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

Percentage Accurate: 99.5% → 99.8%

Time: 10.2s

Alternatives: 17

Speedup: 1.2×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% 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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x + N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * 4.0), $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. +-commutative 99.6%

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

   2. *-commutative 99.6%

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

   3. associate-*l* 99.5%

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

   4. fma-def 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. flip-- 89.6%

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

   2. associate-*r/ 84.3%

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

   3. metadata-eval 84.3%

      \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

   4. pow2 84.3%

      \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

5. Applied egg-rr 84.3%

   \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
6. Step-by-step derivation

   1. *-commutative 84.3%

      \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

   2. associate-/l* 89.1%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

7. Simplified 89.1%

   \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

8. Taylor expanded in z around inf 99.7%

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

   1. fma-def 99.8%

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

10. Simplified 99.8%

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

11. Final simplification 99.8%

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

Alternative 2: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.7%

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

   3. fma-def 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 3: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+224}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.112:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+114} \lor \neg \left(z \leq 5.8 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -8e+224)
     t_0
     (if (<= z -4e+209)
       t_1
       (if (<= z -0.112)
         t_0
         (if (<= z -1.3e-225)
           (* x -3.0)
           (if (<= z 2.9e-205)
             (* y 4.0)
             (if (<= z 1.9e-91)
               (* x -3.0)
               (if (<= z 0.65)
                 (* y 4.0)
                 (if (or (<= z 2.7e+114) (not (<= z 5.8e+251)))
                   t_1
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8e+224) {
		tmp = t_0;
	} else if (z <= -4e+209) {
		tmp = t_1;
	} else if (z <= -0.112) {
		tmp = t_0;
	} else if (z <= -1.3e-225) {
		tmp = x * -3.0;
	} else if (z <= 2.9e-205) {
		tmp = y * 4.0;
	} else if (z <= 1.9e-91) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 2.7e+114) || !(z <= 5.8e+251)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-8d+224)) then
        tmp = t_0
    else if (z <= (-4d+209)) then
        tmp = t_1
    else if (z <= (-0.112d0)) then
        tmp = t_0
    else if (z <= (-1.3d-225)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.9d-205) then
        tmp = y * 4.0d0
    else if (z <= 1.9d-91) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if ((z <= 2.7d+114) .or. (.not. (z <= 5.8d+251))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8e+224) {
		tmp = t_0;
	} else if (z <= -4e+209) {
		tmp = t_1;
	} else if (z <= -0.112) {
		tmp = t_0;
	} else if (z <= -1.3e-225) {
		tmp = x * -3.0;
	} else if (z <= 2.9e-205) {
		tmp = y * 4.0;
	} else if (z <= 1.9e-91) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 2.7e+114) || !(z <= 5.8e+251)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -8e+224:
		tmp = t_0
	elif z <= -4e+209:
		tmp = t_1
	elif z <= -0.112:
		tmp = t_0
	elif z <= -1.3e-225:
		tmp = x * -3.0
	elif z <= 2.9e-205:
		tmp = y * 4.0
	elif z <= 1.9e-91:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif (z <= 2.7e+114) or not (z <= 5.8e+251):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8e+224)
		tmp = t_0;
	elseif (z <= -4e+209)
		tmp = t_1;
	elseif (z <= -0.112)
		tmp = t_0;
	elseif (z <= -1.3e-225)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.9e-205)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.9e-91)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif ((z <= 2.7e+114) || !(z <= 5.8e+251))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8e+224)
		tmp = t_0;
	elseif (z <= -4e+209)
		tmp = t_1;
	elseif (z <= -0.112)
		tmp = t_0;
	elseif (z <= -1.3e-225)
		tmp = x * -3.0;
	elseif (z <= 2.9e-205)
		tmp = y * 4.0;
	elseif (z <= 1.9e-91)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif ((z <= 2.7e+114) || ~((z <= 5.8e+251)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+224], t$95$0, If[LessEqual[z, -4e+209], t$95$1, If[LessEqual[z, -0.112], t$95$0, If[LessEqual[z, -1.3e-225], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.9e-205], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.9e-91], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 2.7e+114], N[Not[LessEqual[z, 5.8e+251]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.99999999999999976e224 or -4.0000000000000003e209 < z < -0.112000000000000002 or 2.7e114 < z < 5.7999999999999999e251

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      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. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. distribute-rgt-neg-out 99.7%

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

      8. *-commutative 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. fma-def 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 70.1%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -7.99999999999999976e224 < z < -4.0000000000000003e209 or 0.650000000000000022 < z < 2.7e114 or 5.7999999999999999e251 < 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. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.6%

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

      5. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. flip-- 85.7%

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

      2. associate-*r/ 76.1%

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

      3. metadata-eval 76.1%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 76.1%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 76.1%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 76.1%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 83.4%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 83.4%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 98.9%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. neg-sub0 98.9%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 98.9%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 98.9%

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

      6. neg-mul-1 98.9%

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

      7. +-commutative 98.9%

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

      8. neg-mul-1 98.9%

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

      9. sub-neg 98.9%

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

   10. Simplified 98.9%

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

   11. Taylor expanded in z around inf 99.0%

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

   12. Taylor expanded in x around inf 73.7%

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

   if -0.112000000000000002 < z < -1.30000000000000007e-225 or 2.90000000000000018e-205 < z < 1.89999999999999989e-91

