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

Percentage Accurate: 99.5% → 99.8%

Time: 12.9s

Alternatives: 12

Speedup: 1.2×

• 21.1% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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* 99.7%

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

   3. fma-def 99.7%

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

   4. sub-neg 99.7%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-222}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-153}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-115}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* z (* x 6.0))))
   (if (<= z -1.16e+198)
     t_0
     (if (<= z -1.25e+97)
       t_1
       (if (<= z -2.6e-11)
         t_0
         (if (<= z -4.9e-67)
           (* x -3.0)
           (if (<= z -2.2e-174)
             (* y 4.0)
             (if (<= z 1.15e-306)
               (* x -3.0)
               (if (<= z 1.1e-222)
                 (* y 4.0)
                 (if (<= z 9.5e-153)
                   (* x -3.0)
                   (if (<= z 2.4e-115)
                     (* y 4.0)
                     (if (<= z 5e-70)
                       (* x -3.0)
                       (if (<= z 0.54) (* y 4.0) t_1)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -1.16e+198) {
		tmp = t_0;
	} else if (z <= -1.25e+97) {
		tmp = t_1;
	} else if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -4.9e-67) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-174) {
		tmp = y * 4.0;
	} else if (z <= 1.15e-306) {
		tmp = x * -3.0;
	} else if (z <= 1.1e-222) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-153) {
		tmp = x * -3.0;
	} else if (z <= 2.4e-115) {
		tmp = y * 4.0;
	} else if (z <= 5e-70) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} 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 = (-6.0d0) * (y * z)
    t_1 = z * (x * 6.0d0)
    if (z <= (-1.16d+198)) then
        tmp = t_0
    else if (z <= (-1.25d+97)) then
        tmp = t_1
    else if (z <= (-2.6d-11)) then
        tmp = t_0
    else if (z <= (-4.9d-67)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.2d-174)) then
        tmp = y * 4.0d0
    else if (z <= 1.15d-306) then
        tmp = x * (-3.0d0)
    else if (z <= 1.1d-222) then
        tmp = y * 4.0d0
    else if (z <= 9.5d-153) then
        tmp = x * (-3.0d0)
    else if (z <= 2.4d-115) then
        tmp = y * 4.0d0
    else if (z <= 5d-70) then
        tmp = x * (-3.0d0)
    else if (z <= 0.54d0) then
        tmp = y * 4.0d0
    else
        tmp = t_1
    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 = z * (x * 6.0);
	double tmp;
	if (z <= -1.16e+198) {
		tmp = t_0;
	} else if (z <= -1.25e+97) {
		tmp = t_1;
	} else if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -4.9e-67) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-174) {
		tmp = y * 4.0;
	} else if (z <= 1.15e-306) {
		tmp = x * -3.0;
	} else if (z <= 1.1e-222) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-153) {
		tmp = x * -3.0;
	} else if (z <= 2.4e-115) {
		tmp = y * 4.0;
	} else if (z <= 5e-70) {
		tmp = x * -3.0;
	} else if (z <= 0.54) {
		tmp = y * 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = z * (x * 6.0)
	tmp = 0
	if z <= -1.16e+198:
		tmp = t_0
	elif z <= -1.25e+97:
		tmp = t_1
	elif z <= -2.6e-11:
		tmp = t_0
	elif z <= -4.9e-67:
		tmp = x * -3.0
	elif z <= -2.2e-174:
		tmp = y * 4.0
	elif z <= 1.15e-306:
		tmp = x * -3.0
	elif z <= 1.1e-222:
		tmp = y * 4.0
	elif z <= 9.5e-153:
		tmp = x * -3.0
	elif z <= 2.4e-115:
		tmp = y * 4.0
	elif z <= 5e-70:
		tmp = x * -3.0
	elif z <= 0.54:
		tmp = y * 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -1.16e+198)
		tmp = t_0;
	elseif (z <= -1.25e+97)
		tmp = t_1;
	elseif (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -4.9e-67)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.2e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.15e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.1e-222)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e-153)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.4e-115)
		tmp = Float64(y * 4.0);
	elseif (z <= 5e-70)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.54)
		tmp = Float64(y * 4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -1.16e+198)
		tmp = t_0;
	elseif (z <= -1.25e+97)
		tmp = t_1;
	elseif (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -4.9e-67)
		tmp = x * -3.0;
	elseif (z <= -2.2e-174)
		tmp = y * 4.0;
	elseif (z <= 1.15e-306)
		tmp = x * -3.0;
	elseif (z <= 1.1e-222)
		tmp = y * 4.0;
	elseif (z <= 9.5e-153)
		tmp = x * -3.0;
	elseif (z <= 2.4e-115)
		tmp = y * 4.0;
	elseif (z <= 5e-70)
		tmp = x * -3.0;
	elseif (z <= 0.54)
		tmp = y * 4.0;
	else
		tmp = t_1;
	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[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+198], t$95$0, If[LessEqual[z, -1.25e+97], t$95$1, If[LessEqual[z, -2.6e-11], t$95$0, If[LessEqual[z, -4.9e-67], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.2e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.15e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.1e-222], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e-153], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.4e-115], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5e-70], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.54], N[(y * 4.0), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.16000000000000001e198 or -1.25e97 < z < -2.6000000000000001e-11

