. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

      2. +-commutative 78.3%

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

      3. sub-neg 78.3%

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

      4. distribute-rgt-in 78.3%

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

      5. metadata-eval 78.3%

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

      6. metadata-eval 78.3%

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

      7. neg-mul-1 78.3%

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

      8. associate-*r* 78.3%

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

      9. *-commutative 78.3%

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

      10. distribute-lft-in 78.3%

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

      11. +-commutative 78.3%

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

      12. distribute-lft-in 78.3%

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

      13. associate-+r+ 78.3%

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

      14. metadata-eval 78.3%

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

      15. metadata-eval 78.3%

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

      16. metadata-eval 78.3%

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

      17. distribute-lft-in 78.3%

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

      18. +-commutative 78.3%

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

      19. distribute-rgt-in 78.3%

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

      20. *-commutative 78.3%

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

      21. associate-*l* 78.3%

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

      22. metadata-eval 78.3%

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

      23. metadata-eval 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 99.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-104}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;z \leq -410000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= z -410000000.0)
     (* z (* (- y x) -6.0))
     (if (<= z -9.5e-295)
       (* x (+ -3.0 (* 6.0 z)))
       (if (<= z 1.26e-102)
         t_0
         (if (<= z 6.5e-72)
           (* x -3.0)
           (if (<= z 4.2e+15) t_0 (* -6.0 (* (- y x) z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (z <= -410000000.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -9.5e-295) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 1.26e-102) {
		tmp = t_0;
	} else if (z <= 6.5e-72) {
		tmp = x * -3.0;
	} else if (z <= 4.2e+15) {
		tmp = t_0;
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    if (z <= (-410000000.0d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= (-9.5d-295)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 1.26d-102) then
        tmp = t_0
    else if (z <= 6.5d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d+15) then
        tmp = t_0
    else
        tmp = (-6.0d0) * ((y - x) * z)
    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 tmp;
	if (z <= -410000000.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -9.5e-295) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 1.26e-102) {
		tmp = t_0;
	} else if (z <= 6.5e-72) {
		tmp = x * -3.0;
	} else if (z <= 4.2e+15) {
		tmp = t_0;
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if z <= -410000000.0:
		tmp = z * ((y - x) * -6.0)
	elif z <= -9.5e-295:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 1.26e-102:
		tmp = t_0
	elif z <= 6.5e-72:
		tmp = x * -3.0
	elif z <= 4.2e+15:
		tmp = t_0
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (z <= -410000000.0)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= -9.5e-295)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 1.26e-102)
		tmp = t_0;
	elseif (z <= 6.5e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e+15)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (z <= -410000000.0)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= -9.5e-295)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 1.26e-102)
		tmp = t_0;
	elseif (z <= 6.5e-72)
		tmp = x * -3.0;
	elseif (z <= 4.2e+15)
		tmp = t_0;
	else
		tmp = -6.0 * ((y - x) * z);
	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]}, If[LessEqual[z, -410000000.0], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-295], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e-102], t$95$0, If[LessEqual[z, 6.5e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e+15], t$95$0, N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.1e8

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.6%

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

      5. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r* 99.8%

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

      3. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   if -4.1e8 < z < -9.5e-295

   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. Taylor expanded in x around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. +-commutative 62.9%

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

      3. sub-neg 62.9%

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

      4. distribute-rgt-in 62.9%

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

      5. metadata-eval 62.9%

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

      6. metadata-eval 62.9%

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

      7. neg-mul-1 62.9%

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

      8. associate-*r* 62.9%

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

      9. *-commutative 62.9%

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

      10. distribute-lft-in 62.9%

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

      11. +-commutative 62.9%

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

      12. distribute-lft-in 62.9%

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

      13. associate-+r+ 62.9%

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

      14. metadata-eval 62.9%

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

      15. metadata-eval 62.9%

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

      16. metadata-eval 62.9%

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

      17. distribute-lft-in 62.9%

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

      18. +-commutative 62.9%

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

      19. distribute-rgt-in 62.9%

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

      20. *-commutative 62.9%

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

      21. associate-*l* 62.9%

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

      22. metadata-eval 62.9%

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

      23. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   if -9.5e-295 < z < 1.2600000000000001e-102 or 6.4999999999999997e-72 < z < 4.2e15

   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-def 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. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. distribute-rgt-neg-out 99.9%