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -1.30000000000000007e-225 < z < 2.90000000000000018e-205 or 1.89999999999999989e-91 < z < 0.650000000000000022

   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. +-commutative 99.5%

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

      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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 62.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+224}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+209}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.112:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-225}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+114} \lor \neg \left(z \leq 5.8 \cdot 10^{+251}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 4: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.039:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 10^{-92}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+249}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1e+225)
     t_0
     (if (<= z -3.6e+192)
       t_1
       (if (<= z -0.039)
         t_0
         (if (<= z -3.8e-230)
           (* x -3.0)
           (if (<= z 1.4e-204)
             (* y 4.0)
             (if (<= z 1e-92)
               (* x -3.0)
               (if (<= z 0.56)
                 (* y 4.0)
                 (if (<= z 2.9e+114)
                   t_1
                   (if (<= z 6.2e+249) t_0 (* x (* z 6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1e+225) {
		tmp = t_0;
	} else if (z <= -3.6e+192) {
		tmp = t_1;
	} else if (z <= -0.039) {
		tmp = t_0;
	} else if (z <= -3.8e-230) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-204) {
		tmp = y * 4.0;
	} else if (z <= 1e-92) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else if (z <= 2.9e+114) {
		tmp = t_1;
	} else if (z <= 6.2e+249) {
		tmp = t_0;
	} else {
		tmp = x * (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1d+225)) then
        tmp = t_0
    else if (z <= (-3.6d+192)) then
        tmp = t_1
    else if (z <= (-0.039d0)) then
        tmp = t_0
    else if (z <= (-3.8d-230)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.4d-204) then
        tmp = y * 4.0d0
    else if (z <= 1d-92) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) then
        tmp = y * 4.0d0
    else if (z <= 2.9d+114) then
        tmp = t_1
    else if (z <= 6.2d+249) then
        tmp = t_0
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1e+225) {
		tmp = t_0;
	} else if (z <= -3.6e+192) {
		tmp = t_1;
	} else if (z <= -0.039) {
		tmp = t_0;
	} else if (z <= -3.8e-230) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-204) {
		tmp = y * 4.0;
	} else if (z <= 1e-92) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else if (z <= 2.9e+114) {
		tmp = t_1;
	} else if (z <= 6.2e+249) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1e+225:
		tmp = t_0
	elif z <= -3.6e+192:
		tmp = t_1
	elif z <= -0.039:
		tmp = t_0
	elif z <= -3.8e-230:
		tmp = x * -3.0
	elif z <= 1.4e-204:
		tmp = y * 4.0
	elif z <= 1e-92:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	elif z <= 2.9e+114:
		tmp = t_1
	elif z <= 6.2e+249:
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1e+225)
		tmp = t_0;
	elseif (z <= -3.6e+192)
		tmp = t_1;
	elseif (z <= -0.039)
		tmp = t_0;
	elseif (z <= -3.8e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.4e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= 1e-92)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.9e+114)
		tmp = t_1;
	elseif (z <= 6.2e+249)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1e+225)
		tmp = t_0;
	elseif (z <= -3.6e+192)
		tmp = t_1;
	elseif (z <= -0.039)
		tmp = t_0;
	elseif (z <= -3.8e-230)
		tmp = x * -3.0;
	elseif (z <= 1.4e-204)
		tmp = y * 4.0;
	elseif (z <= 1e-92)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	elseif (z <= 2.9e+114)
		tmp = t_1;
	elseif (z <= 6.2e+249)
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+225], t$95$0, If[LessEqual[z, -3.6e+192], t$95$1, If[LessEqual[z, -0.039], t$95$0, If[LessEqual[z, -3.8e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.4e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1e-92], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.9e+114], t$95$1, If[LessEqual[z, 6.2e+249], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.99999999999999928e224 or -3.6000000000000002e192 < z < -0.0389999999999999999 or 2.9e114 < z < 6.20000000000000031e249

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      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. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. distribute-rgt-neg-out 99.7%

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

      8. *-commutative 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. fma-def 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 70.1%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -9.99999999999999928e224 < z < -3.6000000000000002e192 or 0.56000000000000005 < z < 2.9e114

   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. *-commutative 99.7%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.6%

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

      5. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. flip-- 91.2%

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

      2. associate-*r/ 78.0%

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

      3. metadata-eval 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 78.0%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 88.4%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 88.4%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 98.6%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 98.6%

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

      2. distribute-rgt-neg-in 98.6%

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

      3. neg-sub0 98.6%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 98.6%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 98.6%

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

      6. neg-mul-1 98.6%

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

      7. +-commutative 98.6%

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

      8. neg-mul-1 98.6%

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

      9. sub-neg 98.6%

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

   10. Simplified 98.6%

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

   11. Taylor expanded in z around inf 98.7%

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

   12. Taylor expanded in x around inf 69.5%

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

   if -0.0389999999999999999 < z < -3.7999999999999998e-230 or 1.4e-204 < z < 9.99999999999999988e-93

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -3.7999999999999998e-230 < z < 1.4e-204 or 9.99999999999999988e-93 < z < 0.56000000000000005

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 62.1%

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

   if 6.20000000000000031e249 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 84.6%

