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

Percentage Accurate: 99.5% → 99.8%

Time: 13.1s

Alternatives: 16

Speedup: 1.2×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

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

   3. fma-define 99.7%

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

   4. sub-neg 99.7%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

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

   3. fma-define 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. Add Preprocessing

5. Final simplification 99.7%

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

Alternative 3: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+218}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.115:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-292}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+60} \lor \neg \left(z \leq 6.5 \cdot 10^{+148}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.45e+218)
     t_0
     (if (<= z -1.3e+107)
       t_1
       (if (<= z -0.115)
         t_0
         (if (<= z -1.8e-101)
           (* y 4.0)
           (if (<= z -3.55e-161)
             (* x -3.0)
             (if (<= z -1.1e-204)
               (* y 4.0)
               (if (<= z -1.15e-292)
                 (* x -3.0)
                 (if (<= z 8.5e-174)
                   (* y 4.0)
                   (if (<= z 1.2e-152)
                     (* x -3.0)
                     (if (<= z 0.52)
                       (* y 4.0)
                       (if (or (<= z 1.5e+60) (not (<= z 6.5e+148)))
                         t_0
                         t_1)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.45e+218) {
		tmp = t_0;
	} else if (z <= -1.3e+107) {
		tmp = t_1;
	} else if (z <= -0.115) {
		tmp = t_0;
	} else if (z <= -1.8e-101) {
		tmp = y * 4.0;
	} else if (z <= -3.55e-161) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.15e-292) {
		tmp = x * -3.0;
	} else if (z <= 8.5e-174) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-152) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if ((z <= 1.5e+60) || !(z <= 6.5e+148)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-1.45d+218)) then
        tmp = t_0
    else if (z <= (-1.3d+107)) then
        tmp = t_1
    else if (z <= (-0.115d0)) then
        tmp = t_0
    else if (z <= (-1.8d-101)) then
        tmp = y * 4.0d0
    else if (z <= (-3.55d-161)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.1d-204)) then
        tmp = y * 4.0d0
    else if (z <= (-1.15d-292)) then
        tmp = x * (-3.0d0)
    else if (z <= 8.5d-174) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-152) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else if ((z <= 1.5d+60) .or. (.not. (z <= 6.5d+148))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.45e+218) {
		tmp = t_0;
	} else if (z <= -1.3e+107) {
		tmp = t_1;
	} else if (z <= -0.115) {
		tmp = t_0;
	} else if (z <= -1.8e-101) {
		tmp = y * 4.0;
	} else if (z <= -3.55e-161) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.15e-292) {
		tmp = x * -3.0;
	} else if (z <= 8.5e-174) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-152) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if ((z <= 1.5e+60) || !(z <= 6.5e+148)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.45e+218:
		tmp = t_0
	elif z <= -1.3e+107:
		tmp = t_1
	elif z <= -0.115:
		tmp = t_0
	elif z <= -1.8e-101:
		tmp = y * 4.0
	elif z <= -3.55e-161:
		tmp = x * -3.0
	elif z <= -1.1e-204:
		tmp = y * 4.0
	elif z <= -1.15e-292:
		tmp = x * -3.0
	elif z <= 8.5e-174:
		tmp = y * 4.0
	elif z <= 1.2e-152:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	elif (z <= 1.5e+60) or not (z <= 6.5e+148):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.45e+218)
		tmp = t_0;
	elseif (z <= -1.3e+107)
		tmp = t_1;
	elseif (z <= -0.115)
		tmp = t_0;
	elseif (z <= -1.8e-101)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.55e-161)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.1e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.15e-292)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.5e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-152)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	elseif ((z <= 1.5e+60) || !(z <= 6.5e+148))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.45e+218)
		tmp = t_0;
	elseif (z <= -1.3e+107)
		tmp = t_1;
	elseif (z <= -0.115)
		tmp = t_0;
	elseif (z <= -1.8e-101)
		tmp = y * 4.0;
	elseif (z <= -3.55e-161)
		tmp = x * -3.0;
	elseif (z <= -1.1e-204)
		tmp = y * 4.0;
	elseif (z <= -1.15e-292)
		tmp = x * -3.0;
	elseif (z <= 8.5e-174)
		tmp = y * 4.0;
	elseif (z <= 1.2e-152)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	elseif ((z <= 1.5e+60) || ~((z <= 6.5e+148)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+218], t$95$0, If[LessEqual[z, -1.3e+107], t$95$1, If[LessEqual[z, -0.115], t$95$0, If[LessEqual[z, -1.8e-101], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.55e-161], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.1e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.15e-292], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.5e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-152], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 1.5e+60], N[Not[LessEqual[z, 6.5e+148]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e218 or -1.3000000000000001e107 < z < -0.115000000000000005 or 0.52000000000000002 < z < 1.4999999999999999e60 or 6.49999999999999947e148 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 70.6%

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

      1. metadata-eval 70.6%

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

      2. cancel-sign-sub-inv 70.6%

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

      3. *-commutative 70.6%

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

      4. cancel-sign-sub-inv 70.6%

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

      5. distribute-lft-neg-in 70.6%

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

      6. *-commutative 70.6%

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

      7. distribute-lft-neg-in 70.6%

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

      8. metadata-eval 70.6%

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

      9. sub-neg 70.6%

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

      10. distribute-lft-in 70.6%

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

      11. metadata-eval 70.6%

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

      12. neg-mul-1 70.6%

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

      13. *-commutative 70.6%

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

      14. associate-*l* 70.6%

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

      15. associate-+r+ 70.6%

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

      16. metadata-eval 70.6%

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

      17. *-commutative 70.6%

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

      18. associate-*l* 70.6%

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

      19. metadata-eval 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

   10. Simplified 65.1%

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

   if -1.45e218 < z < -1.3000000000000001e107 or 1.4999999999999999e60 < z < 6.49999999999999947e148

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in z around inf 99.7%

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

   7. Taylor expanded in y around inf 67.5%

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

      1. *-commutative 67.5%

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

   9. Simplified 67.5%

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

   if -0.115000000000000005 < z < -1.8e-101 or -3.55e-161 < z < -1.0999999999999999e-204 or -1.1499999999999999e-292 < z < 8.4999999999999996e-174 or 1.2e-152 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 95.7%

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

   6. Taylor expanded in y around inf 84.0%

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

      1. distribute-lft1-in 84.8%

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

      2. metadata-eval 84.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 84.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 59.7%

