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

Percentage Accurate: 99.5% → 99.7%

Time: 11.6s

Alternatives: 16

Speedup: 1.2×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Final simplification 99.8%

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

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -15200000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-138}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-249}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -15200000.0)
     t_1
     (if (<= z -2e-100)
       t_0
       (if (<= z -5.5e-138)
         (* y 4.0)
         (if (<= z -3.8e-179)
           t_0
           (if (<= z -2e-249) (* y 4.0) (if (<= z 9000.0) 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 <= -15200000.0) {
		tmp = t_1;
	} else if (z <= -2e-100) {
		tmp = t_0;
	} else if (z <= -5.5e-138) {
		tmp = y * 4.0;
	} else if (z <= -3.8e-179) {
		tmp = t_0;
	} else if (z <= -2e-249) {
		tmp = y * 4.0;
	} else if (z <= 9000.0) {
		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 <= (-15200000.0d0)) then
        tmp = t_1
    else if (z <= (-2d-100)) then
        tmp = t_0
    else if (z <= (-5.5d-138)) then
        tmp = y * 4.0d0
    else if (z <= (-3.8d-179)) then
        tmp = t_0
    else if (z <= (-2d-249)) then
        tmp = y * 4.0d0
    else if (z <= 9000.0d0) 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 <= -15200000.0) {
		tmp = t_1;
	} else if (z <= -2e-100) {
		tmp = t_0;
	} else if (z <= -5.5e-138) {
		tmp = y * 4.0;
	} else if (z <= -3.8e-179) {
		tmp = t_0;
	} else if (z <= -2e-249) {
		tmp = y * 4.0;
	} else if (z <= 9000.0) {
		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 <= -15200000.0:
		tmp = t_1
	elif z <= -2e-100:
		tmp = t_0
	elif z <= -5.5e-138:
		tmp = y * 4.0
	elif z <= -3.8e-179:
		tmp = t_0
	elif z <= -2e-249:
		tmp = y * 4.0
	elif z <= 9000.0:
		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 <= -15200000.0)
		tmp = t_1;
	elseif (z <= -2e-100)
		tmp = t_0;
	elseif (z <= -5.5e-138)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.8e-179)
		tmp = t_0;
	elseif (z <= -2e-249)
		tmp = Float64(y * 4.0);
	elseif (z <= 9000.0)
		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 <= -15200000.0)
		tmp = t_1;
	elseif (z <= -2e-100)
		tmp = t_0;
	elseif (z <= -5.5e-138)
		tmp = y * 4.0;
	elseif (z <= -3.8e-179)
		tmp = t_0;
	elseif (z <= -2e-249)
		tmp = y * 4.0;
	elseif (z <= 9000.0)
		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, -15200000.0], t$95$1, If[LessEqual[z, -2e-100], t$95$0, If[LessEqual[z, -5.5e-138], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.8e-179], t$95$0, If[LessEqual[z, -2e-249], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52e7 or 9e3 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 99.4%

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

   if -1.52e7 < z < -2e-100 or -5.5000000000000003e-138 < z < -3.79999999999999974e-179 or -2.00000000000000011e-249 < z < 9e3

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. metadata-eval 61.9%

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

      4. cancel-sign-sub-inv 61.9%

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

      5. *-commutative 61.9%

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

      6. cancel-sign-sub-inv 61.9%

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

      7. distribute-lft-neg-in 61.9%

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

      8. *-commutative 61.9%

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

      9. sub-neg 61.9%

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

      10. distribute-lft-in 61.9%

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

      11. metadata-eval 61.9%

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

      12. distribute-rgt-neg-in 61.9%

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

      13. distribute-lft-neg-in 61.9%

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

      14. metadata-eval 61.9%

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

      15. mul-1-neg 61.9%

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

      16. +-commutative 61.9%

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

      17. +-commutative 61.9%

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

      18. distribute-lft-in 61.9%

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

      19. metadata-eval 61.9%

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

   7. Simplified 61.9%

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

   if -2e-100 < z < -5.5000000000000003e-138 or -3.79999999999999974e-179 < z < -2.00000000000000011e-249