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

      1. sub-neg 84.6%

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

      2. distribute-rgt-in 84.6%

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

      3. metadata-eval 84.6%

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

      4. metadata-eval 84.6%

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

      5. neg-mul-1 84.6%

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

      6. associate-*r* 84.6%

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

      7. *-commutative 84.6%

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

      8. distribute-lft-in 84.6%

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

      9. distribute-lft-in 84.6%

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

      10. associate-+r+ 84.6%

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

      11. metadata-eval 84.6%

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

      12. metadata-eval 84.6%

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

      13. associate-*r* 84.6%

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

      14. metadata-eval 84.6%

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

      15. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around inf 84.6%

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

      1. *-commutative 84.6%

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

   9. Simplified 84.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+225}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+192}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.039:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 10^{-92}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+249}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 5: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-227}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+242}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -8.5e+225)
     t_0
     (if (<= z -2.7e+202)
       t_1
       (if (<= z -4.5)
         (* y (* -6.0 z))
         (if (<= z -7.8e-227)
           (* x -3.0)
           (if (<= z 2.5e-204)
             (* y 4.0)
             (if (<= z 1.2e-91)
               (* x -3.0)
               (if (<= z 0.5)
                 (* y 4.0)
                 (if (<= z 5e+114)
                   t_1
                   (if (<= z 6.7e+242) t_0 (* x (* z 6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.5e+225) {
		tmp = t_0;
	} else if (z <= -2.7e+202) {
		tmp = t_1;
	} else if (z <= -4.5) {
		tmp = y * (-6.0 * z);
	} else if (z <= -7.8e-227) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-204) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-91) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 5e+114) {
		tmp = t_1;
	} else if (z <= 6.7e+242) {
		tmp = t_0;
	} else {
		tmp = x * (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-8.5d+225)) then
        tmp = t_0
    else if (z <= (-2.7d+202)) then
        tmp = t_1
    else if (z <= (-4.5d0)) then
        tmp = y * ((-6.0d0) * z)
    else if (z <= (-7.8d-227)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-204) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-91) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else if (z <= 5d+114) then
        tmp = t_1
    else if (z <= 6.7d+242) then
        tmp = t_0
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.5e+225) {
		tmp = t_0;
	} else if (z <= -2.7e+202) {
		tmp = t_1;
	} else if (z <= -4.5) {
		tmp = y * (-6.0 * z);
	} else if (z <= -7.8e-227) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-204) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-91) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 5e+114) {
		tmp = t_1;
	} else if (z <= 6.7e+242) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -8.5e+225:
		tmp = t_0
	elif z <= -2.7e+202:
		tmp = t_1
	elif z <= -4.5:
		tmp = y * (-6.0 * z)
	elif z <= -7.8e-227:
		tmp = x * -3.0
	elif z <= 2.5e-204:
		tmp = y * 4.0
	elif z <= 1.2e-91:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	elif z <= 5e+114:
		tmp = t_1
	elif z <= 6.7e+242:
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8.5e+225)
		tmp = t_0;
	elseif (z <= -2.7e+202)
		tmp = t_1;
	elseif (z <= -4.5)
		tmp = Float64(y * Float64(-6.0 * z));
	elseif (z <= -7.8e-227)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-91)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	elseif (z <= 5e+114)
		tmp = t_1;
	elseif (z <= 6.7e+242)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8.5e+225)
		tmp = t_0;
	elseif (z <= -2.7e+202)
		tmp = t_1;
	elseif (z <= -4.5)
		tmp = y * (-6.0 * z);
	elseif (z <= -7.8e-227)
		tmp = x * -3.0;
	elseif (z <= 2.5e-204)
		tmp = y * 4.0;
	elseif (z <= 1.2e-91)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	elseif (z <= 5e+114)
		tmp = t_1;
	elseif (z <= 6.7e+242)
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+225], t$95$0, If[LessEqual[z, -2.7e+202], t$95$1, If[LessEqual[z, -4.5], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-227], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-91], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5e+114], t$95$1, If[LessEqual[z, 6.7e+242], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.49999999999999947e225 or 5.0000000000000001e114 < z < 6.7e242

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      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. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. distribute-rgt-neg-out 99.7%

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

      8. *-commutative 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. fma-def 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 74.2%

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

   5. Taylor expanded in z around inf 74.2%

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

   if -8.49999999999999947e225 < z < -2.69999999999999995e202 or 0.5 < z < 5.0000000000000001e114

   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. *-commutative 99.7%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.6%

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

      5. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. flip-- 91.2%

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

      2. associate-*r/ 78.0%

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

      3. metadata-eval 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 78.0%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 88.4%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 88.4%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 98.6%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 98.6%

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

      2. distribute-rgt-neg-in 98.6%

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

      3. neg-sub0 98.6%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 98.6%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 98.6%

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

      6. neg-mul-1 98.6%

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

      7. +-commutative 98.6%

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

      8. neg-mul-1 98.6%

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

      9. sub-neg 98.6%

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

   10. Simplified 98.6%

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

   11. Taylor expanded in z around inf 98.7%

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

   12. Taylor expanded in x around inf 69.5%

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

   if -2.69999999999999995e202 < z < -4.5

   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* 99.6%

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

      3. fma-def 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-lft-in 99.7%

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

      7. distribute-rgt-neg-out 99.7%

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

      8. *-commutative 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. fma-def 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 64.3%

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

   5. Taylor expanded in z around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*r* 59.5%

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

      3. *-commutative 59.5%

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

   7. Simplified 59.5%

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

   if -4.5 < z < -7.7999999999999999e-227 or 2.5000000000000001e-204 < z < 1.20000000000000005e-91