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

       1. *-commutative 59.7%

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

   11. Simplified 59.7%

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

   if -1.8e-101 < z < -3.55e-161 or -1.0999999999999999e-204 < z < -1.1499999999999999e-292 or 8.4999999999999996e-174 < z < 1.2e-152

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 87.7%

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

      1. metadata-eval 87.7%

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

      2. cancel-sign-sub-inv 87.7%

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

      3. *-commutative 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-neg-in 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-lft-in 87.7%

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

      11. metadata-eval 87.7%

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

      12. neg-mul-1 87.7%

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

      13. *-commutative 87.7%

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

      14. associate-*l* 87.7%

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

      15. associate-+r+ 87.7%

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

      16. metadata-eval 87.7%

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

      17. *-commutative 87.7%

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

      18. associate-*l* 87.7%

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

      19. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   10. Simplified 87.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+218}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+107}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.115:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-292}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-152}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+60} \lor \neg \left(z \leq 6.5 \cdot 10^{+148}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+212}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.062:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+56} \lor \neg \left(z \leq 4.4 \cdot 10^{+149}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -6.5e+212)
     t_0
     (if (<= z -4.7e+142)
       t_1
       (if (<= z -0.062)
         (* x (* z 6.0))
         (if (<= z -1.55e-104)
           (* y 4.0)
           (if (<= z -2.25e-161)
             (* x -3.0)
             (if (<= z -2.3e-204)
               (* y 4.0)
               (if (<= z -1.85e-293)
                 (* x -3.0)
                 (if (<= z 3e-174)
                   (* y 4.0)
                   (if (<= z 7.5e-147)
                     (* x -3.0)
                     (if (<= z 0.52)
                       (* y 4.0)
                       (if (or (<= z 3.3e+56) (not (<= z 4.4e+149)))
                         t_0
                         t_1)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.5e+212) {
		tmp = t_0;
	} else if (z <= -4.7e+142) {
		tmp = t_1;
	} else if (z <= -0.062) {
		tmp = x * (z * 6.0);
	} else if (z <= -1.55e-104) {
		tmp = y * 4.0;
	} else if (z <= -2.25e-161) {
		tmp = x * -3.0;
	} else if (z <= -2.3e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.85e-293) {
		tmp = x * -3.0;
	} else if (z <= 3e-174) {
		tmp = y * 4.0;
	} else if (z <= 7.5e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if ((z <= 3.3e+56) || !(z <= 4.4e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-6.5d+212)) then
        tmp = t_0
    else if (z <= (-4.7d+142)) then
        tmp = t_1
    else if (z <= (-0.062d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-1.55d-104)) then
        tmp = y * 4.0d0
    else if (z <= (-2.25d-161)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.3d-204)) then
        tmp = y * 4.0d0
    else if (z <= (-1.85d-293)) then
        tmp = x * (-3.0d0)
    else if (z <= 3d-174) then
        tmp = y * 4.0d0
    else if (z <= 7.5d-147) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else if ((z <= 3.3d+56) .or. (.not. (z <= 4.4d+149))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.5e+212) {
		tmp = t_0;
	} else if (z <= -4.7e+142) {
		tmp = t_1;
	} else if (z <= -0.062) {
		tmp = x * (z * 6.0);
	} else if (z <= -1.55e-104) {
		tmp = y * 4.0;
	} else if (z <= -2.25e-161) {
		tmp = x * -3.0;
	} else if (z <= -2.3e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.85e-293) {
		tmp = x * -3.0;
	} else if (z <= 3e-174) {
		tmp = y * 4.0;
	} else if (z <= 7.5e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if ((z <= 3.3e+56) || !(z <= 4.4e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -6.5e+212:
		tmp = t_0
	elif z <= -4.7e+142:
		tmp = t_1
	elif z <= -0.062:
		tmp = x * (z * 6.0)
	elif z <= -1.55e-104:
		tmp = y * 4.0
	elif z <= -2.25e-161:
		tmp = x * -3.0
	elif z <= -2.3e-204:
		tmp = y * 4.0
	elif z <= -1.85e-293:
		tmp = x * -3.0
	elif z <= 3e-174:
		tmp = y * 4.0
	elif z <= 7.5e-147:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	elif (z <= 3.3e+56) or not (z <= 4.4e+149):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -6.5e+212)
		tmp = t_0;
	elseif (z <= -4.7e+142)
		tmp = t_1;
	elseif (z <= -0.062)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -1.55e-104)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.25e-161)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.3e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.85e-293)
		tmp = Float64(x * -3.0);
	elseif (z <= 3e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.5e-147)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	elseif ((z <= 3.3e+56) || !(z <= 4.4e+149))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -6.5e+212)
		tmp = t_0;
	elseif (z <= -4.7e+142)
		tmp = t_1;
	elseif (z <= -0.062)
		tmp = x * (z * 6.0);
	elseif (z <= -1.55e-104)
		tmp = y * 4.0;
	elseif (z <= -2.25e-161)
		tmp = x * -3.0;
	elseif (z <= -2.3e-204)
		tmp = y * 4.0;
	elseif (z <= -1.85e-293)
		tmp = x * -3.0;
	elseif (z <= 3e-174)
		tmp = y * 4.0;
	elseif (z <= 7.5e-147)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	elseif ((z <= 3.3e+56) || ~((z <= 4.4e+149)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+212], t$95$0, If[LessEqual[z, -4.7e+142], t$95$1, If[LessEqual[z, -0.062], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-104], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.25e-161], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.3e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.85e-293], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.5e-147], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 3.3e+56], N[Not[LessEqual[z, 4.4e+149]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.49999999999999997e212 or 0.52000000000000002 < z < 3.30000000000000002e56 or 4.4e149 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 72.1%

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

      1. metadata-eval 72.1%

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

      2. cancel-sign-sub-inv 72.1%

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

      3. *-commutative 72.1%

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

      4. cancel-sign-sub-inv 72.1%

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

      5. distribute-lft-neg-in 72.1%

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

      6. *-commutative 72.1%

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

      7. distribute-lft-neg-in 72.1%

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

      8. metadata-eval 72.1%

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

      9. sub-neg 72.1%

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

      10. distribute-lft-in 72.1%

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

      11. metadata-eval 72.1%

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

      12. neg-mul-1 72.1%

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

      13. *-commutative 72.1%

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

      14. associate-*l* 72.1%

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

      15. associate-+r+ 72.1%

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

      16. metadata-eval 72.1%

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

      17. *-commutative 72.1%

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

      18. associate-*l* 72.1%

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

      19. metadata-eval 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   10. Simplified 68.1%