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

      8. distribute-lft-neg-in 99.9%

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

      9. *-commutative 99.9%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 68.3%

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

   if 1.2600000000000001e-102 < z < 6.4999999999999997e-72

   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. Taylor expanded in x around inf 78.3%

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

      1. *-commutative 78.3%

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

      2. +-commutative 78.3%

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

      3. sub-neg 78.3%

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

      4. distribute-rgt-in 78.3%

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

      5. metadata-eval 78.3%

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

      6. metadata-eval 78.3%

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

      7. neg-mul-1 78.3%

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

      8. associate-*r* 78.3%

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

      9. *-commutative 78.3%

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

      10. distribute-lft-in 78.3%

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

      11. +-commutative 78.3%

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

      12. distribute-lft-in 78.3%

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

      13. associate-+r+ 78.3%

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

      14. metadata-eval 78.3%

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

      15. metadata-eval 78.3%

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

      16. metadata-eval 78.3%

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

      17. distribute-lft-in 78.3%

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

      18. +-commutative 78.3%

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

      19. distribute-rgt-in 78.3%

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

      20. *-commutative 78.3%

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

      21. associate-*l* 78.3%

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

      22. metadata-eval 78.3%

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

      23. metadata-eval 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if 4.2e15 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 99.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 9: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1600:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.4:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.6e+52)
     (* y (* z -6.0))
     (if (<= z -1600.0)
       (* x (* 6.0 z))
       (if (<= z -1.4)
         t_0
         (if (<= z 0.68)
           (* x -3.0)
           (if (<= z 4.4e+89) t_0 (* 6.0 (* x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.6e+52) {
		tmp = y * (z * -6.0);
	} else if (z <= -1600.0) {
		tmp = x * (6.0 * z);
	} else if (z <= -1.4) {
		tmp = t_0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else if (z <= 4.4e+89) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-2.6d+52)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1600.0d0)) then
        tmp = x * (6.0d0 * z)
    else if (z <= (-1.4d0)) then
        tmp = t_0
    else if (z <= 0.68d0) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d+89) then
        tmp = t_0
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.6e+52) {
		tmp = y * (z * -6.0);
	} else if (z <= -1600.0) {
		tmp = x * (6.0 * z);
	} else if (z <= -1.4) {
		tmp = t_0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else if (z <= 4.4e+89) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.6e+52:
		tmp = y * (z * -6.0)
	elif z <= -1600.0:
		tmp = x * (6.0 * z)
	elif z <= -1.4:
		tmp = t_0
	elif z <= 0.68:
		tmp = x * -3.0
	elif z <= 4.4e+89:
		tmp = t_0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.6e+52)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1600.0)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= -1.4)
		tmp = t_0;
	elseif (z <= 0.68)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e+89)
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.6e+52)
		tmp = y * (z * -6.0);
	elseif (z <= -1600.0)
		tmp = x * (6.0 * z);
	elseif (z <= -1.4)
		tmp = t_0;
	elseif (z <= 0.68)
		tmp = x * -3.0;
	elseif (z <= 4.4e+89)
		tmp = t_0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+52], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1600.0], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4], t$95$0, If[LessEqual[z, 0.68], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e+89], t$95$0, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6e52

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 59.2%

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

       1. *-commutative 59.2%

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

       2. associate-*r* 61.1%

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

       3. *-commutative 61.1%

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

   11. Simplified 61.1%

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

   if -2.6e52 < z < -1600

   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. Taylor expanded in x around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. +-commutative 82.3%

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

      3. sub-neg 82.3%

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

      4. distribute-rgt-in 82.0%

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

      5. metadata-eval 82.0%

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

      6. metadata-eval 82.0%

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

      7. neg-mul-1 82.0%

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

      8. associate-*r* 82.0%

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

      9. *-commutative 82.0%

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

      10. distribute-lft-in 82.0%

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

      11. +-commutative 82.0%

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

      12. distribute-lft-in 82.0%

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

      13. associate-+r+ 82.0%

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

      14. metadata-eval 82.0%

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

      15. metadata-eval 82.0%

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

      16. metadata-eval 82.0%

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

      17. distribute-lft-in 82.0%

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

      18. +-commutative 82.0%

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

      19. distribute-rgt-in 82.0%

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

      20. *-commutative 82.0%

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

      21. associate-*l* 82.0%

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

      22. metadata-eval 82.0%

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

      23. metadata-eval 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in z around inf 70.7%