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.5%

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

      3. fma-def 99.5%

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

      4. sub-neg 99.5%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 69.6%

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

   5. Taylor expanded in z around inf 61.8%

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

   if -1.16000000000000001e198 < z < -1.25e97 or 0.54000000000000004 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip3-+ 9.6%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 9.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 9.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-*l* 99.7%

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

      7. fma-def 99.7%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around -inf 67.1%

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

      1. associate-/r* 67.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 67.0%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 67.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 67.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 67.0%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 67.2%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 67.2%

          \[\leadsto \color{blue}{\left(x \cdot \frac{1}{0.16666666666666666}\right)} \cdot z \]

       4. metadata-eval 67.2%

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

   11. Applied egg-rr 67.2%

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

   if -2.6000000000000001e-11 < z < -4.89999999999999993e-67 or -2.20000000000000022e-174 < z < 1.14999999999999995e-306 or 1.1e-222 < z < 9.50000000000000031e-153 or 2.40000000000000021e-115 < z < 4.9999999999999998e-70

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 71.1%

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

   5. Taylor expanded in z around 0 70.8%

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

      1. distribute-rgt1-in 70.8%

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

      2. metadata-eval 70.8%

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

      3. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -4.89999999999999993e-67 < z < -2.20000000000000022e-174 or 1.14999999999999995e-306 < z < 1.1e-222 or 9.50000000000000031e-153 < z < 2.40000000000000021e-115 or 4.9999999999999998e-70 < z < 0.54000000000000004

   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* 99.9%

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

      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. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 69.1%