   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 0 99.9%

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

   6. Taylor expanded in x around 0 74.3%

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

      1. *-commutative 74.3%

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

   8. Simplified 74.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15200000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-138}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-249}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+248}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.34:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-180}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -8.6e+248)
     t_0
     (if (<= z -1.16e+170)
       t_1
       (if (<= z -0.34)
         t_0
         (if (<= z -7.4e-180)
           (* x -3.0)
           (if (<= z -1.85e-266)
             (* y 4.0)
             (if (<= z 0.5) (* x -3.0) t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.6e+248) {
		tmp = t_0;
	} else if (z <= -1.16e+170) {
		tmp = t_1;
	} else if (z <= -0.34) {
		tmp = t_0;
	} else if (z <= -7.4e-180) {
		tmp = x * -3.0;
	} else if (z <= -1.85e-266) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-8.6d+248)) then
        tmp = t_0
    else if (z <= (-1.16d+170)) then
        tmp = t_1
    else if (z <= (-0.34d0)) then
        tmp = t_0
    else if (z <= (-7.4d-180)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.85d-266)) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.6e+248) {
		tmp = t_0;
	} else if (z <= -1.16e+170) {
		tmp = t_1;
	} else if (z <= -0.34) {
		tmp = t_0;
	} else if (z <= -7.4e-180) {
		tmp = x * -3.0;
	} else if (z <= -1.85e-266) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -8.6e+248:
		tmp = t_0
	elif z <= -1.16e+170:
		tmp = t_1
	elif z <= -0.34:
		tmp = t_0
	elif z <= -7.4e-180:
		tmp = x * -3.0
	elif z <= -1.85e-266:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8.6e+248)
		tmp = t_0;
	elseif (z <= -1.16e+170)
		tmp = t_1;
	elseif (z <= -0.34)
		tmp = t_0;
	elseif (z <= -7.4e-180)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.85e-266)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8.6e+248)
		tmp = t_0;
	elseif (z <= -1.16e+170)
		tmp = t_1;
	elseif (z <= -0.34)
		tmp = t_0;
	elseif (z <= -7.4e-180)
		tmp = x * -3.0;
	elseif (z <= -1.85e-266)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+248], t$95$0, If[LessEqual[z, -1.16e+170], t$95$1, If[LessEqual[z, -0.34], t$95$0, If[LessEqual[z, -7.4e-180], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.85e-266], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.6000000000000001e248 or -1.16e170 < z < -0.340000000000000024

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 78.4%

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

   6. Taylor expanded in z around inf 78.0%

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

   7. Taylor expanded in x around 0 71.4%

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

      1. *-commutative 71.4%

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

   9. Simplified 71.4%

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

   if -8.6000000000000001e248 < z < -1.16e170 or 0.5 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.1%

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

   6. Taylor expanded in z around inf 90.5%

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

   7. Taylor expanded in x around inf 57.3%

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

   if -0.340000000000000024 < z < -7.40000000000000032e-180 or -1.8500000000000001e-266 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. +-commutative 58.6%

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

      3. metadata-eval 58.6%

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

      4. cancel-sign-sub-inv 58.6%

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

      5. *-commutative 58.6%

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

      6. cancel-sign-sub-inv 58.6%

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

      7. distribute-lft-neg-in 58.6%

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

      8. *-commutative 58.6%

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

      9. sub-neg 58.6%

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

      10. distribute-lft-in 58.6%

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

      11. metadata-eval 58.6%

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

      12. distribute-rgt-neg-in 58.6%

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

      13. distribute-lft-neg-in 58.6%

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

      14. metadata-eval 58.6%

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

      15. mul-1-neg 58.6%

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

      16. +-commutative 58.6%

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

      17. +-commutative 58.6%

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

      18. distribute-lft-in 58.6%

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

      19. metadata-eval 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if -7.40000000000000032e-180 < z < -1.8500000000000001e-266