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

      1. *-commutative 70.7%

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

   9. Simplified 70.7%

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

   if -1600 < z < -1.3999999999999999 or 0.680000000000000049 < z < 4.4e89

   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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 92.6%

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

   7. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   9. Simplified 69.9%

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

   if -1.3999999999999999 < z < 0.680000000000000049

   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. Taylor expanded in x around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. +-commutative 52.7%

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

      3. sub-neg 52.7%

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

      4. distribute-rgt-in 52.7%

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

      5. metadata-eval 52.7%

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

      6. metadata-eval 52.7%

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

      7. neg-mul-1 52.7%

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

      8. associate-*r* 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-in 52.7%

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

      11. +-commutative 52.7%

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

      12. distribute-lft-in 52.7%

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

      13. associate-+r+ 52.7%

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

      14. metadata-eval 52.7%

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

      15. metadata-eval 52.7%

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

      16. metadata-eval 52.7%

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

      17. distribute-lft-in 52.7%

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

      18. +-commutative 52.7%

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

      19. distribute-rgt-in 52.7%

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

      20. *-commutative 52.7%

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

      21. associate-*l* 52.7%

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

      22. metadata-eval 52.7%

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

      23. metadata-eval 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in z around 0 51.8%

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

      1. *-commutative 51.8%

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

   9. Simplified 51.8%

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

   if 4.4e89 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. +-commutative 66.9%

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

      3. sub-neg 66.9%

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

      4. distribute-rgt-in 66.9%

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

      5. metadata-eval 66.9%

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

      6. metadata-eval 66.9%

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

      7. neg-mul-1 66.9%

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

      8. associate-*r* 66.9%

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

      9. *-commutative 66.9%

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

      10. distribute-lft-in 66.9%

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

      11. +-commutative 66.9%

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

      12. distribute-lft-in 66.9%

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

      13. associate-+r+ 66.9%

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

      14. metadata-eval 66.9%

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

      15. metadata-eval 66.9%

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

      16. metadata-eval 66.9%

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

      17. distribute-lft-in 66.9%

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

      18. +-commutative 66.9%

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

      19. distribute-rgt-in 66.9%

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

      20. *-commutative 66.9%

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

      21. associate-*l* 66.9%

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

      22. metadata-eval 66.9%

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

      23. metadata-eval 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around inf 66.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1600:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.4:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+89}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 10: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1600:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.95:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -4.5e+52)
     (* y (* z -6.0))
     (if (<= z -1600.0)
       (* z (* x 6.0))
       (if (<= z -0.95)
         t_0
         (if (<= z 0.5)
           (* x -3.0)
           (if (<= z 8.6e+85) t_0 (* 6.0 (* x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.5e+52) {
		tmp = y * (z * -6.0);
	} else if (z <= -1600.0) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.95) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 8.6e+85) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-4.5d+52)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1600.0d0)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-0.95d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 8.6d+85) then
        tmp = t_0
    else
        tmp = 6.0d0 * (x * z)
    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 <= -4.5e+52) {
		tmp = y * (z * -6.0);
	} else if (z <= -1600.0) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.95) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 8.6e+85) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -4.5e+52:
		tmp = y * (z * -6.0)
	elif z <= -1600.0:
		tmp = z * (x * 6.0)
	elif z <= -0.95:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 8.6e+85:
		tmp = t_0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.5e+52)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1600.0)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -0.95)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.6e+85)
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.5e+52)
		tmp = y * (z * -6.0);
	elseif (z <= -1600.0)
		tmp = z * (x * 6.0);
	elseif (z <= -0.95)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 8.6e+85)
		tmp = t_0;
	else
		tmp = 6.0 * (x * z);
	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, -4.5e+52], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1600.0], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.95], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.6e+85], t$95$0, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5e52

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 59.2%

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

       1. *-commutative 59.2%

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

       2. associate-*r* 61.1%

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

       3. *-commutative 61.1%

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

   11. Simplified 61.1%

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

   if -4.5e52 < z < -1600

   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. Taylor expanded in x around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. +-commutative 82.3%