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

   5. Taylor expanded in z around 0 67.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+198}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-222}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-153}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-115}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 3: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-217}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 10^{-114}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-61}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.95e+198)
     t_0
     (if (<= z -7e+97)
       (* x (* z 6.0))
       (if (<= z -2.6e-11)
         t_0
         (if (<= z -5.9e-68)
           (* x -3.0)
           (if (<= z -1.2e-167)
             (* y 4.0)
             (if (<= z 1.9e-306)
               (* x -3.0)
               (if (<= z 6.8e-217)
                 (* y 4.0)
                 (if (<= z 2.3e-152)
                   (* x -3.0)
                   (if (<= z 1e-114)
                     (* y 4.0)
                     (if (<= z 7.6e-61)
                       (* x -3.0)
                       (if (<= z 0.65) (* y 4.0) (* z (* x 6.0)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.95e+198) {
		tmp = t_0;
	} else if (z <= -7e+97) {
		tmp = x * (z * 6.0);
	} else if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -5.9e-68) {
		tmp = x * -3.0;
	} else if (z <= -1.2e-167) {
		tmp = y * 4.0;
	} else if (z <= 1.9e-306) {
		tmp = x * -3.0;
	} else if (z <= 6.8e-217) {
		tmp = y * 4.0;
	} else if (z <= 2.3e-152) {
		tmp = x * -3.0;
	} else if (z <= 1e-114) {
		tmp = y * 4.0;
	} else if (z <= 7.6e-61) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-2.95d+198)) then
        tmp = t_0
    else if (z <= (-7d+97)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-2.6d-11)) then
        tmp = t_0
    else if (z <= (-5.9d-68)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.2d-167)) then
        tmp = y * 4.0d0
    else if (z <= 1.9d-306) then
        tmp = x * (-3.0d0)
    else if (z <= 6.8d-217) then
        tmp = y * 4.0d0
    else if (z <= 2.3d-152) then
        tmp = x * (-3.0d0)
    else if (z <= 1d-114) then
        tmp = y * 4.0d0
    else if (z <= 7.6d-61) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = z * (x * 6.0d0)
    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 <= -2.95e+198) {
		tmp = t_0;
	} else if (z <= -7e+97) {
		tmp = x * (z * 6.0);
	} else if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -5.9e-68) {
		tmp = x * -3.0;
	} else if (z <= -1.2e-167) {
		tmp = y * 4.0;
	} else if (z <= 1.9e-306) {
		tmp = x * -3.0;
	} else if (z <= 6.8e-217) {
		tmp = y * 4.0;
	} else if (z <= 2.3e-152) {
		tmp = x * -3.0;
	} else if (z <= 1e-114) {
		tmp = y * 4.0;
	} else if (z <= 7.6e-61) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.95e+198:
		tmp = t_0
	elif z <= -7e+97:
		tmp = x * (z * 6.0)
	elif z <= -2.6e-11:
		tmp = t_0
	elif z <= -5.9e-68:
		tmp = x * -3.0
	elif z <= -1.2e-167:
		tmp = y * 4.0
	elif z <= 1.9e-306:
		tmp = x * -3.0
	elif z <= 6.8e-217:
		tmp = y * 4.0
	elif z <= 2.3e-152:
		tmp = x * -3.0
	elif z <= 1e-114:
		tmp = y * 4.0
	elif z <= 7.6e-61:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.95e+198)
		tmp = t_0;
	elseif (z <= -7e+97)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -5.9e-68)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.2e-167)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.9e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.8e-217)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.3e-152)
		tmp = Float64(x * -3.0);
	elseif (z <= 1e-114)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.6e-61)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(z * Float64(x * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.95e+198)
		tmp = t_0;
	elseif (z <= -7e+97)
		tmp = x * (z * 6.0);
	elseif (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -5.9e-68)
		tmp = x * -3.0;
	elseif (z <= -1.2e-167)
		tmp = y * 4.0;
	elseif (z <= 1.9e-306)
		tmp = x * -3.0;
	elseif (z <= 6.8e-217)
		tmp = y * 4.0;
	elseif (z <= 2.3e-152)
		tmp = x * -3.0;
	elseif (z <= 1e-114)
		tmp = y * 4.0;
	elseif (z <= 7.6e-61)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.95e+198], t$95$0, If[LessEqual[z, -7e+97], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-11], t$95$0, If[LessEqual[z, -5.9e-68], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.2e-167], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.9e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.8e-217], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.3e-152], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1e-114], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.6e-61], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.94999999999999987e198 or -7.0000000000000001e97 < z < -2.6000000000000001e-11

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.5%

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

      3. fma-def 99.5%

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

      4. sub-neg 99.5%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 69.6%

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

   5. Taylor expanded in z around inf 61.8%

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

   if -2.94999999999999987e198 < z < -7.0000000000000001e97

   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. Step-by-step derivation

      1. flip3-+ 0.8%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 0.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 0.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.4%

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

      5. +-commutative 99.4%

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

      6. associate-*l* 99.9%

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

      7. fma-def 99.9%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around -inf 69.9%

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

      1. associate-/r* 69.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 69.8%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 69.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 69.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 69.7%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 69.7%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 69.7%

          \[\leadsto \color{blue}{z \cdot \left(\frac{1}{0.16666666666666666} \cdot x\right)} \]

       4. associate-*l* 69.9%

          \[\leadsto \color{blue}{\left(z \cdot \frac{1}{0.16666666666666666}\right) \cdot x} \]

       5. metadata-eval 69.9%

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

   11. Applied egg-rr 69.9%

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

   if -2.6000000000000001e-11 < z < -5.9e-68 or -1.19999999999999997e-167 < z < 1.9e-306 or 6.80000000000000032e-217 < z < 2.3000000000000001e-152 or 1.0000000000000001e-114 < z < 7.59999999999999961e-61

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 71.1%

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

   5. Taylor expanded in z around 0 70.8%

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

      1. distribute-rgt1-in 70.8%

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

      2. metadata-eval 70.8%

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

      3. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -5.9e-68 < z < -1.19999999999999997e-167 or 1.9e-306 < z < 6.80000000000000032e-217 or 2.3000000000000001e-152 < z < 1.0000000000000001e-114 or 7.59999999999999961e-61 < z < 0.650000000000000022

   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* 99.9%

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

      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. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 69.1%

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

   5. Taylor expanded in z around 0 67.8%

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

   if 0.650000000000000022 < 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. flip3-+ 12.8%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 12.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 12.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-*l* 99.7%

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

      7. fma-def 99.7%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around -inf 66.1%