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+248}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+170}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.34:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-180}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+249}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+172}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.053:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-265}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2e+249)
     t_0
     (if (<= z -1.8e+172)
       (* 6.0 (* x z))
       (if (<= z -0.053)
         t_0
         (if (<= z -5e-182)
           (* x -3.0)
           (if (<= z -2.3e-265)
             (* y 4.0)
             (if (<= z 0.5) (* x -3.0) (* x (* z 6.0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2e+249) {
		tmp = t_0;
	} else if (z <= -1.8e+172) {
		tmp = 6.0 * (x * z);
	} else if (z <= -0.053) {
		tmp = t_0;
	} else if (z <= -5e-182) {
		tmp = x * -3.0;
	} else if (z <= -2.3e-265) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-2d+249)) then
        tmp = t_0
    else if (z <= (-1.8d+172)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-0.053d0)) then
        tmp = t_0
    else if (z <= (-5d-182)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.3d-265)) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2e+249) {
		tmp = t_0;
	} else if (z <= -1.8e+172) {
		tmp = 6.0 * (x * z);
	} else if (z <= -0.053) {
		tmp = t_0;
	} else if (z <= -5e-182) {
		tmp = x * -3.0;
	} else if (z <= -2.3e-265) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2e+249:
		tmp = t_0
	elif z <= -1.8e+172:
		tmp = 6.0 * (x * z)
	elif z <= -0.053:
		tmp = t_0
	elif z <= -5e-182:
		tmp = x * -3.0
	elif z <= -2.3e-265:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2e+249)
		tmp = t_0;
	elseif (z <= -1.8e+172)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -0.053)
		tmp = t_0;
	elseif (z <= -5e-182)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.3e-265)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2e+249)
		tmp = t_0;
	elseif (z <= -1.8e+172)
		tmp = 6.0 * (x * z);
	elseif (z <= -0.053)
		tmp = t_0;
	elseif (z <= -5e-182)
		tmp = x * -3.0;
	elseif (z <= -2.3e-265)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+249], t$95$0, If[LessEqual[z, -1.8e+172], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.053], t$95$0, If[LessEqual[z, -5e-182], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.3e-265], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.9999999999999998e249 or -1.79999999999999987e172 < z < -0.0529999999999999985

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 78.4%

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

   6. Taylor expanded in z around inf 78.0%

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

   7. Taylor expanded in x around 0 71.4%

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

      1. *-commutative 71.4%

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

   9. Simplified 71.4%

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

   if -1.9999999999999998e249 < z < -1.79999999999999987e172

   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 83.5%

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

   6. Taylor expanded in z around inf 94.6%

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

   7. Taylor expanded in x around inf 68.3%

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

   if -0.0529999999999999985 < z < -5.00000000000000024e-182 or -2.2999999999999999e-265 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. +-commutative 58.6%

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

      3. metadata-eval 58.6%

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

      4. cancel-sign-sub-inv 58.6%

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

      5. *-commutative 58.6%

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

      6. cancel-sign-sub-inv 58.6%

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

      7. distribute-lft-neg-in 58.6%

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

      8. *-commutative 58.6%

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

      9. sub-neg 58.6%

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

      10. distribute-lft-in 58.6%

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

      11. metadata-eval 58.6%

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

      12. distribute-rgt-neg-in 58.6%

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

      13. distribute-lft-neg-in 58.6%

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

      14. metadata-eval 58.6%

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

      15. mul-1-neg 58.6%

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

      16. +-commutative 58.6%

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

      17. +-commutative 58.6%

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

      18. distribute-lft-in 58.6%

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

      19. metadata-eval 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if -5.00000000000000024e-182 < z < -2.2999999999999999e-265

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. +-commutative 53.7%

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

      3. metadata-eval 53.7%

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

      4. cancel-sign-sub-inv 53.7%

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

      5. *-commutative 53.7%

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

      6. cancel-sign-sub-inv 53.7%

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

      7. distribute-lft-neg-in 53.7%

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

      8. *-commutative 53.7%

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

      9. sub-neg 53.7%

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

      10. distribute-lft-in 53.7%

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

      11. metadata-eval 53.7%

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

      12. distribute-rgt-neg-in 53.7%

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

      13. distribute-lft-neg-in 53.7%

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

      14. metadata-eval 53.7%

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

      15. mul-1-neg 53.7%

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

      16. +-commutative 53.7%

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

      17. +-commutative 53.7%

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

      18. distribute-lft-in 53.7%

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

      19. metadata-eval 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in z around inf 53.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+249}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+172}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.053:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-265}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.031:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-179}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.031)
     t_0
     (if (<= z -1.22e-179)
       (* x -3.0)
       (if (<= z -8e-250) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.031) {
		tmp = t_0;
	} else if (z <= -1.22e-179) {
		tmp = x * -3.0;
	} else if (z <= -8e-250) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 <= (-0.031d0)) then
        tmp = t_0
    else if (z <= (-1.22d-179)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8d-250)) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 <= -0.031) {
		tmp = t_0;
	} else if (z <= -1.22e-179) {
		tmp = x * -3.0;
	} else if (z <= -8e-250) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.031:
		tmp = t_0
	elif z <= -1.22e-179:
		tmp = x * -3.0
	elif z <= -8e-250:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	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 <= -0.031)
		tmp = t_0;
	elseif (z <= -1.22e-179)
		tmp = Float64(x * -3.0);
	elseif (z <= -8e-250)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	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 <= -0.031)
		tmp = t_0;
	elseif (z <= -1.22e-179)
		tmp = x * -3.0;
	elseif (z <= -8e-250)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	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, -0.031], t$95$0, If[LessEqual[z, -1.22e-179], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8e-250], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.031 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 99.4%