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

      3. sub-neg 82.3%

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

      4. distribute-rgt-in 82.0%

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

      5. metadata-eval 82.0%

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

      6. metadata-eval 82.0%

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

      7. neg-mul-1 82.0%

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

      8. associate-*r* 82.0%

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

      9. *-commutative 82.0%

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

      10. distribute-lft-in 82.0%

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

      11. +-commutative 82.0%

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

      12. distribute-lft-in 82.0%

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

      13. associate-+r+ 82.0%

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

      14. metadata-eval 82.0%

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

      15. metadata-eval 82.0%

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

      16. metadata-eval 82.0%

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

      17. distribute-lft-in 82.0%

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

      18. +-commutative 82.0%

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

      19. distribute-rgt-in 82.0%

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

      20. *-commutative 82.0%

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

      21. associate-*l* 82.0%

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

      22. metadata-eval 82.0%

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

      23. metadata-eval 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in z around inf 70.7%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*r* 70.9%

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

   9. Simplified 70.9%

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

   if -1600 < z < -0.94999999999999996 or 0.5 < z < 8.5999999999999998e85

   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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 92.6%

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

   7. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   9. Simplified 69.9%

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

   if -0.94999999999999996 < z < 0.5

   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. Taylor expanded in x around inf 52.7%

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

      1. *-commutative 52.7%

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

      2. +-commutative 52.7%

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

      3. sub-neg 52.7%

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

      4. distribute-rgt-in 52.7%

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

      5. metadata-eval 52.7%

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

      6. metadata-eval 52.7%

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

      7. neg-mul-1 52.7%

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

      8. associate-*r* 52.7%

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

      9. *-commutative 52.7%

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

      10. distribute-lft-in 52.7%

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

      11. +-commutative 52.7%

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

      12. distribute-lft-in 52.7%

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

      13. associate-+r+ 52.7%

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

      14. metadata-eval 52.7%

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

      15. metadata-eval 52.7%

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

      16. metadata-eval 52.7%

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

      17. distribute-lft-in 52.7%

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

      18. +-commutative 52.7%

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

      19. distribute-rgt-in 52.7%

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

      20. *-commutative 52.7%

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

      21. associate-*l* 52.7%

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

      22. metadata-eval 52.7%

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

      23. metadata-eval 52.7%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in z around 0 51.8%

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

      1. *-commutative 51.8%

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

   9. Simplified 51.8%

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

   if 8.5999999999999998e85 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. +-commutative 66.9%

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

      3. sub-neg 66.9%

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

      4. distribute-rgt-in 66.9%

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

      5. metadata-eval 66.9%

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

      6. metadata-eval 66.9%

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

      7. neg-mul-1 66.9%

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

      8. associate-*r* 66.9%

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

      9. *-commutative 66.9%

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

      10. distribute-lft-in 66.9%

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

      11. +-commutative 66.9%

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

      12. distribute-lft-in 66.9%

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

      13. associate-+r+ 66.9%

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

      14. metadata-eval 66.9%

          \[\leadsto x \cdot \left(\left(1 + \color{blue}{-4}\right) + -1 \cdot \left(-6 \cdot z\right)\right) \]

      15. metadata-eval 66.9%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      16. metadata-eval 66.9%

          \[\leadsto x \cdot \left(\color{blue}{-1 \cdot 3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. distribute-lft-in 66.9%

          \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(3 + -6 \cdot z\right)\right)} \]

      18. +-commutative 66.9%

          \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(-6 \cdot z + 3\right)}\right) \]

      19. distribute-rgt-in 66.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot -1 + 3 \cdot -1\right)} \]

      20. *-commutative 66.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(z \cdot -6\right)} \cdot -1 + 3 \cdot -1\right) \]

      21. associate-*l* 66.9%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-6 \cdot -1\right)} + 3 \cdot -1\right) \]

      22. metadata-eval 66.9%

          \[\leadsto x \cdot \left(z \cdot \color{blue}{6} + 3 \cdot -1\right) \]

      23. metadata-eval 66.9%

          \[\leadsto x \cdot \left(z \cdot 6 + \color{blue}{-3}\right) \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot 6 + -3\right)} \]

   7. Taylor expanded in z around inf 66.9%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1600:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.95:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+85}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* z (* (- y x) -6.0))
   (if (<= z 0.55) (+ (* y 4.0) (* x -3.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.55d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.55:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.55)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.55)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. associate-*l* 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6} + x \]

      5. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right)} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right)} \]

   6. Taylor expanded in z around inf 97.1%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 97.1%

         \[\leadsto \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot -6} \]