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -7.7999999999999999e-227 < z < 2.5000000000000001e-204 or 1.20000000000000005e-91 < z < 0.5

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 62.1%

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

   if 6.7e242 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 84.6%

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

      1. sub-neg 84.6%

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

      2. distribute-rgt-in 84.6%

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

      3. metadata-eval 84.6%

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

      4. metadata-eval 84.6%

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

      5. neg-mul-1 84.6%

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

      6. associate-*r* 84.6%

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

      7. *-commutative 84.6%

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

      8. distribute-lft-in 84.6%

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

      9. distribute-lft-in 84.6%

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

      10. associate-+r+ 84.6%

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

      11. metadata-eval 84.6%

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

      12. metadata-eval 84.6%

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

      13. associate-*r* 84.6%

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

      14. metadata-eval 84.6%

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

      15. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around inf 84.6%

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

      1. *-commutative 84.6%

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

   9. Simplified 84.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+225}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+202}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-227}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+242}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 6: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-6 \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+225}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -26.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-91}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+250}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* -6.0 y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -4.9e+225)
     (* -6.0 (* z y))
     (if (<= z -3.1e+205)
       t_1
       (if (<= z -26.5)
         t_0
         (if (<= z -7.5e-231)
           (* x -3.0)
           (if (<= z 2.5e-205)
             (* y 4.0)
             (if (<= z 1.25e-91)
               (* x -3.0)
               (if (<= z 0.62)
                 (* y 4.0)
                 (if (<= z 2.6e+114)
                   t_1
                   (if (<= z 1.25e+250) t_0 (* x (* z 6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-6.0 * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -4.9e+225) {
		tmp = -6.0 * (z * y);
	} else if (z <= -3.1e+205) {
		tmp = t_1;
	} else if (z <= -26.5) {
		tmp = t_0;
	} else if (z <= -7.5e-231) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-205) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-91) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else if (z <= 2.6e+114) {
		tmp = t_1;
	} else if (z <= 1.25e+250) {
		tmp = t_0;
	} else {
		tmp = x * (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * ((-6.0d0) * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-4.9d+225)) then
        tmp = (-6.0d0) * (z * y)
    else if (z <= (-3.1d+205)) then
        tmp = t_1
    else if (z <= (-26.5d0)) then
        tmp = t_0
    else if (z <= (-7.5d-231)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-205) then
        tmp = y * 4.0d0
    else if (z <= 1.25d-91) then
        tmp = x * (-3.0d0)
    else if (z <= 0.62d0) then
        tmp = y * 4.0d0
    else if (z <= 2.6d+114) then
        tmp = t_1
    else if (z <= 1.25d+250) then
        tmp = t_0
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-6.0 * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -4.9e+225) {
		tmp = -6.0 * (z * y);
	} else if (z <= -3.1e+205) {
		tmp = t_1;
	} else if (z <= -26.5) {
		tmp = t_0;
	} else if (z <= -7.5e-231) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-205) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-91) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else if (z <= 2.6e+114) {
		tmp = t_1;
	} else if (z <= 1.25e+250) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-6.0 * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -4.9e+225:
		tmp = -6.0 * (z * y)
	elif z <= -3.1e+205:
		tmp = t_1
	elif z <= -26.5:
		tmp = t_0
	elif z <= -7.5e-231:
		tmp = x * -3.0
	elif z <= 2.5e-205:
		tmp = y * 4.0
	elif z <= 1.25e-91:
		tmp = x * -3.0
	elif z <= 0.62:
		tmp = y * 4.0
	elif z <= 2.6e+114:
		tmp = t_1
	elif z <= 1.25e+250:
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-6.0 * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -4.9e+225)
		tmp = Float64(-6.0 * Float64(z * y));
	elseif (z <= -3.1e+205)
		tmp = t_1;
	elseif (z <= -26.5)
		tmp = t_0;
	elseif (z <= -7.5e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-205)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.25e-91)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.62)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.6e+114)
		tmp = t_1;
	elseif (z <= 1.25e+250)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-6.0 * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -4.9e+225)
		tmp = -6.0 * (z * y);
	elseif (z <= -3.1e+205)
		tmp = t_1;
	elseif (z <= -26.5)
		tmp = t_0;
	elseif (z <= -7.5e-231)
		tmp = x * -3.0;
	elseif (z <= 2.5e-205)
		tmp = y * 4.0;
	elseif (z <= 1.25e-91)
		tmp = x * -3.0;
	elseif (z <= 0.62)
		tmp = y * 4.0;
	elseif (z <= 2.6e+114)
		tmp = t_1;
	elseif (z <= 1.25e+250)
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+225], N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e+205], t$95$1, If[LessEqual[z, -26.5], t$95$0, If[LessEqual[z, -7.5e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-205], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.25e-91], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.6e+114], t$95$1, If[LessEqual[z, 1.25e+250], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.90000000000000032e225

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. distribute-rgt-neg-out 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. fma-def 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 73.8%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -4.90000000000000032e225 < z < -3.10000000000000017e205 or 0.619999999999999996 < z < 2.6e114

   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. *-commutative 99.7%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.6%

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

      5. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. flip-- 91.2%

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

      2. associate-*r/ 78.0%

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

      3. metadata-eval 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 78.0%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 88.4%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 88.4%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 98.6%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 98.6%