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

      1. associate-/r* 66.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 66.0%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 66.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 66.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 66.1%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 66.3%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 66.3%

          \[\leadsto \color{blue}{\left(x \cdot \frac{1}{0.16666666666666666}\right)} \cdot z \]

       4. metadata-eval 66.3%

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

   11. Applied egg-rr 66.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+198}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-167}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-217}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 10^{-114}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-61}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 4: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-166}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{1}{\frac{-0.3333333333333333}{x}}\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.6e+198)
     t_0
     (if (<= z -1.15e+97)
       (* x (* z 6.0))
       (if (<= z -2.6e-11)
         t_0
         (if (<= z -1.46e-68)
           (* x -3.0)
           (if (<= z -1.15e-166)
             (* y 4.0)
             (if (<= z 5.8e-307)
               (* x -3.0)
               (if (<= z 1.8e-223)
                 (* y 4.0)
                 (if (<= z 1.35e-151)
                   (* x -3.0)
                   (if (<= z 5.8e-117)
                     (* y 4.0)
                     (if (<= z 5.5e-64)
                       (/ 1.0 (/ -0.3333333333333333 x))
                       (if (<= z 0.65) (* y 4.0) (* z (* x 6.0)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.6e+198) {
		tmp = t_0;
	} else if (z <= -1.15e+97) {
		tmp = x * (z * 6.0);
	} else if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -1.46e-68) {
		tmp = x * -3.0;
	} else if (z <= -1.15e-166) {
		tmp = y * 4.0;
	} else if (z <= 5.8e-307) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-223) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-151) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-64) {
		tmp = 1.0 / (-0.3333333333333333 / x);
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.6d+198)) then
        tmp = t_0
    else if (z <= (-1.15d+97)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-2.6d-11)) then
        tmp = t_0
    else if (z <= (-1.46d-68)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.15d-166)) then
        tmp = y * 4.0d0
    else if (z <= 5.8d-307) then
        tmp = x * (-3.0d0)
    else if (z <= 1.8d-223) then
        tmp = y * 4.0d0
    else if (z <= 1.35d-151) then
        tmp = x * (-3.0d0)
    else if (z <= 5.8d-117) then
        tmp = y * 4.0d0
    else if (z <= 5.5d-64) then
        tmp = 1.0d0 / ((-0.3333333333333333d0) / x)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = z * (x * 6.0d0)
    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 <= -1.6e+198) {
		tmp = t_0;
	} else if (z <= -1.15e+97) {
		tmp = x * (z * 6.0);
	} else if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -1.46e-68) {
		tmp = x * -3.0;
	} else if (z <= -1.15e-166) {
		tmp = y * 4.0;
	} else if (z <= 5.8e-307) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-223) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-151) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-64) {
		tmp = 1.0 / (-0.3333333333333333 / x);
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.6e+198:
		tmp = t_0
	elif z <= -1.15e+97:
		tmp = x * (z * 6.0)
	elif z <= -2.6e-11:
		tmp = t_0
	elif z <= -1.46e-68:
		tmp = x * -3.0
	elif z <= -1.15e-166:
		tmp = y * 4.0
	elif z <= 5.8e-307:
		tmp = x * -3.0
	elif z <= 1.8e-223:
		tmp = y * 4.0
	elif z <= 1.35e-151:
		tmp = x * -3.0
	elif z <= 5.8e-117:
		tmp = y * 4.0
	elif z <= 5.5e-64:
		tmp = 1.0 / (-0.3333333333333333 / x)
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.6e+198)
		tmp = t_0;
	elseif (z <= -1.15e+97)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -1.46e-68)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.15e-166)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.8e-307)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.8e-223)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.35e-151)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.8e-117)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.5e-64)
		tmp = Float64(1.0 / Float64(-0.3333333333333333 / x));
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(z * Float64(x * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.6e+198)
		tmp = t_0;
	elseif (z <= -1.15e+97)
		tmp = x * (z * 6.0);
	elseif (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -1.46e-68)
		tmp = x * -3.0;
	elseif (z <= -1.15e-166)
		tmp = y * 4.0;
	elseif (z <= 5.8e-307)
		tmp = x * -3.0;
	elseif (z <= 1.8e-223)
		tmp = y * 4.0;
	elseif (z <= 1.35e-151)
		tmp = x * -3.0;
	elseif (z <= 5.8e-117)
		tmp = y * 4.0;
	elseif (z <= 5.5e-64)
		tmp = 1.0 / (-0.3333333333333333 / x);
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+198], t$95$0, If[LessEqual[z, -1.15e+97], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-11], t$95$0, If[LessEqual[z, -1.46e-68], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.15e-166], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.8e-307], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.8e-223], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.35e-151], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.8e-117], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.5e-64], N[(1.0 / N[(-0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.5999999999999999e198 or -1.15000000000000003e97 < z < -2.6000000000000001e-11