      2. associate-*r* 97.2%

         \[\leadsto \color{blue}{z \cdot \left(\left(y - x\right) \cdot -6\right)} \]

      3. *-commutative 97.2%

         \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]

   8. Simplified 97.2%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -0.55000000000000004 < z < 0.55000000000000004

   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. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 + -6 \cdot \left(0.6666666666666666 - z\right), x, 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. associate-*r* 99.7%

         \[\leadsto \mathsf{fma}\left(1 + -6 \cdot \left(0.6666666666666666 - z\right), x, \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)}\right) \]

   6. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 + -6 \cdot \left(0.6666666666666666 - z\right), x, \left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)\right)} \]

   7. Taylor expanded in z around 0 98.6%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.55000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot 6\right)} + x \]

      4. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6} + x \]

      5. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right)} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right)} \]

   6. Taylor expanded in z around inf 99.4%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 12: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- 0.6666666666666666 z) (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(0.6666666666666666 - z) * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(0.6666666666666666 - z), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. 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. Final simplification 99.6%

   \[\leadsto x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \]

Alternative 13: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95) (not (<= z 0.55))) (* -6.0 (* y z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95) || !(z <= 0.55)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.95d0)) .or. (.not. (z <= 0.55d0))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95) || !(z <= 0.55)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95) or not (z <= 0.55):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95) || !(z <= 0.55))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.95) || ~((z <= 0.55)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95], N[Not[LessEqual[z, 0.55]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999996 or 0.55000000000000004 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6} + x \]

      5. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right)} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right), 6, x\right)} \]

   6. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   7. Taylor expanded in y around inf 49.3%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 49.3%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -1.94999999999999996 < z < 0.55000000000000004

   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. Taylor expanded in x around inf 52.7%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 52.7%

         \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

      2. +-commutative 52.7%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right) + 1\right)} \]

      3. sub-neg 52.7%

         \[\leadsto x \cdot \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)} + 1\right) \]

      4. distribute-rgt-in 52.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} + 1\right) \]

      5. metadata-eval 52.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{-4} + \left(-z\right) \cdot -6\right) + 1\right) \]

      6. metadata-eval 52.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{-1 \cdot 4} + \left(-z\right) \cdot -6\right) + 1\right) \]

      7. neg-mul-1 52.7%

         \[\leadsto x \cdot \left(\left(-1 \cdot 4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right) + 1\right) \]

      8. associate-*r* 52.7%

         \[\leadsto x \cdot \left(\left(-1 \cdot 4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right) + 1\right) \]

      9. *-commutative 52.7%

         \[\leadsto x \cdot \left(\left(-1 \cdot 4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right) + 1\right) \]

      10. distribute-lft-in 52.7%

          \[\leadsto x \cdot \left(\color{blue}{-1 \cdot \left(4 + -6 \cdot z\right)} + 1\right) \]

      11. +-commutative 52.7%

          \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(4 + -6 \cdot z\right)\right)} \]

      12. distribute-lft-in 52.7%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-1 \cdot 4 + -1 \cdot \left(-6 \cdot z\right)\right)}\right) \]

      13. associate-+r+ 52.7%

          \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot 4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      14. metadata-eval 52.7%

          \[\leadsto x \cdot \left(\left(1 + \color{blue}{-4}\right) + -1 \cdot \left(-6 \cdot z\right)\right) \]

      15. metadata-eval 52.7%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      16. metadata-eval 52.7%

          \[\leadsto x \cdot \left(\color{blue}{-1 \cdot 3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. distribute-lft-in 52.7%

          \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(3 + -6 \cdot z\right)\right)} \]

      18. +-commutative 52.7%

          \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(-6 \cdot z + 3\right)}\right) \]

      19. distribute-rgt-in 52.7%

          \[\leadsto x \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot -1 + 3 \cdot -1\right)} \]

      20. *-commutative 52.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(z \cdot -6\right)} \cdot -1 + 3 \cdot -1\right) \]

      21. associate-*l* 52.7%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-6 \cdot -1\right)} + 3 \cdot -1\right) \]

      22. metadata-eval 52.7%

          \[\leadsto x \cdot \left(z \cdot \color{blue}{6} + 3 \cdot -1\right) \]

      23. metadata-eval 52.7%

          \[\leadsto x \cdot \left(z \cdot 6 + \color{blue}{-3}\right) \]

   6. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot 6 + -3\right)} \]