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

   if -0.031 < z < -1.22e-179 or -8.0000000000000004e-250 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. +-commutative 58.6%

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

      3. metadata-eval 58.6%

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

      4. cancel-sign-sub-inv 58.6%

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

      5. *-commutative 58.6%

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

      6. cancel-sign-sub-inv 58.6%

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

      7. distribute-lft-neg-in 58.6%

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

      8. *-commutative 58.6%

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

      9. sub-neg 58.6%

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

      10. distribute-lft-in 58.6%

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

      11. metadata-eval 58.6%

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

      12. distribute-rgt-neg-in 58.6%

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

      13. distribute-lft-neg-in 58.6%

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

      14. metadata-eval 58.6%

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

      15. mul-1-neg 58.6%

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

      16. +-commutative 58.6%

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

      17. +-commutative 58.6%

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

      18. distribute-lft-in 58.6%

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

      19. metadata-eval 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if -1.22e-179 < z < -8.0000000000000004e-250

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.031:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-179}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.245:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-252}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.245)
     t_0
     (if (<= z -3.8e-180)
       (* x -3.0)
       (if (<= z -7e-252) (* y 4.0) (if (<= z 0.68) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.245) {
		tmp = t_0;
	} else if (z <= -3.8e-180) {
		tmp = x * -3.0;
	} else if (z <= -7e-252) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} 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 <= (-0.245d0)) then
        tmp = t_0
    else if (z <= (-3.8d-180)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7d-252)) then
        tmp = y * 4.0d0
    else if (z <= 0.68d0) then
        tmp = x * (-3.0d0)
    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 <= -0.245) {
		tmp = t_0;
	} else if (z <= -3.8e-180) {
		tmp = x * -3.0;
	} else if (z <= -7e-252) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.245:
		tmp = t_0
	elif z <= -3.8e-180:
		tmp = x * -3.0
	elif z <= -7e-252:
		tmp = y * 4.0
	elif z <= 0.68:
		tmp = x * -3.0
	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 <= -0.245)
		tmp = t_0;
	elseif (z <= -3.8e-180)
		tmp = Float64(x * -3.0);
	elseif (z <= -7e-252)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.68)
		tmp = Float64(x * -3.0);
	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 <= -0.245)
		tmp = t_0;
	elseif (z <= -3.8e-180)
		tmp = x * -3.0;
	elseif (z <= -7e-252)
		tmp = y * 4.0;
	elseif (z <= 0.68)
		tmp = x * -3.0;
	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, -0.245], t$95$0, If[LessEqual[z, -3.8e-180], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7e-252], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.245 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 84.4%

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

   6. Taylor expanded in z around inf 85.8%

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

   7. Taylor expanded in x around 0 56.3%

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

      1. *-commutative 56.3%

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

   9. Simplified 56.3%

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

   if -0.245 < z < -3.79999999999999999e-180 or -6.99999999999999972e-252 < z < 0.680000000000000049

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. +-commutative 58.6%

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

      3. metadata-eval 58.6%

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

      4. cancel-sign-sub-inv 58.6%

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

      5. *-commutative 58.6%

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

      6. cancel-sign-sub-inv 58.6%

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

      7. distribute-lft-neg-in 58.6%

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

      8. *-commutative 58.6%

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

      9. sub-neg 58.6%

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

      10. distribute-lft-in 58.6%

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

      11. metadata-eval 58.6%

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

      12. distribute-rgt-neg-in 58.6%

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

      13. distribute-lft-neg-in 58.6%

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

      14. metadata-eval 58.6%

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

      15. mul-1-neg 58.6%

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

      16. +-commutative 58.6%

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

      17. +-commutative 58.6%

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

      18. distribute-lft-in 58.6%

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

      19. metadata-eval 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in z around 0 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if -3.79999999999999999e-180 < z < -6.99999999999999972e-252