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

      2. distribute-rgt-neg-in 98.6%

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

      3. neg-sub0 98.6%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 98.6%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 98.6%

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

      6. neg-mul-1 98.6%

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

      7. +-commutative 98.6%

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

      8. neg-mul-1 98.6%

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

      9. sub-neg 98.6%

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

   10. Simplified 98.6%

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

   11. Taylor expanded in z around inf 98.7%

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

   12. Taylor expanded in x around inf 69.5%

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

   if -3.10000000000000017e205 < z < -26.5 or 2.6e114 < z < 1.2500000000000001e250

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-- 80.8%

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

      2. associate-*r/ 67.7%

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

      3. metadata-eval 67.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 67.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 67.7%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 67.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 80.6%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 80.6%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 95.7%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 95.7%

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

      2. distribute-rgt-neg-in 95.7%

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

      3. neg-sub0 95.7%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 95.7%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 95.7%

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

      6. neg-mul-1 95.7%

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

      7. +-commutative 95.7%

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

      8. neg-mul-1 95.7%

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

      9. sub-neg 95.7%

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

   10. Simplified 95.7%

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

   11. Taylor expanded in z around inf 95.6%

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

   12. Taylor expanded in x around 0 66.7%

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

       1. *-commutative 66.7%

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

       2. *-commutative 66.7%

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

       3. associate-*l* 66.8%

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

   14. Simplified 66.8%

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

   if -26.5 < z < -7.5000000000000001e-231 or 2.5e-205 < z < 1.24999999999999999e-91

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -7.5000000000000001e-231 < z < 2.5e-205 or 1.24999999999999999e-91 < z < 0.619999999999999996

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 62.1%

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

   if 1.2500000000000001e250 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 84.6%

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

      1. sub-neg 84.6%

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

      2. distribute-rgt-in 84.6%

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

      3. metadata-eval 84.6%

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

      4. metadata-eval 84.6%

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

      5. neg-mul-1 84.6%

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

      6. associate-*r* 84.6%

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

      7. *-commutative 84.6%

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

      8. distribute-lft-in 84.6%

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

      9. distribute-lft-in 84.6%

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

      10. associate-+r+ 84.6%

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

      11. metadata-eval 84.6%

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

      12. metadata-eval 84.6%

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

      13. associate-*r* 84.6%

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

      14. metadata-eval 84.6%

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

      15. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around inf 84.6%

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

      1. *-commutative 84.6%

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

   9. Simplified 84.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+225}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+205}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -26.5:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-91}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+250}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 7: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.024:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-93}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.024)
     t_0
     (if (<= z -2.6e-226)
       (* x -3.0)
       (if (<= z 1.76e-205)
         (* y 4.0)
         (if (<= z 7e-93) (* x -3.0) (if (<= z 0.56) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.024) {
		tmp = t_0;
	} else if (z <= -2.6e-226) {
		tmp = x * -3.0;
	} else if (z <= 1.76e-205) {
		tmp = y * 4.0;
	} else if (z <= 7e-93) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * (y - x))
    if (z <= (-0.024d0)) then
        tmp = t_0
    else if (z <= (-2.6d-226)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.76d-205) then
        tmp = y * 4.0d0
    else if (z <= 7d-93) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.024) {
		tmp = t_0;
	} else if (z <= -2.6e-226) {
		tmp = x * -3.0;
	} else if (z <= 1.76e-205) {
		tmp = y * 4.0;
	} else if (z <= 7e-93) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.024:
		tmp = t_0
	elif z <= -2.6e-226:
		tmp = x * -3.0
	elif z <= 1.76e-205:
		tmp = y * 4.0
	elif z <= 7e-93:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.024)
		tmp = t_0;
	elseif (z <= -2.6e-226)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.76e-205)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-93)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.024)
		tmp = t_0;
	elseif (z <= -2.6e-226)
		tmp = x * -3.0;
	elseif (z <= 1.76e-205)
		tmp = y * 4.0;
	elseif (z <= 7e-93)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.024], t$95$0, If[LessEqual[z, -2.6e-226], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.76e-205], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-93], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.024 or 0.56000000000000005 < 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. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-- 80.9%

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

      2. associate-*r/ 70.7%

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

      3. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 70.7%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 79.8%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 79.8%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 97.4%

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

   if -0.024 < z < -2.5999999999999998e-226 or 1.7599999999999999e-205 < z < 7e-93

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -2.5999999999999998e-226 < z < 1.7599999999999999e-205 or 7e-93 < z < 0.56000000000000005