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

   if -6.49999999999999997e212 < z < -4.7e142 or 3.30000000000000002e56 < z < 4.4e149

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in z around inf 99.7%

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

   7. Taylor expanded in y around inf 69.1%

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

      1. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   if -4.7e142 < z < -0.062

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 63.5%

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

      1. metadata-eval 63.5%

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

      2. cancel-sign-sub-inv 63.5%

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

      3. *-commutative 63.5%

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

      4. cancel-sign-sub-inv 63.5%

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

      5. distribute-lft-neg-in 63.5%

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

      6. *-commutative 63.5%

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

      7. distribute-lft-neg-in 63.5%

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

      8. metadata-eval 63.5%

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

      9. sub-neg 63.5%

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

      10. distribute-lft-in 63.6%

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

      11. metadata-eval 63.6%

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

      12. neg-mul-1 63.6%

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

      13. *-commutative 63.6%

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

      14. associate-*l* 63.6%

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

      15. associate-+r+ 63.6%

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

      16. metadata-eval 63.6%

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

      17. *-commutative 63.6%

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

      18. associate-*l* 63.6%

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

      19. metadata-eval 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in z around inf 55.4%

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

   if -0.062 < z < -1.54999999999999988e-104 or -2.2499999999999998e-161 < z < -2.2999999999999999e-204 or -1.85000000000000004e-293 < z < 3.00000000000000021e-174 or 7.50000000000000047e-147 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 95.7%

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

   6. Taylor expanded in y around inf 84.0%

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

      1. distribute-lft1-in 84.8%

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

      2. metadata-eval 84.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 84.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 59.7%

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

       1. *-commutative 59.7%

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

   11. Simplified 59.7%

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

   if -1.54999999999999988e-104 < z < -2.2499999999999998e-161 or -2.2999999999999999e-204 < z < -1.85000000000000004e-293 or 3.00000000000000021e-174 < z < 7.50000000000000047e-147

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 87.7%

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

      1. metadata-eval 87.7%

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

      2. cancel-sign-sub-inv 87.7%

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

      3. *-commutative 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-neg-in 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-lft-in 87.7%

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

      11. metadata-eval 87.7%

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

      12. neg-mul-1 87.7%

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

      13. *-commutative 87.7%

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

      14. associate-*l* 87.7%

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

      15. associate-+r+ 87.7%

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

      16. metadata-eval 87.7%

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

      17. *-commutative 87.7%

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

      18. associate-*l* 87.7%

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

      19. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   10. Simplified 87.7%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+212}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+142}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.062:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+56} \lor \neg \left(z \leq 4.4 \cdot 10^{+149}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+144}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.1:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-160}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-141}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+60} \lor \neg \left(z \leq 9.2 \cdot 10^{+151}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -4.2e+215)
     (* z (* x 6.0))
     (if (<= z -1.26e+144)
       t_0
       (if (<= z -2.1)
         (* x (* z 6.0))
         (if (<= z -2.4e-101)
           (* y 4.0)
           (if (<= z -8.8e-160)
             (* x -3.0)
             (if (<= z -1.26e-204)
               (* y 4.0)
               (if (<= z -1.6e-293)
                 (* x -3.0)
                 (if (<= z 8.8e-174)
                   (* y 4.0)
                   (if (<= z 6.5e-141)
                     (* x -3.0)
                     (if (<= z 0.52)
                       (* y 4.0)
                       (if (or (<= z 1.1e+60) (not (<= z 9.2e+151)))
                         (* 6.0 (* x z))
                         t_0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.2e+215) {
		tmp = z * (x * 6.0);
	} else if (z <= -1.26e+144) {
		tmp = t_0;
	} else if (z <= -2.1) {
		tmp = x * (z * 6.0);
	} else if (z <= -2.4e-101) {
		tmp = y * 4.0;
	} else if (z <= -8.8e-160) {
		tmp = x * -3.0;
	} else if (z <= -1.26e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.6e-293) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-174) {
		tmp = y * 4.0;
	} else if (z <= 6.5e-141) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if ((z <= 1.1e+60) || !(z <= 9.2e+151)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-4.2d+215)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-1.26d+144)) then
        tmp = t_0
    else if (z <= (-2.1d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-2.4d-101)) then
        tmp = y * 4.0d0
    else if (z <= (-8.8d-160)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.26d-204)) then
        tmp = y * 4.0d0
    else if (z <= (-1.6d-293)) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-174) then
        tmp = y * 4.0d0
    else if (z <= 6.5d-141) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else if ((z <= 1.1d+60) .or. (.not. (z <= 9.2d+151))) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.2e+215) {
		tmp = z * (x * 6.0);
	} else if (z <= -1.26e+144) {
		tmp = t_0;
	} else if (z <= -2.1) {
		tmp = x * (z * 6.0);
	} else if (z <= -2.4e-101) {
		tmp = y * 4.0;
	} else if (z <= -8.8e-160) {
		tmp = x * -3.0;
	} else if (z <= -1.26e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.6e-293) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-174) {
		tmp = y * 4.0;
	} else if (z <= 6.5e-141) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if ((z <= 1.1e+60) || !(z <= 9.2e+151)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -4.2e+215:
		tmp = z * (x * 6.0)
	elif z <= -1.26e+144:
		tmp = t_0
	elif z <= -2.1:
		tmp = x * (z * 6.0)
	elif z <= -2.4e-101:
		tmp = y * 4.0
	elif z <= -8.8e-160:
		tmp = x * -3.0
	elif z <= -1.26e-204:
		tmp = y * 4.0
	elif z <= -1.6e-293:
		tmp = x * -3.0
	elif z <= 8.8e-174:
		tmp = y * 4.0
	elif z <= 6.5e-141:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	elif (z <= 1.1e+60) or not (z <= 9.2e+151):
		tmp = 6.0 * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.2e+215)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -1.26e+144)
		tmp = t_0;
	elseif (z <= -2.1)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -2.4e-101)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.8e-160)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.26e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.6e-293)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.5e-141)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	elseif ((z <= 1.1e+60) || !(z <= 9.2e+151))
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.2e+215)
		tmp = z * (x * 6.0);
	elseif (z <= -1.26e+144)
		tmp = t_0;
	elseif (z <= -2.1)
		tmp = x * (z * 6.0);
	elseif (z <= -2.4e-101)
		tmp = y * 4.0;
	elseif (z <= -8.8e-160)
		tmp = x * -3.0;
	elseif (z <= -1.26e-204)
		tmp = y * 4.0;
	elseif (z <= -1.6e-293)
		tmp = x * -3.0;
	elseif (z <= 8.8e-174)
		tmp = y * 4.0;
	elseif (z <= 6.5e-141)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	elseif ((z <= 1.1e+60) || ~((z <= 9.2e+151)))
		tmp = 6.0 * (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+215], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.26e+144], t$95$0, If[LessEqual[z, -2.1], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-101], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.8e-160], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.26e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.6e-293], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.5e-141], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 1.1e+60], N[Not[LessEqual[z, 9.2e+151]], $MachinePrecision]], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.2000000000000003e215