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.5%

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

      3. fma-def 99.5%

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

      4. sub-neg 99.5%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 69.6%

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

   5. Taylor expanded in z around inf 61.8%

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

   if -1.5999999999999999e198 < z < -1.15000000000000003e97

   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. Step-by-step derivation

      1. flip3-+ 0.8%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 0.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 0.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.4%

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

      5. +-commutative 99.4%

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

      6. associate-*l* 99.9%

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

      7. fma-def 99.9%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around -inf 69.9%

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

      1. associate-/r* 69.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 69.8%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 69.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 69.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 69.7%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 69.7%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 69.7%

          \[\leadsto \color{blue}{z \cdot \left(\frac{1}{0.16666666666666666} \cdot x\right)} \]

       4. associate-*l* 69.9%

          \[\leadsto \color{blue}{\left(z \cdot \frac{1}{0.16666666666666666}\right) \cdot x} \]

       5. metadata-eval 69.9%

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

   11. Applied egg-rr 69.9%

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

   if -2.6000000000000001e-11 < z < -1.45999999999999998e-68 or -1.14999999999999999e-166 < z < 5.8000000000000001e-307 or 1.8000000000000002e-223 < z < 1.35000000000000004e-151

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 70.1%

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

   5. Taylor expanded in z around 0 69.8%

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

      1. distribute-rgt1-in 69.8%

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

      2. metadata-eval 69.8%

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

      3. *-commutative 69.8%

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

   7. Simplified 69.8%

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

   if -1.45999999999999998e-68 < z < -1.14999999999999999e-166 or 5.8000000000000001e-307 < z < 1.8000000000000002e-223 or 1.35000000000000004e-151 < z < 5.8000000000000001e-117 or 5.4999999999999999e-64 < z < 0.650000000000000022

   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* 99.9%

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

      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. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 69.1%

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

   5. Taylor expanded in z around 0 67.8%

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

   if 5.8000000000000001e-117 < z < 5.4999999999999999e-64

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. flip3-+ 22.5%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 22.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 22.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.4%

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

      5. +-commutative 99.4%

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

      6. associate-*l* 99.7%

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

      7. fma-def 99.7%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around -inf 77.7%

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

      1. associate-/r* 77.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 77.7%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 77.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around 0 77.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{-0.3333333333333333}{x}}} \]

   if 0.650000000000000022 < 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. flip3-+ 12.8%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 12.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 12.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-*l* 99.7%

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

      7. fma-def 99.7%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around -inf 66.1%

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

      1. associate-/r* 66.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 66.0%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 66.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 66.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 66.1%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 66.3%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 66.3%

          \[\leadsto \color{blue}{\left(x \cdot \frac{1}{0.16666666666666666}\right)} \cdot z \]