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 63.1%

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

   5. Taylor expanded in z around 0 62.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.024:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-93}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 8: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.0022:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-225}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-93}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 32000000000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.0022)
     t_0
     (if (<= z -4.7e-225)
       (* x -3.0)
       (if (<= z 9.6e-205)
         (* y 4.0)
         (if (<= z 4.8e-93)
           (* x -3.0)
           (if (<= z 32000000000.0)
             (* 6.0 (* y (- 0.6666666666666666 z)))
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0022) {
		tmp = t_0;
	} else if (z <= -4.7e-225) {
		tmp = x * -3.0;
	} else if (z <= 9.6e-205) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-93) {
		tmp = x * -3.0;
	} else if (z <= 32000000000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * (y - x))
    if (z <= (-0.0022d0)) then
        tmp = t_0
    else if (z <= (-4.7d-225)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.6d-205) then
        tmp = y * 4.0d0
    else if (z <= 4.8d-93) then
        tmp = x * (-3.0d0)
    else if (z <= 32000000000.0d0) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0022) {
		tmp = t_0;
	} else if (z <= -4.7e-225) {
		tmp = x * -3.0;
	} else if (z <= 9.6e-205) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-93) {
		tmp = x * -3.0;
	} else if (z <= 32000000000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.0022:
		tmp = t_0
	elif z <= -4.7e-225:
		tmp = x * -3.0
	elif z <= 9.6e-205:
		tmp = y * 4.0
	elif z <= 4.8e-93:
		tmp = x * -3.0
	elif z <= 32000000000.0:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.0022)
		tmp = t_0;
	elseif (z <= -4.7e-225)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.6e-205)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.8e-93)
		tmp = Float64(x * -3.0);
	elseif (z <= 32000000000.0)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.0022)
		tmp = t_0;
	elseif (z <= -4.7e-225)
		tmp = x * -3.0;
	elseif (z <= 9.6e-205)
		tmp = y * 4.0;
	elseif (z <= 4.8e-93)
		tmp = x * -3.0;
	elseif (z <= 32000000000.0)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0022], t$95$0, If[LessEqual[z, -4.7e-225], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.6e-205], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.8e-93], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 32000000000.0], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.00220000000000000013 or 3.2e10 < 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. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.7%

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

      4. fma-def 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-- 80.7%

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

      2. associate-*r/ 70.5%

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

      3. metadata-eval 70.5%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 70.5%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 70.5%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 70.5%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 79.6%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 79.6%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 97.5%

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

   if -0.00220000000000000013 < z < -4.70000000000000014e-225 or 9.6000000000000007e-205 < z < 4.8000000000000002e-93

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -4.70000000000000014e-225 < z < 9.6000000000000007e-205

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 63.3%

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

   5. Taylor expanded in z around 0 63.3%

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

   if 4.8000000000000002e-93 < z < 3.2e10

   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 x around 0 99.5%

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

   5. Taylor expanded in y around inf 64.2%

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

      1. *-commutative 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0022:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-225}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-93}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 32000000000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9: 50.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -0.49:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-222}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-92}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.05:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -0.49)
     t_0
     (if (<= z -3e-222)
       (* x -3.0)
       (if (<= z 1.25e-205)
         (* y 4.0)
         (if (<= z 1.3e-92) (* x -3.0) (if (<= z 0.05) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -0.49) {
		tmp = t_0;
	} else if (z <= -3e-222) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-205) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-92) {
		tmp = x * -3.0;
	} else if (z <= 0.05) {
		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) * (z * y)
    if (z <= (-0.49d0)) then
        tmp = t_0
    else if (z <= (-3d-222)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.25d-205) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-92) then
        tmp = x * (-3.0d0)
    else if (z <= 0.05d0) 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 * (z * y);
	double tmp;
	if (z <= -0.49) {
		tmp = t_0;
	} else if (z <= -3e-222) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-205) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-92) {
		tmp = x * -3.0;
	} else if (z <= 0.05) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -0.49:
		tmp = t_0
	elif z <= -3e-222:
		tmp = x * -3.0
	elif z <= 1.25e-205:
		tmp = y * 4.0
	elif z <= 1.3e-92:
		tmp = x * -3.0
	elif z <= 0.05:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -0.49)
		tmp = t_0;
	elseif (z <= -3e-222)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.25e-205)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-92)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.05)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -0.49)
		tmp = t_0;
	elseif (z <= -3e-222)
		tmp = x * -3.0;
	elseif (z <= 1.25e-205)
		tmp = y * 4.0;
	elseif (z <= 1.3e-92)
		tmp = x * -3.0;
	elseif (z <= 0.05)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.49], t$95$0, If[LessEqual[z, -3e-222], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.25e-205], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-92], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.05], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.48999999999999999 or 0.050000000000000003 < 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. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      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. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. distribute-rgt-neg-out 99.7%

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

      8. *-commutative 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. fma-def 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 55.9%

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

   5. Taylor expanded in z around inf 54.5%

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

   if -0.48999999999999999 < z < -3.0000000000000003e-222 or 1.25e-205 < z < 1.3e-92

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. distribute-lft-in 67.2%

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

      9. distribute-lft-in 67.2%

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

      10. associate-+r+ 67.2%

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

      11. metadata-eval 67.2%

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

      12. metadata-eval 67.2%

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

      13. associate-*r* 67.2%

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

      14. metadata-eval 67.2%

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

      15. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in z around 0 65.1%

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

   if -3.0000000000000003e-222 < z < 1.25e-205 or 1.3e-92 < z < 0.050000000000000003

   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. +-commutative 99.5%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. distribute-rgt-neg-out 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. fma-def 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 65.3%

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

   5. Taylor expanded in z around 0 64.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.49:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-222}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-205}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-92}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.05:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 10: 75.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+19} \lor \neg \left(y \leq 2.8 \cdot 10^{-49}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e+19) (not (<= y 2.8e-49)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e+19) || !(y <= 2.8e-49)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} 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 <= (-2.1d+19)) .or. (.not. (y <= 2.8d-49))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    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 <= -2.1e+19) || !(y <= 2.8e-49)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e+19) or not (y <= 2.8e-49):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e+19) || !(y <= 2.8e-49))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	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 <= -2.1e+19) || ~((y <= 2.8e-49)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e+19], N[Not[LessEqual[y, 2.8e-49]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $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 < -2.1e19 or 2.79999999999999997e-49 < y