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.2%

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

      1. metadata-eval 80.2%

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

      2. cancel-sign-sub-inv 80.2%

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

      3. *-commutative 80.2%

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

      4. cancel-sign-sub-inv 80.2%

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

      5. distribute-lft-neg-in 80.2%

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

      6. *-commutative 80.2%

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

      7. distribute-lft-neg-in 80.2%

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

      8. metadata-eval 80.2%

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

      9. sub-neg 80.2%

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

      10. distribute-lft-in 80.2%

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

      11. metadata-eval 80.2%

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

      12. neg-mul-1 80.2%

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

      13. *-commutative 80.2%

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

      14. associate-*l* 80.2%

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

      15. associate-+r+ 80.2%

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

      16. metadata-eval 80.2%

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

      17. *-commutative 80.2%

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

      18. associate-*l* 80.2%

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

      19. metadata-eval 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in z around inf 80.2%

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

   9. Taylor expanded in x around 0 80.2%

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

       1. *-commutative 80.2%

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

       2. *-commutative 80.2%

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

       3. associate-*r* 80.3%

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

       4. *-commutative 80.3%

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

   11. Simplified 80.3%

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

   if -4.2000000000000003e215 < z < -1.26000000000000001e144 or 1.09999999999999998e60 < z < 9.2000000000000003e151

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in z around inf 99.7%

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

   7. Taylor expanded in y around inf 69.1%

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

      1. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   if -1.26000000000000001e144 < z < -2.10000000000000009

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 63.5%

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

      1. metadata-eval 63.5%

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

      2. cancel-sign-sub-inv 63.5%

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

      3. *-commutative 63.5%

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

      4. cancel-sign-sub-inv 63.5%

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

      5. distribute-lft-neg-in 63.5%

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

      6. *-commutative 63.5%

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

      7. distribute-lft-neg-in 63.5%

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

      8. metadata-eval 63.5%

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

      9. sub-neg 63.5%

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

      10. distribute-lft-in 63.6%

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

      11. metadata-eval 63.6%

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

      12. neg-mul-1 63.6%

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

      13. *-commutative 63.6%

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

      14. associate-*l* 63.6%

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

      15. associate-+r+ 63.6%

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

      16. metadata-eval 63.6%

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

      17. *-commutative 63.6%

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

      18. associate-*l* 63.6%

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

      19. metadata-eval 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in z around inf 55.4%

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

   if -2.10000000000000009 < z < -2.4e-101 or -8.8e-160 < z < -1.26e-204 or -1.60000000000000003e-293 < z < 8.80000000000000086e-174 or 6.4999999999999995e-141 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 95.7%

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

   6. Taylor expanded in y around inf 84.0%

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

      1. distribute-lft1-in 84.8%

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

      2. metadata-eval 84.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 84.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 59.7%

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

       1. *-commutative 59.7%

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

   11. Simplified 59.7%

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

   if -2.4e-101 < z < -8.8e-160 or -1.26e-204 < z < -1.60000000000000003e-293 or 8.80000000000000086e-174 < z < 6.4999999999999995e-141

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 87.7%

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

      1. metadata-eval 87.7%

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

      2. cancel-sign-sub-inv 87.7%

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

      3. *-commutative 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-neg-in 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-lft-in 87.7%

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

      11. metadata-eval 87.7%

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

      12. neg-mul-1 87.7%

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

      13. *-commutative 87.7%

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

      14. associate-*l* 87.7%

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

      15. associate-+r+ 87.7%

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

      16. metadata-eval 87.7%

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

      17. *-commutative 87.7%

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

      18. associate-*l* 87.7%

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

      19. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   10. Simplified 87.7%

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

   if 0.52000000000000002 < z < 1.09999999999999998e60 or 9.2000000000000003e151 < z