   7. Taylor expanded in z around 0 51.8%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 51.8%

      \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 14: 26.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. 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. Taylor expanded in x around inf 54.2%

   \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x} \]
5. Step-by-step derivation

   1. *-commutative 54.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   2. +-commutative 54.2%

      \[\leadsto x \cdot \color{blue}{\left(-6 \cdot \left(0.6666666666666666 - z\right) + 1\right)} \]

   3. sub-neg 54.2%

      \[\leadsto x \cdot \left(-6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)} + 1\right) \]

   4. distribute-rgt-in 54.2%

      \[\leadsto x \cdot \left(\color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)} + 1\right) \]

   5. metadata-eval 54.2%

      \[\leadsto x \cdot \left(\left(\color{blue}{-4} + \left(-z\right) \cdot -6\right) + 1\right) \]

   6. metadata-eval 54.2%

      \[\leadsto x \cdot \left(\left(\color{blue}{-1 \cdot 4} + \left(-z\right) \cdot -6\right) + 1\right) \]

   7. neg-mul-1 54.2%

      \[\leadsto x \cdot \left(\left(-1 \cdot 4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right) + 1\right) \]

   8. associate-*r* 54.2%

      \[\leadsto x \cdot \left(\left(-1 \cdot 4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right) + 1\right) \]

   9. *-commutative 54.2%

      \[\leadsto x \cdot \left(\left(-1 \cdot 4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right) + 1\right) \]

   10. distribute-lft-in 54.2%

       \[\leadsto x \cdot \left(\color{blue}{-1 \cdot \left(4 + -6 \cdot z\right)} + 1\right) \]

   11. +-commutative 54.2%

       \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(4 + -6 \cdot z\right)\right)} \]

   12. distribute-lft-in 54.2%

       \[\leadsto x \cdot \left(1 + \color{blue}{\left(-1 \cdot 4 + -1 \cdot \left(-6 \cdot z\right)\right)}\right) \]

   13. associate-+r+ 54.2%

       \[\leadsto x \cdot \color{blue}{\left(\left(1 + -1 \cdot 4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

   14. metadata-eval 54.2%

       \[\leadsto x \cdot \left(\left(1 + \color{blue}{-4}\right) + -1 \cdot \left(-6 \cdot z\right)\right) \]

   15. metadata-eval 54.2%

       \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   16. metadata-eval 54.2%

       \[\leadsto x \cdot \left(\color{blue}{-1 \cdot 3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   17. distribute-lft-in 54.2%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(3 + -6 \cdot z\right)\right)} \]

   18. +-commutative 54.2%

       \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(-6 \cdot z + 3\right)}\right) \]

   19. distribute-rgt-in 54.2%

       \[\leadsto x \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot -1 + 3 \cdot -1\right)} \]

   20. *-commutative 54.2%

       \[\leadsto x \cdot \left(\color{blue}{\left(z \cdot -6\right)} \cdot -1 + 3 \cdot -1\right) \]

   21. associate-*l* 54.2%

       \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-6 \cdot -1\right)} + 3 \cdot -1\right) \]

   22. metadata-eval 54.2%

       \[\leadsto x \cdot \left(z \cdot \color{blue}{6} + 3 \cdot -1\right) \]

   23. metadata-eval 54.2%

       \[\leadsto x \cdot \left(z \cdot 6 + \color{blue}{-3}\right) \]

6. Simplified 54.2%

   \[\leadsto \color{blue}{x \cdot \left(z \cdot 6 + -3\right)} \]

7. Taylor expanded in z around 0 29.0%

   \[\leadsto \color{blue}{-3 \cdot x} \]
8. Step-by-step derivation

   1. *-commutative 29.0%

      \[\leadsto \color{blue}{x \cdot -3} \]

9. Simplified 29.0%

   \[\leadsto \color{blue}{x \cdot -3} \]

10. Final simplification 29.0%

    \[\leadsto x \cdot -3 \]

Alternative 15: 2.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Taylor expanded in y around inf 48.7%

   \[\leadsto x + \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
5. Step-by-step derivation

   1. associate-*r* 48.7%

      \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

6. Simplified 48.7%

   \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot \left(0.6666666666666666 - z\right)} \]

7. Taylor expanded in x around inf 2.5%

   \[\leadsto \color{blue}{x} \]

8. Final simplification 2.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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))))