       4. metadata-eval 66.3%

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

   11. Applied egg-rr 66.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+198}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-166}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{1}{\frac{-0.3333333333333333}{x}}\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 5: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-216}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.048:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.6e-11)
     t_0
     (if (<= z -1.5e-68)
       (* x -3.0)
       (if (<= z -8e-175)
         (* y 4.0)
         (if (<= z 2.25e-306)
           (* x -3.0)
           (if (<= z 1.7e-216)
             (* y 4.0)
             (if (<= z 1.1e-152)
               (* x -3.0)
               (if (<= z 3.2e-115)
                 (* y 4.0)
                 (if (<= z 4.7e-73)
                   (* x -3.0)
                   (if (<= z 0.048) (* y 4.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -1.5e-68) {
		tmp = x * -3.0;
	} else if (z <= -8e-175) {
		tmp = y * 4.0;
	} else if (z <= 2.25e-306) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-216) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-152) {
		tmp = x * -3.0;
	} else if (z <= 3.2e-115) {
		tmp = y * 4.0;
	} else if (z <= 4.7e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.048) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-2.6d-11)) then
        tmp = t_0
    else if (z <= (-1.5d-68)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8d-175)) then
        tmp = y * 4.0d0
    else if (z <= 2.25d-306) then
        tmp = x * (-3.0d0)
    else if (z <= 1.7d-216) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-152) then
        tmp = x * (-3.0d0)
    else if (z <= 3.2d-115) then
        tmp = y * 4.0d0
    else if (z <= 4.7d-73) then
        tmp = x * (-3.0d0)
    else if (z <= 0.048d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.6e-11) {
		tmp = t_0;
	} else if (z <= -1.5e-68) {
		tmp = x * -3.0;
	} else if (z <= -8e-175) {
		tmp = y * 4.0;
	} else if (z <= 2.25e-306) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-216) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-152) {
		tmp = x * -3.0;
	} else if (z <= 3.2e-115) {
		tmp = y * 4.0;
	} else if (z <= 4.7e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.048) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.6e-11:
		tmp = t_0
	elif z <= -1.5e-68:
		tmp = x * -3.0
	elif z <= -8e-175:
		tmp = y * 4.0
	elif z <= 2.25e-306:
		tmp = x * -3.0
	elif z <= 1.7e-216:
		tmp = y * 4.0
	elif z <= 1.1e-152:
		tmp = x * -3.0
	elif z <= 3.2e-115:
		tmp = y * 4.0
	elif z <= 4.7e-73:
		tmp = x * -3.0
	elif z <= 0.048:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -1.5e-68)
		tmp = Float64(x * -3.0);
	elseif (z <= -8e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.25e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.7e-216)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-152)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.2e-115)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.7e-73)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.048)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.6e-11)
		tmp = t_0;
	elseif (z <= -1.5e-68)
		tmp = x * -3.0;
	elseif (z <= -8e-175)
		tmp = y * 4.0;
	elseif (z <= 2.25e-306)
		tmp = x * -3.0;
	elseif (z <= 1.7e-216)
		tmp = y * 4.0;
	elseif (z <= 1.1e-152)
		tmp = x * -3.0;
	elseif (z <= 3.2e-115)
		tmp = y * 4.0;
	elseif (z <= 4.7e-73)
		tmp = x * -3.0;
	elseif (z <= 0.048)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-11], t$95$0, If[LessEqual[z, -1.5e-68], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.25e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.7e-216], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-152], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.2e-115], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.7e-73], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.048], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000001e-11 or 0.048000000000000001 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 51.6%

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

   5. Taylor expanded in z around inf 47.7%

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

   if -2.6000000000000001e-11 < z < -1.5e-68 or -8e-175 < z < 2.25000000000000002e-306 or 1.6999999999999999e-216 < z < 1.09999999999999992e-152 or 3.2e-115 < z < 4.69999999999999994e-73

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 71.1%

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

   5. Taylor expanded in z around 0 70.8%

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

      1. distribute-rgt1-in 70.8%

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

      2. metadata-eval 70.8%

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

      3. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -1.5e-68 < z < -8e-175 or 2.25000000000000002e-306 < z < 1.6999999999999999e-216 or 1.09999999999999992e-152 < z < 3.2e-115 or 4.69999999999999994e-73 < z < 0.048000000000000001

   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* 99.9%

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

      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. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 70.2%

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

   5. Taylor expanded in z around 0 69.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-216}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-115}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.048:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq 1900000000000:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= y -8e-74)
     t_0
     (if (<= y -1.65e-274)
       (* x (* z 6.0))
       (if (<= y 4.2e-171)
         (* x -3.0)
         (if (<= y 1900000000000.0) (* z (* x 6.0)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -8e-74) {
		tmp = t_0;
	} else if (y <= -1.65e-274) {
		tmp = x * (z * 6.0);
	} else if (y <= 4.2e-171) {
		tmp = x * -3.0;
	} else if (y <= 1900000000000.0) {
		tmp = z * (x * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    if (y <= (-8d-74)) then
        tmp = t_0
    else if (y <= (-1.65d-274)) then
        tmp = x * (z * 6.0d0)
    else if (y <= 4.2d-171) then
        tmp = x * (-3.0d0)
    else if (y <= 1900000000000.0d0) then
        tmp = z * (x * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -8e-74) {
		tmp = t_0;
	} else if (y <= -1.65e-274) {
		tmp = x * (z * 6.0);
	} else if (y <= 4.2e-171) {
		tmp = x * -3.0;
	} else if (y <= 1900000000000.0) {
		tmp = z * (x * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if y <= -8e-74:
		tmp = t_0
	elif y <= -1.65e-274:
		tmp = x * (z * 6.0)
	elif y <= 4.2e-171:
		tmp = x * -3.0
	elif y <= 1900000000000.0:
		tmp = z * (x * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -8e-74)
		tmp = t_0;
	elseif (y <= -1.65e-274)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (y <= 4.2e-171)
		tmp = Float64(x * -3.0);
	elseif (y <= 1900000000000.0)
		tmp = Float64(z * Float64(x * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -8e-74)
		tmp = t_0;
	elseif (y <= -1.65e-274)
		tmp = x * (z * 6.0);
	elseif (y <= 4.2e-171)
		tmp = x * -3.0;
	elseif (y <= 1900000000000.0)
		tmp = z * (x * 6.0);
	else
		tmp = t_0;
	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[y, -8e-74], t$95$0, If[LessEqual[y, -1.65e-274], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-171], N[(x * -3.0), $MachinePrecision], If[LessEqual[y, 1900000000000.0], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.99999999999999966e-74 or 1.9e12 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 77.1%