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 68.1%

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

      1. metadata-eval 68.1%

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

      2. cancel-sign-sub-inv 68.1%

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

      3. *-commutative 68.1%

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

      4. cancel-sign-sub-inv 68.1%

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

      5. distribute-lft-neg-in 68.1%

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

      6. *-commutative 68.1%

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

      7. distribute-lft-neg-in 68.1%

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

      8. metadata-eval 68.1%

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

      9. sub-neg 68.1%

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

      10. distribute-lft-in 68.1%

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

      11. metadata-eval 68.1%

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

      12. neg-mul-1 68.1%

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

      13. *-commutative 68.1%

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

      14. associate-*l* 68.1%

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

      15. associate-+r+ 68.1%

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

      16. metadata-eval 68.1%

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

      17. *-commutative 68.1%

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

      18. associate-*l* 68.1%

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

      19. metadata-eval 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

   10. Simplified 62.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+144}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.1:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-160}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-141}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+60} \lor \neg \left(z \leq 9.2 \cdot 10^{+151}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -480000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -480000.0)
     t_1
     (if (<= z -1.76e-42)
       t_0
       (if (<= z -2.75e-102)
         (* y 4.0)
         (if (<= z -1.15e-161)
           (* x -3.0)
           (if (<= z -1.8e-204)
             (* y 4.0)
             (if (<= z -5.1e-294)
               (* x -3.0)
               (if (<= z 2.95e-173)
                 (* y 4.0)
                 (if (<= z 9.2e-151)
                   (* x -3.0)
                   (if (<= z 1.8e-32)
                     (* y 4.0)
                     (if (<= z 12000000000000.0) t_0 t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -480000.0) {
		tmp = t_1;
	} else if (z <= -1.76e-42) {
		tmp = t_0;
	} else if (z <= -2.75e-102) {
		tmp = y * 4.0;
	} else if (z <= -1.15e-161) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-204) {
		tmp = y * 4.0;
	} else if (z <= -5.1e-294) {
		tmp = x * -3.0;
	} else if (z <= 2.95e-173) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-151) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-32) {
		tmp = y * 4.0;
	} else if (z <= 12000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-480000.0d0)) then
        tmp = t_1
    else if (z <= (-1.76d-42)) then
        tmp = t_0
    else if (z <= (-2.75d-102)) then
        tmp = y * 4.0d0
    else if (z <= (-1.15d-161)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.8d-204)) then
        tmp = y * 4.0d0
    else if (z <= (-5.1d-294)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.95d-173) then
        tmp = y * 4.0d0
    else if (z <= 9.2d-151) then
        tmp = x * (-3.0d0)
    else if (z <= 1.8d-32) then
        tmp = y * 4.0d0
    else if (z <= 12000000000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -480000.0) {
		tmp = t_1;
	} else if (z <= -1.76e-42) {
		tmp = t_0;
	} else if (z <= -2.75e-102) {
		tmp = y * 4.0;
	} else if (z <= -1.15e-161) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-204) {
		tmp = y * 4.0;
	} else if (z <= -5.1e-294) {
		tmp = x * -3.0;
	} else if (z <= 2.95e-173) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-151) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-32) {
		tmp = y * 4.0;
	} else if (z <= 12000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -480000.0:
		tmp = t_1
	elif z <= -1.76e-42:
		tmp = t_0
	elif z <= -2.75e-102:
		tmp = y * 4.0
	elif z <= -1.15e-161:
		tmp = x * -3.0
	elif z <= -1.8e-204:
		tmp = y * 4.0
	elif z <= -5.1e-294:
		tmp = x * -3.0
	elif z <= 2.95e-173:
		tmp = y * 4.0
	elif z <= 9.2e-151:
		tmp = x * -3.0
	elif z <= 1.8e-32:
		tmp = y * 4.0
	elif z <= 12000000000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -480000.0)
		tmp = t_1;
	elseif (z <= -1.76e-42)
		tmp = t_0;
	elseif (z <= -2.75e-102)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.15e-161)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.8e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.1e-294)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.95e-173)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.2e-151)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.8e-32)
		tmp = Float64(y * 4.0);
	elseif (z <= 12000000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -480000.0)
		tmp = t_1;
	elseif (z <= -1.76e-42)
		tmp = t_0;
	elseif (z <= -2.75e-102)
		tmp = y * 4.0;
	elseif (z <= -1.15e-161)
		tmp = x * -3.0;
	elseif (z <= -1.8e-204)
		tmp = y * 4.0;
	elseif (z <= -5.1e-294)
		tmp = x * -3.0;
	elseif (z <= 2.95e-173)
		tmp = y * 4.0;
	elseif (z <= 9.2e-151)
		tmp = x * -3.0;
	elseif (z <= 1.8e-32)
		tmp = y * 4.0;
	elseif (z <= 12000000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -480000.0], t$95$1, If[LessEqual[z, -1.76e-42], t$95$0, If[LessEqual[z, -2.75e-102], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.15e-161], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.8e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.1e-294], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.95e-173], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.2e-151], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.8e-32], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 12000000000000.0], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e5 or 1.2e13 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 99.8%

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

   if -4.8e5 < z < -1.75999999999999998e-42 or 1.79999999999999996e-32 < z < 1.2e13

   1. Initial program 98.9%

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

      1. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around inf 82.3%

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

      1. metadata-eval 82.3%

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

      2. cancel-sign-sub-inv 82.3%

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

      3. *-commutative 82.3%

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

      4. cancel-sign-sub-inv 82.3%

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

      5. distribute-lft-neg-in 82.3%

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

      6. *-commutative 82.3%

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

      7. distribute-lft-neg-in 82.3%

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

      8. metadata-eval 82.3%

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

      9. sub-neg 82.3%

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

      10. distribute-lft-in 82.5%

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

      11. metadata-eval 82.5%

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

      12. neg-mul-1 82.5%

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

      13. *-commutative 82.5%

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

      14. associate-*l* 82.5%

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

      15. associate-+r+ 82.5%

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

      16. metadata-eval 82.5%

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

      17. *-commutative 82.5%

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

      18. associate-*l* 82.5%

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

      19. metadata-eval 82.5%

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

   7. Simplified 82.5%

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

   if -1.75999999999999998e-42 < z < -2.7499999999999999e-102 or -1.15e-161 < z < -1.79999999999999982e-204 or -5.10000000000000007e-294 < z < 2.94999999999999998e-173 or 9.19999999999999984e-151 < z < 1.79999999999999996e-32

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.5%

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

   6. Taylor expanded in y around inf 89.0%

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

      1. distribute-lft1-in 89.8%

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

      2. metadata-eval 89.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 89.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 66.1%

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

       1. *-commutative 66.1%

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

   11. Simplified 66.1%

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

   if -2.7499999999999999e-102 < z < -1.15e-161 or -1.79999999999999982e-204 < z < -5.10000000000000007e-294 or 2.94999999999999998e-173 < z < 9.19999999999999984e-151

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 87.7%

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

      1. metadata-eval 87.7%

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

      2. cancel-sign-sub-inv 87.7%

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

      3. *-commutative 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-neg-in 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-lft-in 87.7%