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.245:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-252}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+94} \lor \neg \left(x \leq 6.6 \cdot 10^{-50}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e+94) (not (<= x 6.6e-50)))
   (* 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 <= -7e+94) || !(x <= 6.6e-50)) {
		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 <= (-7d+94)) .or. (.not. (x <= 6.6d-50))) 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 <= -7e+94) || !(x <= 6.6e-50)) {
		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 <= -7e+94) or not (x <= 6.6e-50):
		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 <= -7e+94) || !(x <= 6.6e-50))
		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 <= -7e+94) || ~((x <= 6.6e-50)))
		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, -7e+94], N[Not[LessEqual[x, 6.6e-50]], $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 < -6.9999999999999994e94 or 6.5999999999999997e-50 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 86.5%

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

      1. +-commutative 86.5%

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

      2. +-commutative 86.5%

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

      3. metadata-eval 86.5%

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

      4. cancel-sign-sub-inv 86.5%

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

      5. *-commutative 86.5%

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

      6. cancel-sign-sub-inv 86.5%

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

      7. distribute-lft-neg-in 86.5%

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

      8. *-commutative 86.5%

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

      9. sub-neg 86.5%

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

      10. distribute-lft-in 86.5%

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

      11. metadata-eval 86.5%

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

      12. distribute-rgt-neg-in 86.5%

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

      13. distribute-lft-neg-in 86.5%

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

      14. metadata-eval 86.5%

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

      15. mul-1-neg 86.5%

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

      16. +-commutative 86.5%

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

      17. +-commutative 86.5%

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

      18. distribute-lft-in 86.5%

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

      19. metadata-eval 86.5%

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

   7. Simplified 86.5%

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

   if -6.9999999999999994e94 < x < 6.5999999999999997e-50

   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 78.5%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+94} \lor \neg \left(x \leq 6.6 \cdot 10^{-50}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.7% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (* (- y x) (* z -6.0)))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (y - x) * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = (y - x) * (z * -6.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.5%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 95.6%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in x around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-*r* 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*r* 85.8%

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

      5. distribute-rgt-out 89.5%

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

      6. *-commutative 89.5%

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

      7. remove-double-neg 89.5%

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

      8. neg-mul-1 89.5%

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

      9. associate-*r* 89.5%

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

      10. metadata-eval 89.5%

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

      11. distribute-lft-in 89.5%

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

      12. sub-neg 89.5%

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

   10. Simplified 89.5%

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

   11. Taylor expanded in z around inf 99.3%

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

       1. *-commutative 99.3%

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

       2. *-commutative 99.3%

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

       3. associate-*l* 99.4%

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

   13. Simplified 99.4%

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

4. Final simplification 97.3%

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

Alternative 9: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.5) (+ (* y 4.0) (* x -3.0)) (* (- y x) (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.5d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (y - x) * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.5:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = (y - x) * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.5)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.5)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = (y - x) * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.5%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 95.6%

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

   6. Taylor expanded in x around 0 95.6%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in x around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-*r* 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*r* 85.8%

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

      5. distribute-rgt-out 89.5%

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

      6. *-commutative 89.5%

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

      7. remove-double-neg 89.5%

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

      8. neg-mul-1 89.5%

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

      9. associate-*r* 89.5%

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

      10. metadata-eval 89.5%

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

      11. distribute-lft-in 89.5%

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

      12. sub-neg 89.5%

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

   10. Simplified 89.5%

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

   11. Taylor expanded in z around inf 99.3%

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

       1. *-commutative 99.3%

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

       2. *-commutative 99.3%

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

       3. associate-*l* 99.4%

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

   13. Simplified 99.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.65)
   (+ x (* z (* 6.0 (- x y))))
   (if (<= z 0.54) (+ (* y 4.0) (* x -3.0)) (* (- y x) (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (z * (6.0 * (x - y)));
	} else if (z <= 0.54) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.65d0)) then
        tmp = x + (z * (6.0d0 * (x - y)))
    else if (z <= 0.54d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (y - x) * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (z * (6.0 * (x - y)));
	} else if (z <= 0.54) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = (y - x) * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.65:
		tmp = x + (z * (6.0 * (x - y)))
	elif z <= 0.54:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = (y - x) * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.65)
		tmp = Float64(x + Float64(z * Float64(6.0 * Float64(x - y))));
	elseif (z <= 0.54)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.65)
		tmp = x + (z * (6.0 * (x - y)));
	elseif (z <= 0.54)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = (y - x) * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.65], N[(x + N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.54], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. neg-mul-1 99.6%