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

   if -7.99999999999999966e-74 < y < -1.6499999999999999e-274

   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. Step-by-step derivation

      1. flip3-+ 23.7%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 23.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 23.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.4%

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

      5. +-commutative 99.4%

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

      6. associate-*l* 99.6%

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

      7. fma-def 99.6%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around -inf 82.6%

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

      1. associate-/r* 82.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 82.6%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 82.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 55.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 55.2%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 55.4%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 55.4%

          \[\leadsto \color{blue}{z \cdot \left(\frac{1}{0.16666666666666666} \cdot x\right)} \]

       4. associate-*l* 55.4%

          \[\leadsto \color{blue}{\left(z \cdot \frac{1}{0.16666666666666666}\right) \cdot x} \]

       5. metadata-eval 55.4%

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

   11. Applied egg-rr 55.4%

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

   if -1.6499999999999999e-274 < y < 4.2e-171

   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 y around 0 94.6%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. distribute-rgt1-in 60.8%

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

      2. metadata-eval 60.8%

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

      3. *-commutative 60.8%

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

   7. Simplified 60.8%

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

   if 4.2e-171 < y < 1.9e12

   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. Step-by-step derivation

      1. flip3-+ 18.8%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 18.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 18.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.5%

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

      5. +-commutative 99.5%

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

      6. associate-*l* 99.6%

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

      7. fma-def 99.6%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around -inf 77.0%

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

      1. associate-/r* 77.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 77.0%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 77.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]

   9. Taylor expanded in z around inf 51.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.16666666666666666}{x \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 51.0%

          \[\leadsto \color{blue}{\frac{1}{0.16666666666666666} \cdot \left(x \cdot z\right)} \]

       2. associate-*r* 51.1%

          \[\leadsto \color{blue}{\left(\frac{1}{0.16666666666666666} \cdot x\right) \cdot z} \]

       3. *-commutative 51.1%

          \[\leadsto \color{blue}{\left(x \cdot \frac{1}{0.16666666666666666}\right)} \cdot z \]

       4. metadata-eval 51.1%

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

   11. Applied egg-rr 51.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq 1900000000000:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 7: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.66) (not (<= z 0.58)))
   (+ x (* -6.0 (* (- y x) z)))
   (+ x (* (- y x) 4.0))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.66d0)) .or. (.not. (z <= 0.58d0))) then
        tmp = x + ((-6.0d0) * ((y - x) * z))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.66) or not (z <= 0.58):
		tmp = x + (-6.0 * ((y - x) * z))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.66], N[Not[LessEqual[z, 0.58]], $MachinePrecision]], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.660000000000000031 or 0.57999999999999996 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 97.8%

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

   if -0.660000000000000031 < z < 0.57999999999999996

   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 z around 0 96.9%

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

4. Final simplification 97.3%

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

Alternative 8: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{\frac{\frac{1}{0.6666666666666666 - z}}{6}} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ (- y x) (/ (/ 1.0 (- 0.6666666666666666 z)) 6.0))))

C

double code(double x, double y, double z) {
	return x + ((y - x) / ((1.0 / (0.6666666666666666 - z)) / 6.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / ((1.0d0 / (0.6666666666666666d0 - z)) / 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / ((1.0 / (0.6666666666666666 - z)) / 6.0));
}

Python

def code(x, y, z):
	return x + ((y - x) / ((1.0 / (0.6666666666666666 - z)) / 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / Float64(Float64(1.0 / Float64(0.6666666666666666 - z)) / 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / ((1.0 / (0.6666666666666666 - z)) / 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(1.0 / N[(0.6666666666666666 - z), $MachinePrecision]), $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. Step-by-step derivation