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

      11. metadata-eval 87.7%

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

      12. neg-mul-1 87.7%

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

      13. *-commutative 87.7%

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

      14. associate-*l* 87.7%

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

      15. associate-+r+ 87.7%

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

      16. metadata-eval 87.7%

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

      17. *-commutative 87.7%

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

      18. associate-*l* 87.7%

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

      19. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   10. Simplified 87.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-162}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-143}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.023)
     t_0
     (if (<= z -1.25e-101)
       (* y 4.0)
       (if (<= z -5.2e-162)
         (* x -3.0)
         (if (<= z -1.18e-204)
           (* y 4.0)
           (if (<= z -5.2e-293)
             (* x -3.0)
             (if (<= z 1.6e-173)
               (* y 4.0)
               (if (<= z 2.2e-143)
                 (* x -3.0)
                 (if (<= z 0.52) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.023) {
		tmp = t_0;
	} else if (z <= -1.25e-101) {
		tmp = y * 4.0;
	} else if (z <= -5.2e-162) {
		tmp = x * -3.0;
	} else if (z <= -1.18e-204) {
		tmp = y * 4.0;
	} else if (z <= -5.2e-293) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-173) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-143) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.023d0)) then
        tmp = t_0
    else if (z <= (-1.25d-101)) then
        tmp = y * 4.0d0
    else if (z <= (-5.2d-162)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.18d-204)) then
        tmp = y * 4.0d0
    else if (z <= (-5.2d-293)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-173) then
        tmp = y * 4.0d0
    else if (z <= 2.2d-143) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.023) {
		tmp = t_0;
	} else if (z <= -1.25e-101) {
		tmp = y * 4.0;
	} else if (z <= -5.2e-162) {
		tmp = x * -3.0;
	} else if (z <= -1.18e-204) {
		tmp = y * 4.0;
	} else if (z <= -5.2e-293) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-173) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-143) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.023:
		tmp = t_0
	elif z <= -1.25e-101:
		tmp = y * 4.0
	elif z <= -5.2e-162:
		tmp = x * -3.0
	elif z <= -1.18e-204:
		tmp = y * 4.0
	elif z <= -5.2e-293:
		tmp = x * -3.0
	elif z <= 1.6e-173:
		tmp = y * 4.0
	elif z <= 2.2e-143:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.023)
		tmp = t_0;
	elseif (z <= -1.25e-101)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.2e-162)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.18e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.2e-293)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-173)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.2e-143)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.023)
		tmp = t_0;
	elseif (z <= -1.25e-101)
		tmp = y * 4.0;
	elseif (z <= -5.2e-162)
		tmp = x * -3.0;
	elseif (z <= -1.18e-204)
		tmp = y * 4.0;
	elseif (z <= -5.2e-293)
		tmp = x * -3.0;
	elseif (z <= 1.6e-173)
		tmp = y * 4.0;
	elseif (z <= 2.2e-143)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.023], t$95$0, If[LessEqual[z, -1.25e-101], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.2e-162], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.18e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.2e-293], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-173], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.2e-143], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.023 or 0.52000000000000002 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in z around inf 96.1%

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

   if -0.023 < z < -1.25e-101 or -5.1999999999999999e-162 < z < -1.17999999999999995e-204 or -5.1999999999999996e-293 < z < 1.6e-173 or 2.19999999999999989e-143 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 95.7%

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

   6. Taylor expanded in y around inf 84.0%

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

      1. distribute-lft1-in 84.8%

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

      2. metadata-eval 84.8%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 84.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 59.7%

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

       1. *-commutative 59.7%

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

   11. Simplified 59.7%

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

   if -1.25e-101 < z < -5.1999999999999999e-162 or -1.17999999999999995e-204 < z < -5.1999999999999996e-293 or 1.6e-173 < z < 2.19999999999999989e-143

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 87.7%

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

      1. metadata-eval 87.7%

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

      2. cancel-sign-sub-inv 87.7%

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

      3. *-commutative 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-neg-in 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-lft-in 87.7%

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

      11. metadata-eval 87.7%

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

      12. neg-mul-1 87.7%

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

      13. *-commutative 87.7%

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

      14. associate-*l* 87.7%

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

      15. associate-+r+ 87.7%

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

      16. metadata-eval 87.7%

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

      17. *-commutative 87.7%

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

      18. associate-*l* 87.7%

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

      19. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   10. Simplified 87.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-162}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-143}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-160}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-292}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.66)
     t_0
     (if (<= z -2.9e-103)
       (* y 4.0)
       (if (<= z -1.65e-160)
         (* x -3.0)
         (if (<= z -1.9e-204)
           (* y 4.0)
           (if (<= z -1.15e-292)
             (* x -3.0)
             (if (<= z 1.9e-174)
               (* y 4.0)
               (if (<= z 8e-145)
                 (* x -3.0)
                 (if (<= z 0.66) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -2.9e-103) {
		tmp = y * 4.0;
	} else if (z <= -1.65e-160) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.15e-292) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-174) {
		tmp = y * 4.0;
	} else if (z <= 8e-145) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-2.9d-103)) then
        tmp = y * 4.0d0
    else if (z <= (-1.65d-160)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.9d-204)) then
        tmp = y * 4.0d0
    else if (z <= (-1.15d-292)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.9d-174) then
        tmp = y * 4.0d0
    else if (z <= 8d-145) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -2.9e-103) {
		tmp = y * 4.0;
	} else if (z <= -1.65e-160) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-204) {
		tmp = y * 4.0;
	} else if (z <= -1.15e-292) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-174) {
		tmp = y * 4.0;
	} else if (z <= 8e-145) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= -2.9e-103:
		tmp = y * 4.0
	elif z <= -1.65e-160:
		tmp = x * -3.0
	elif z <= -1.9e-204:
		tmp = y * 4.0
	elif z <= -1.15e-292:
		tmp = x * -3.0
	elif z <= 1.9e-174:
		tmp = y * 4.0
	elif z <= 8e-145:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -2.9e-103)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.65e-160)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.9e-204)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.15e-292)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.9e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= 8e-145)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -2.9e-103)
		tmp = y * 4.0;
	elseif (z <= -1.65e-160)
		tmp = x * -3.0;
	elseif (z <= -1.9e-204)
		tmp = y * 4.0;
	elseif (z <= -1.15e-292)
		tmp = x * -3.0;
	elseif (z <= 1.9e-174)
		tmp = y * 4.0;
	elseif (z <= 8e-145)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -2.9e-103], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.65e-160], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.9e-204], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.15e-292], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.9e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8e-145], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 0.660000000000000031 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in z around inf 96.8%

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

   7. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

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

   9. Simplified 44.7%

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

   if -0.660000000000000031 < z < -2.8999999999999999e-103 or -1.65e-160 < z < -1.89999999999999991e-204 or -1.1499999999999999e-292 < z < 1.9000000000000001e-174 or 7.99999999999999932e-145 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 94.8%

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

   6. Taylor expanded in y around inf 83.2%

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

      1. distribute-lft1-in 84.0%

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

      2. metadata-eval 84.0%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 84.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 59.2%

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

       1. *-commutative 59.2%

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

   11. Simplified 59.2%

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

   if -2.8999999999999999e-103 < z < -1.65e-160 or -1.89999999999999991e-204 < z < -1.1499999999999999e-292 or 1.9000000000000001e-174 < z < 7.99999999999999932e-145

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 87.7%

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

      1. metadata-eval 87.7%

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

      2. cancel-sign-sub-inv 87.7%

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

      3. *-commutative 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-neg-in 87.7%