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

   7. Simplified 99.6%

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

   if -0.650000000000000022 < z < 0.54000000000000004

   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 95.6%

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

   6. Taylor expanded in x around 0 95.6%

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

   if 0.54000000000000004 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in x around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-*r* 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*r* 85.8%

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

      5. distribute-rgt-out 89.5%

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

      6. *-commutative 89.5%

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

      7. remove-double-neg 89.5%

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

      8. neg-mul-1 89.5%

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

      9. associate-*r* 89.5%

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

      10. metadata-eval 89.5%

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

      11. distribute-lft-in 89.5%

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

      12. sub-neg 89.5%

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

   10. Simplified 89.5%

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

   11. Taylor expanded in z around inf 99.3%

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

       1. *-commutative 99.3%

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

       2. *-commutative 99.3%

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

       3. associate-*l* 99.4%

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

   13. Simplified 99.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 99.8%

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

6. Final simplification 99.8%

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

Alternative 12: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-58} \lor \neg \left(y \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e-58) (not (<= y 8e+71))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-58) || !(y <= 8e+71)) {
		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 <= (-7.5d-58)) .or. (.not. (y <= 8d+71))) 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 <= -7.5e-58) || !(y <= 8e+71)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e-58) or not (y <= 8e+71):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e-58) || !(y <= 8e+71))
		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 <= -7.5e-58) || ~((y <= 8e+71)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e-58], N[Not[LessEqual[y, 8e+71]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000002e-58 or 8.0000000000000003e71 < y

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 52.6%

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

   6. Taylor expanded in x around 0 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   if -7.50000000000000002e-58 < y < 8.0000000000000003e71

   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 76.3%

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

      1. +-commutative 76.3%

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

      2. +-commutative 76.3%

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

      3. metadata-eval 76.3%

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

      4. cancel-sign-sub-inv 76.3%

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

      5. *-commutative 76.3%

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

      6. cancel-sign-sub-inv 76.3%

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

      7. distribute-lft-neg-in 76.3%

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

      8. *-commutative 76.3%

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

      9. sub-neg 76.3%

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

      10. distribute-lft-in 76.3%

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

      11. metadata-eval 76.3%

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

      12. distribute-rgt-neg-in 76.3%

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

      13. distribute-lft-neg-in 76.3%

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

      14. metadata-eval 76.3%

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

      15. mul-1-neg 76.3%

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

      16. +-commutative 76.3%

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

      17. +-commutative 76.3%

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

      18. distribute-lft-in 76.3%

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

      19. metadata-eval 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in z around 0 45.7%

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

      1. *-commutative 45.7%

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

   10. Simplified 45.7%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-58} \lor \neg \left(y \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around 0 99.6%

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

6. Final simplification 99.6%

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

Alternative 14: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 15: 25.8% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

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

Java

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

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 52.8%

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

   1. +-commutative 52.8%

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

   2. +-commutative 52.8%

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

   3. metadata-eval 52.8%

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

   4. cancel-sign-sub-inv 52.8%

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

   5. *-commutative 52.8%

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

   6. cancel-sign-sub-inv 52.8%

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

   7. distribute-lft-neg-in 52.8%

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

   8. *-commutative 52.8%

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

   9. sub-neg 52.8%

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

   10. distribute-lft-in 52.8%

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

   11. metadata-eval 52.8%

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

   12. distribute-rgt-neg-in 52.8%

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

   13. distribute-lft-neg-in 52.8%

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

   14. metadata-eval 52.8%

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

   15. mul-1-neg 52.8%

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

   16. +-commutative 52.8%

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

   17. +-commutative 52.8%

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

   18. distribute-lft-in 52.8%

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

   19. metadata-eval 52.8%

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

7. Simplified 52.8%

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

8. Taylor expanded in z around 0 29.9%

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

   1. *-commutative 29.9%

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

10. Simplified 29.9%

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

11. Final simplification 29.9%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Alternative 16: 2.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 y around inf 49.9%

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

   1. associate-*r* 50.0%

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

7. Simplified 50.0%

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

8. Taylor expanded in x around inf 2.3%

   \[\leadsto \color{blue}{x} \]

9. Final simplification 2.3%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024081 
(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))))