   1. flip-- 88.6%

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

   2. clear-num 88.6%

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

   3. un-div-inv 88.7%

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

   4. clear-num 88.7%

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

   5. flip-- 99.7%

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

5. Applied egg-rr 99.7%

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

   1. associate-/l* 99.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{\frac{1}{0.6666666666666666 - z}}{6}}} \]

7. Simplified 99.7%

   \[\leadsto x + \color{blue}{\frac{y - x}{\frac{\frac{1}{0.6666666666666666 - z}}{6}}} \]

8. Final simplification 99.7%

   \[\leadsto x + \frac{y - x}{\frac{\frac{1}{0.6666666666666666 - z}}{6}} \]

Alternative 9: 75.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-73} \lor \neg \left(y \leq 1.5 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 - z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e-73) (not (<= y 1.5e-5)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (- -3.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-73) || !(y <= 1.5e-5)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 - (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.8d-73)) .or. (.not. (y <= 1.5d-5))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) - (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-73) || !(y <= 1.5e-5)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 - (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e-73) or not (y <= 1.5e-5):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 - (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e-73) || !(y <= 1.5e-5))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 - Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.8e-73) || ~((y <= 1.5e-5)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 - (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e-73], N[Not[LessEqual[y, 1.5e-5]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 - N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000012e-73 or 1.50000000000000004e-5 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 76.7%

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

   if -2.80000000000000012e-73 < y < 1.50000000000000004e-5

   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. Step-by-step derivation

      1. flip3-+ 22.3%

         \[\leadsto \color{blue}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}} \]

      2. clear-num 22.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}}} \]

      3. clear-num 22.3%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{{x}^{3} + {\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{3}}{x \cdot x + \left(\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) - x \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right)}}}} \]

      4. flip3-+ 99.4%

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

      5. +-commutative 99.4%

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

      6. associate-*l* 99.6%

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

      7. fma-def 99.6%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}} \]

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around -inf 85.4%

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

      1. associate-/r* 85.4%

         \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + -6 \cdot z}}} \]

      2. *-commutative 85.4%

         \[\leadsto \frac{1}{\frac{\frac{-1}{x}}{3 + \color{blue}{z \cdot -6}}} \]

   8. Simplified 85.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{-1}{x}}{3 + z \cdot -6}}} \]
   9. Step-by-step derivation

      1. associate-/l/ 85.4%

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

      2. associate-/r/ 85.5%

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

      3. metadata-eval 85.5%

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

      4. associate-*r* 85.5%

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

      5. neg-mul-1 85.5%

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

      6. neg-sub0 85.5%

         \[\leadsto \color{blue}{\left(0 - \left(3 + z \cdot -6\right)\right)} \cdot x \]

      7. associate--r+ 85.5%

         \[\leadsto \color{blue}{\left(\left(0 - 3\right) - z \cdot -6\right)} \cdot x \]

      8. metadata-eval 85.5%

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

   10. Applied egg-rr 85.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-73} \lor \neg \left(y \leq 1.5 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 - z \cdot -6\right)\\ \end{array} \]

Alternative 10: 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 11: 36.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+28) (* x -3.0) (if (<= x 1.05e+117) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+28) {
		tmp = x * -3.0;
	} else if (x <= 1.05e+117) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d+28)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.05d+117) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+28) {
		tmp = x * -3.0;
	} else if (x <= 1.05e+117) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e+28:
		tmp = x * -3.0
	elif x <= 1.05e+117:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+28)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.05e+117)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e+28)
		tmp = x * -3.0;
	elseif (x <= 1.05e+117)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+28], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.05e+117], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999995e28 or 1.0500000000000001e117 < x

   1. Initial program 99.6%

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

      1. 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 0 83.2%

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

   5. Taylor expanded in z around 0 43.1%

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

      1. distribute-rgt1-in 43.1%

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

      2. metadata-eval 43.1%

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

      3. *-commutative 43.1%

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

   7. Simplified 43.1%

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

   if -1.04999999999999995e28 < x < 1.0500000000000001e117

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 68.8%

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

   5. Taylor expanded in z around 0 37.9%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 12: 25.5% 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 y around 0 54.6%

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

5. Taylor expanded in z around 0 26.4%

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

   1. distribute-rgt1-in 26.4%

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

   2. metadata-eval 26.4%

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

   3. *-commutative 26.4%

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

7. Simplified 26.4%

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

8. Final simplification 26.4%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023297 
(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))))