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

      6. *-commutative 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

      9. sub-neg 87.7%

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

      10. distribute-lft-in 87.7%

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

      11. metadata-eval 87.7%

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

      12. neg-mul-1 87.7%

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

      13. *-commutative 87.7%

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

      14. associate-*l* 87.7%

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

      15. associate-+r+ 87.7%

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

      16. metadata-eval 87.7%

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

      17. *-commutative 87.7%

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

      18. associate-*l* 87.7%

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

      19. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   10. Simplified 87.7%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-160}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-204}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-292}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+39} \lor \neg \left(x \leq 5.6 \cdot 10^{-74} \lor \neg \left(x \leq 24000000000\right) \land x \leq 9.8 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e+39)
         (not
          (or (<= x 5.6e-74)
              (and (not (<= x 24000000000.0)) (<= x 9.8e+104)))))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e+39) || !((x <= 5.6e-74) || (!(x <= 24000000000.0) && (x <= 9.8e+104)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (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 ((x <= (-8.5d+39)) .or. (.not. (x <= 5.6d-74) .or. (.not. (x <= 24000000000.0d0)) .and. (x <= 9.8d+104))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e+39) || !((x <= 5.6e-74) || (!(x <= 24000000000.0) && (x <= 9.8e+104)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e+39) or not ((x <= 5.6e-74) or (not (x <= 24000000000.0) and (x <= 9.8e+104))):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e+39) || !((x <= 5.6e-74) || (!(x <= 24000000000.0) && (x <= 9.8e+104))))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e+39) || ~(((x <= 5.6e-74) || (~((x <= 24000000000.0)) && (x <= 9.8e+104)))))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e+39], N[Not[Or[LessEqual[x, 5.6e-74], And[N[Not[LessEqual[x, 24000000000.0]], $MachinePrecision], LessEqual[x, 9.8e+104]]]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999971e39 or 5.59999999999999976e-74 < x < 2.4e10 or 9.7999999999999997e104 < x

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 86.2%

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

      1. metadata-eval 86.2%

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

      2. cancel-sign-sub-inv 86.2%

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

      3. *-commutative 86.2%

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

      4. cancel-sign-sub-inv 86.2%

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

      5. distribute-lft-neg-in 86.2%

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

      6. *-commutative 86.2%

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

      7. distribute-lft-neg-in 86.2%

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

      8. metadata-eval 86.2%

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

      9. sub-neg 86.2%

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

      10. distribute-lft-in 86.3%

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

      11. metadata-eval 86.3%

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

      12. neg-mul-1 86.3%

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

      13. *-commutative 86.3%

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

      14. associate-*l* 86.3%

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

      15. associate-+r+ 86.3%

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

      16. metadata-eval 86.3%

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

      17. *-commutative 86.3%

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

      18. associate-*l* 86.3%

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

      19. metadata-eval 86.3%

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

   7. Simplified 86.3%

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

   if -8.49999999999999971e39 < x < 5.59999999999999976e-74 or 2.4e10 < x < 9.7999999999999997e104

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 78.7%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+39} \lor \neg \left(x \leq 5.6 \cdot 10^{-74} \lor \neg \left(x \leq 24000000000\right) \land x \leq 9.8 \cdot 10^{+104}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;z \cdot \left(x \cdot \left(6 - \frac{3}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.58)
     t_0
     (if (<= z 1.02e-8)
       (+ (* y 4.0) (* x -3.0))
       (if (<= z 12000000000000.0) (* z (* x (- 6.0 (/ 3.0 z)))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 1.02e-8) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 12000000000000.0) {
		tmp = z * (x * (6.0 - (3.0 / z)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.58d0)) then
        tmp = t_0
    else if (z <= 1.02d-8) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else if (z <= 12000000000000.0d0) then
        tmp = z * (x * (6.0d0 - (3.0d0 / z)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 1.02e-8) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 12000000000000.0) {
		tmp = z * (x * (6.0 - (3.0 / z)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.58:
		tmp = t_0
	elif z <= 1.02e-8:
		tmp = (y * 4.0) + (x * -3.0)
	elif z <= 12000000000000.0:
		tmp = z * (x * (6.0 - (3.0 / z)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 1.02e-8)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	elseif (z <= 12000000000000.0)
		tmp = Float64(z * Float64(x * Float64(6.0 - Float64(3.0 / z))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 1.02e-8)
		tmp = (y * 4.0) + (x * -3.0);
	elseif (z <= 12000000000000.0)
		tmp = z * (x * (6.0 - (3.0 / z)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.58], t$95$0, If[LessEqual[z, 1.02e-8], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000000000000.0], N[(z * N[(x * N[(6.0 - N[(3.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996 or 1.2e13 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 98.1%

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

   if -0.57999999999999996 < z < 1.02000000000000003e-8

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 98.4%

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

   6. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 1.02000000000000003e-8 < z < 1.2e13

   1. Initial program 98.4%

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

      1. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 99.0%

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

   6. Taylor expanded in x around inf 90.2%

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

      1. associate-*r/ 90.4%

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

      2. metadata-eval 90.4%

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

   8. Simplified 90.4%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;z \cdot \left(x \cdot \left(6 - \frac{3}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.54:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.54)
     t_0
     (if (<= z 2.4e-9)
       (+ x (* (- y x) 4.0))
       (if (<= z 12000000000000.0) (* x (+ -3.0 (* z 6.0))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.54) {
		tmp = t_0;
	} else if (z <= 2.4e-9) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 12000000000000.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.54d0)) then
        tmp = t_0
    else if (z <= 2.4d-9) then
        tmp = x + ((y - x) * 4.0d0)
    else if (z <= 12000000000000.0d0) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.54) {
		tmp = t_0;
	} else if (z <= 2.4e-9) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 12000000000000.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.54:
		tmp = t_0
	elif z <= 2.4e-9:
		tmp = x + ((y - x) * 4.0)
	elif z <= 12000000000000.0:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.54)
		tmp = t_0;
	elseif (z <= 2.4e-9)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	elseif (z <= 12000000000000.0)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.54)
		tmp = t_0;
	elseif (z <= 2.4e-9)
		tmp = x + ((y - x) * 4.0);
	elseif (z <= 12000000000000.0)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.54], t$95$0, If[LessEqual[z, 2.4e-9], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000000000000.0], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.54000000000000004 or 1.2e13 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 98.1%