   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 x around 0 97.3%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. *-commutative 82.9%

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

   7. Simplified 82.9%

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

   if -2.1e19 < y < 2.79999999999999997e-49

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. sub-neg 80.7%

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

      2. distribute-rgt-in 80.7%

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

      3. metadata-eval 80.7%

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

      4. metadata-eval 80.7%

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

      5. neg-mul-1 80.7%

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

      6. associate-*r* 80.7%

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

      7. *-commutative 80.7%

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

      8. distribute-lft-in 80.7%

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

      9. distribute-lft-in 80.7%

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

      10. associate-+r+ 80.7%

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

      11. metadata-eval 80.7%

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

      12. metadata-eval 80.7%

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

      13. associate-*r* 80.7%

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

      14. metadata-eval 80.7%

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

      15. *-commutative 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+19} \lor \neg \left(y \leq 2.8 \cdot 10^{-49}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 11: 75.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18} \lor \neg \left(y \leq 3.3 \cdot 10^{-51}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.15e+18) (not (<= y 3.3e-51)))
   (* y (+ 4.0 (* -6.0 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e+18) || !(y <= 3.3e-51)) {
		tmp = y * (4.0 + (-6.0 * z));
	} 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 <= (-2.15d+18)) .or. (.not. (y <= 3.3d-51))) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    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 <= -2.15e+18) || !(y <= 3.3e-51)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.15e+18) or not (y <= 3.3e-51):
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.15e+18) || !(y <= 3.3e-51))
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	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 <= -2.15e+18) || ~((y <= 3.3e-51)))
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.15e+18], N[Not[LessEqual[y, 3.3e-51]], $MachinePrecision]], N[(y * N[(4.0 + N[(-6.0 * z), $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 < -2.15e18 or 3.29999999999999973e-51 < y

   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* 99.8%

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

      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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 83.1%

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

   if -2.15e18 < y < 3.29999999999999973e-51

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. sub-neg 80.7%

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

      2. distribute-rgt-in 80.7%

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

      3. metadata-eval 80.7%

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

      4. metadata-eval 80.7%

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

      5. neg-mul-1 80.7%

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

      6. associate-*r* 80.7%

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

      7. *-commutative 80.7%

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

      8. distribute-lft-in 80.7%

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

      9. distribute-lft-in 80.7%

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

      10. associate-+r+ 80.7%

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

      11. metadata-eval 80.7%

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

      12. metadata-eval 80.7%

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

      13. associate-*r* 80.7%

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

      14. metadata-eval 80.7%

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

      15. *-commutative 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18} \lor \neg \left(y \leq 3.3 \cdot 10^{-51}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.6)))
   (* z (* 6.0 (- x y)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.6)) {
		tmp = z * (6.0 * (x - y));
	} 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 <= (-0.6d0)) .or. (.not. (z <= 0.6d0))) then
        tmp = z * (6.0d0 * (x - y))
    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 <= -0.6) || !(z <= 0.6)) {
		tmp = z * (6.0 * (x - y));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.6):
		tmp = z * (6.0 * (x - y))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.6))
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	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 <= -0.6) || ~((z <= 0.6)))
		tmp = z * (6.0 * (x - y));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.599999999999999978 < 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. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-- 80.9%

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

      2. associate-*r/ 70.7%

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

      3. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 70.7%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 79.8%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 79.8%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 97.4%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 97.4%

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

      2. distribute-rgt-neg-in 97.4%

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

      3. neg-sub0 97.4%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 97.4%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 97.4%

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

      6. neg-mul-1 97.4%

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

      7. +-commutative 97.4%

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

      8. neg-mul-1 97.4%

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

      9. sub-neg 97.4%

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

   10. Simplified 97.4%

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

   11. Taylor expanded in z around inf 97.4%

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

       1. *-commutative 97.4%

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

       2. associate-*l* 97.4%

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

   13. Simplified 97.4%

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

   if -0.599999999999999978 < z < 0.599999999999999978

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in 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 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]

Alternative 13: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.52)))
   (* z (* 6.0 (- x y)))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.52)) {
		tmp = z * (6.0 * (x - y));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.58d0)) .or. (.not. (z <= 0.52d0))) then
        tmp = z * (6.0d0 * (x - y))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.52)) {
		tmp = z * (6.0 * (x - y));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.52):
		tmp = z * (6.0 * (x - y))
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.52))
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.52)))
		tmp = z * (6.0 * (x - y));
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.52]], $MachinePrecision]], N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.52000000000000002 < 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. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-- 80.9%

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

      2. associate-*r/ 70.7%

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

      3. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

      4. pow2 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

   5. Applied egg-rr 70.7%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
   6. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

      2. associate-/l* 79.8%

         \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   7. Simplified 79.8%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