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

   if -0.54000000000000004 < z < 2.4e-9

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 98.8%

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

   if 2.4e-9 < z < 1.2e13

   1. Initial program 98.4%

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

      1. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in x around inf 89.9%

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

      1. metadata-eval 89.9%

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

      2. cancel-sign-sub-inv 89.9%

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

      3. *-commutative 89.9%

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

      4. cancel-sign-sub-inv 89.9%

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

      5. distribute-lft-neg-in 89.9%

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

      6. *-commutative 89.9%

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

      7. distribute-lft-neg-in 89.9%

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

      8. metadata-eval 89.9%

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

      9. sub-neg 89.9%

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

      10. distribute-lft-in 90.3%

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

      11. metadata-eval 90.3%

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

      12. neg-mul-1 90.3%

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

      13. *-commutative 90.3%

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

      14. associate-*l* 90.3%

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

      15. associate-+r+ 90.3%

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

      16. metadata-eval 90.3%

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

      17. *-commutative 90.3%

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

      18. associate-*l* 90.3%

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

      19. metadata-eval 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.54:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.58)
     t_0
     (if (<= z 4e-9)
       (+ (* y 4.0) (* x -3.0))
       (if (<= z 12000000000000.0) (* x (+ -3.0 (* z 6.0))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 4e-9) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 12000000000000.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.58d0)) then
        tmp = t_0
    else if (z <= 4d-9) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else if (z <= 12000000000000.0d0) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 4e-9) {
		tmp = (y * 4.0) + (x * -3.0);
	} else if (z <= 12000000000000.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.58:
		tmp = t_0
	elif z <= 4e-9:
		tmp = (y * 4.0) + (x * -3.0)
	elif z <= 12000000000000.0:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 4e-9)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	elseif (z <= 12000000000000.0)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 4e-9)
		tmp = (y * 4.0) + (x * -3.0);
	elseif (z <= 12000000000000.0)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.58], t$95$0, If[LessEqual[z, 4e-9], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000000000000.0], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996 or 1.2e13 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 98.1%

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

   if -0.57999999999999996 < z < 4.00000000000000025e-9

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 98.4%

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

   6. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 4.00000000000000025e-9 < z < 1.2e13

   1. Initial program 98.4%

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

      1. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in x around inf 89.9%

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

      1. metadata-eval 89.9%

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

      2. cancel-sign-sub-inv 89.9%

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

      3. *-commutative 89.9%

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

      4. cancel-sign-sub-inv 89.9%

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

      5. distribute-lft-neg-in 89.9%

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

      6. *-commutative 89.9%

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

      7. distribute-lft-neg-in 89.9%

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

      8. metadata-eval 89.9%

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

      9. sub-neg 89.9%

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

      10. distribute-lft-in 90.3%

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

      11. metadata-eval 90.3%

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

      12. neg-mul-1 90.3%

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

      13. *-commutative 90.3%

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

      14. associate-*l* 90.3%

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

      15. associate-+r+ 90.3%

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

      16. metadata-eval 90.3%

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

      17. *-commutative 90.3%

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

      18. associate-*l* 90.3%

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

      19. metadata-eval 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{elif}\;z \leq 12000000000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-34} \lor \neg \left(y \leq 9 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.2e-34) (not (<= y 9e+78))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e-34) || !(y <= 9e+78)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.2d-34)) .or. (.not. (y <= 9d+78))) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e-34) || !(y <= 9e+78)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.2e-34) or not (y <= 9e+78):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.2e-34) || !(y <= 9e+78))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.2e-34) || ~((y <= 9e+78)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.2e-34], N[Not[LessEqual[y, 9e+78]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999996e-34 or 8.9999999999999999e78 < y

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 56.7%

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

   6. Taylor expanded in y around inf 56.9%

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

      1. distribute-lft1-in 56.9%

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

      2. metadata-eval 56.9%

         \[\leadsto y \cdot \left(4 + \color{blue}{-3} \cdot \frac{x}{y}\right) \]

   8. Simplified 56.9%

      \[\leadsto \color{blue}{y \cdot \left(4 + -3 \cdot \frac{x}{y}\right)} \]

   9. Taylor expanded in y around inf 47.0%

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

       1. *-commutative 47.0%

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

   11. Simplified 47.0%

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

   if -1.19999999999999996e-34 < y < 8.9999999999999999e78

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 79.8%

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

      1. metadata-eval 79.8%

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

      2. cancel-sign-sub-inv 79.8%

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

      3. *-commutative 79.8%

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

      4. cancel-sign-sub-inv 79.8%

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

      5. distribute-lft-neg-in 79.8%

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

      6. *-commutative 79.8%

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

      7. distribute-lft-neg-in 79.8%

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

      8. metadata-eval 79.8%

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

      9. sub-neg 79.8%

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

      10. distribute-lft-in 79.8%

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

      11. metadata-eval 79.8%

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

      12. neg-mul-1 79.8%

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

      13. *-commutative 79.8%

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

      14. associate-*l* 79.8%

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

      15. associate-+r+ 79.8%

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

      16. metadata-eval 79.8%

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

      17. *-commutative 79.8%

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

      18. associate-*l* 79.8%

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

      19. metadata-eval 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in z around 0 38.0%

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

      1. *-commutative 38.0%

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

   10. Simplified 38.0%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-34} \lor \neg \left(y \leq 9 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((x * -6.0) + (y * 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) * ((x * (-6.0d0)) + (y * 6.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around 0 99.5%

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

6. Final simplification 99.5%

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

Alternative 15: 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 16: 25.9% 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf 53.6%

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

   1. metadata-eval 53.6%

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

   2. cancel-sign-sub-inv 53.6%

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

   3. *-commutative 53.6%

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

   4. cancel-sign-sub-inv 53.6%

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

   5. distribute-lft-neg-in 53.6%

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

   6. *-commutative 53.6%

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

   7. distribute-lft-neg-in 53.6%

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

   8. metadata-eval 53.6%

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

   9. sub-neg 53.6%

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

   10. distribute-lft-in 53.6%

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

   11. metadata-eval 53.6%

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

   12. neg-mul-1 53.6%

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

   13. *-commutative 53.6%

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

   14. associate-*l* 53.6%

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

   15. associate-+r+ 53.6%

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

   16. metadata-eval 53.6%

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

   17. *-commutative 53.6%

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

   18. associate-*l* 53.6%

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

   19. metadata-eval 53.6%

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

7. Simplified 53.6%

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

8. Taylor expanded in z around 0 25.4%

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

   1. *-commutative 25.4%

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

10. Simplified 25.4%

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

11. Final simplification 25.4%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(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))))