   8. Taylor expanded in z around inf 97.4%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 97.4%

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

      2. distribute-rgt-neg-in 97.4%

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

      3. neg-sub0 97.4%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

      4. associate--r- 97.4%

         \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

      5. neg-sub0 97.4%

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

      6. neg-mul-1 97.4%

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

      7. +-commutative 97.4%

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

      8. neg-mul-1 97.4%

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

      9. sub-neg 97.4%

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

   10. Simplified 97.4%

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

   11. Taylor expanded in z around inf 97.4%

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

       1. *-commutative 97.4%

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

       2. associate-*l* 97.4%

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

   13. Simplified 97.4%

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

   if -0.57999999999999996 < z < 0.52000000000000002

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.6%

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

   5. Taylor expanded in z around 0 96.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 14: 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 15: 38.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11000000000 \lor \neg \left(x \leq 5.4 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -11000000000.0) (not (<= x 5.4e-37))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11000000000.0) || !(x <= 5.4e-37)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 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 ((x <= (-11000000000.0d0)) .or. (.not. (x <= 5.4d-37))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11000000000.0) || !(x <= 5.4e-37)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -11000000000.0) or not (x <= 5.4e-37):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -11000000000.0) || !(x <= 5.4e-37))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -11000000000.0) || ~((x <= 5.4e-37)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -11000000000.0], N[Not[LessEqual[x, 5.4e-37]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e10 or 5.40000000000000032e-37 < 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 x around inf 78.6%

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

      1. sub-neg 78.6%

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

      2. distribute-rgt-in 78.6%

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

      3. metadata-eval 78.6%

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

      4. metadata-eval 78.6%

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

      5. neg-mul-1 78.6%

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

      6. associate-*r* 78.6%

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

      7. *-commutative 78.6%

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

      8. distribute-lft-in 78.6%

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

      9. distribute-lft-in 78.6%

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

      10. associate-+r+ 78.6%

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

      11. metadata-eval 78.6%

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

      12. metadata-eval 78.6%

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

      13. associate-*r* 78.6%

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

      14. metadata-eval 78.6%

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

      15. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in z around 0 40.6%

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

   if -1.1e10 < x < 5.40000000000000032e-37

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. distribute-rgt-neg-out 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 78.0%

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

   5. Taylor expanded in z around 0 38.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11000000000 \lor \neg \left(x \leq 5.4 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 16: 26.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around inf 51.0%

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

   1. sub-neg 51.0%

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

   2. distribute-rgt-in 51.0%

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

   3. metadata-eval 51.0%

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

   4. metadata-eval 51.0%

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

   5. neg-mul-1 51.0%

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

   6. associate-*r* 51.0%

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

   7. *-commutative 51.0%

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

   8. distribute-lft-in 51.0%

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

   9. distribute-lft-in 51.0%

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

   10. associate-+r+ 51.0%

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

   11. metadata-eval 51.0%

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

   12. metadata-eval 51.0%

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

   13. associate-*r* 51.0%

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

   14. metadata-eval 51.0%

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

   15. *-commutative 51.0%

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

6. Simplified 51.0%

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

7. Taylor expanded in z around 0 25.6%

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

8. Final simplification 25.6%

   \[\leadsto x \cdot -3 \]

Alternative 17: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. *-commutative 99.6%

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

   3. associate-*l* 99.5%

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

   4. fma-def 99.5%

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

   5. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. flip-- 89.6%

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

   2. associate-*r/ 84.3%

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

   3. metadata-eval 84.3%

      \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(\color{blue}{0.4444444444444444} - z \cdot z\right)}{0.6666666666666666 + z}, x\right) \]

   4. pow2 84.3%

      \[\leadsto \mathsf{fma}\left(6, \frac{\left(y - x\right) \cdot \left(0.4444444444444444 - \color{blue}{{z}^{2}}\right)}{0.6666666666666666 + z}, x\right) \]

5. Applied egg-rr 84.3%

   \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{\left(y - x\right) \cdot \left(0.4444444444444444 - {z}^{2}\right)}{0.6666666666666666 + z}}, x\right) \]
6. Step-by-step derivation

   1. *-commutative 84.3%

      \[\leadsto \mathsf{fma}\left(6, \frac{\color{blue}{\left(0.4444444444444444 - {z}^{2}\right) \cdot \left(y - x\right)}}{0.6666666666666666 + z}, x\right) \]

   2. associate-/l* 89.1%

      \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

7. Simplified 89.1%

   \[\leadsto \mathsf{fma}\left(6, \color{blue}{\frac{0.4444444444444444 - {z}^{2}}{\frac{0.6666666666666666 + z}{y - x}}}, x\right) \]

8. Taylor expanded in z around inf 52.3%

   \[\leadsto \mathsf{fma}\left(6, \color{blue}{-1 \cdot \left(z \cdot \left(y - x\right)\right)}, x\right) \]
9. Step-by-step derivation

   1. mul-1-neg 52.3%

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

   2. distribute-rgt-neg-in 52.3%

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

   3. neg-sub0 52.3%

      \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}, x\right) \]

   4. associate--r- 52.3%

      \[\leadsto \mathsf{fma}\left(6, z \cdot \color{blue}{\left(\left(0 - y\right) + x\right)}, x\right) \]

   5. neg-sub0 52.3%

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

   6. neg-mul-1 52.3%

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

   7. +-commutative 52.3%

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

   8. neg-mul-1 52.3%

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

   9. sub-neg 52.3%

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

10. Simplified 52.3%

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

11. Taylor expanded in z around 0 2.5%

    \[\leadsto \color{blue}{x} \]

12. Final simplification 2.5%

    \[\leadsto x \]

Reproduce

herbie shell --seed 2023320 
(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))))