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

Percentage Accurate: 99.5% → 99.8%

Time: 13.2s

Alternatives: 13

Speedup: 1.2×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   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: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x + y \cdot 4\\ \mathbf{if}\;z \leq -0.3:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-200}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (+ x (* y 4.0))))
   (if (<= z -0.3)
     t_0
     (if (<= z -9e-203)
       t_1
       (if (<= z -2.5e-299)
         (* x -3.0)
         (if (<= z 7e-300)
           t_1
           (if (<= z 3.9e-200)
             (* x -3.0)
             (if (<= z 1.3e-22)
               t_1
               (if (<= z 0.5)
                 (* x -3.0)
                 (if (<= z 3.3e+164) (* x (* z 6.0)) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x + (y * 4.0);
	double tmp;
	if (z <= -0.3) {
		tmp = t_0;
	} else if (z <= -9e-203) {
		tmp = t_1;
	} else if (z <= -2.5e-299) {
		tmp = x * -3.0;
	} else if (z <= 7e-300) {
		tmp = t_1;
	} else if (z <= 3.9e-200) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-22) {
		tmp = t_1;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 3.3e+164) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x + (y * 4.0d0)
    if (z <= (-0.3d0)) then
        tmp = t_0
    else if (z <= (-9d-203)) then
        tmp = t_1
    else if (z <= (-2.5d-299)) then
        tmp = x * (-3.0d0)
    else if (z <= 7d-300) then
        tmp = t_1
    else if (z <= 3.9d-200) then
        tmp = x * (-3.0d0)
    else if (z <= 1.3d-22) then
        tmp = t_1
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 3.3d+164) then
        tmp = x * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x + (y * 4.0);
	double tmp;
	if (z <= -0.3) {
		tmp = t_0;
	} else if (z <= -9e-203) {
		tmp = t_1;
	} else if (z <= -2.5e-299) {
		tmp = x * -3.0;
	} else if (z <= 7e-300) {
		tmp = t_1;
	} else if (z <= 3.9e-200) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-22) {
		tmp = t_1;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 3.3e+164) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x + (y * 4.0)
	tmp = 0
	if z <= -0.3:
		tmp = t_0
	elif z <= -9e-203:
		tmp = t_1
	elif z <= -2.5e-299:
		tmp = x * -3.0
	elif z <= 7e-300:
		tmp = t_1
	elif z <= 3.9e-200:
		tmp = x * -3.0
	elif z <= 1.3e-22:
		tmp = t_1
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 3.3e+164:
		tmp = x * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x + Float64(y * 4.0))
	tmp = 0.0
	if (z <= -0.3)
		tmp = t_0;
	elseif (z <= -9e-203)
		tmp = t_1;
	elseif (z <= -2.5e-299)
		tmp = Float64(x * -3.0);
	elseif (z <= 7e-300)
		tmp = t_1;
	elseif (z <= 3.9e-200)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.3e-22)
		tmp = t_1;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.3e+164)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x + (y * 4.0);
	tmp = 0.0;
	if (z <= -0.3)
		tmp = t_0;
	elseif (z <= -9e-203)
		tmp = t_1;
	elseif (z <= -2.5e-299)
		tmp = x * -3.0;
	elseif (z <= 7e-300)
		tmp = t_1;
	elseif (z <= 3.9e-200)
		tmp = x * -3.0;
	elseif (z <= 1.3e-22)
		tmp = t_1;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 3.3e+164)
		tmp = x * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.3], t$95$0, If[LessEqual[z, -9e-203], t$95$1, If[LessEqual[z, -2.5e-299], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7e-300], t$95$1, If[LessEqual[z, 3.9e-200], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.3e-22], t$95$1, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.3e+164], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.299999999999999989 or 3.29999999999999995e164 < 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 99.8%

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

   6. Taylor expanded in z around inf 98.0%

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

   7. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if -0.299999999999999989 < z < -9.0000000000000003e-203 or -2.49999999999999978e-299 < z < 7.0000000000000003e-300 or 3.89999999999999999e-200 < z < 1.3e-22

   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 y around inf 65.8%

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

      1. associate-*r* 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if -9.0000000000000003e-203 < z < -2.49999999999999978e-299 or 7.0000000000000003e-300 < z < 3.89999999999999999e-200 or 1.3e-22 < 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 69.2%

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

      1. sub-neg 69.2%

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

      2. distribute-lft-in 69.2%

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

      3. metadata-eval 69.2%

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

      4. metadata-eval 69.2%

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

      5. neg-mul-1 69.2%

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

      6. *-commutative 69.2%

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

      7. associate-*l* 69.2%

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

      8. distribute-rgt-in 69.2%

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

      9. distribute-lft-in 69.2%

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

      10. metadata-eval 69.2%

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

      11. metadata-eval 69.2%

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

      12. associate-+r+ 69.2%

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

      13. metadata-eval 69.2%

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

      14. metadata-eval 69.2%

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

      15. associate-*r* 69.2%

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

      16. metadata-eval 69.2%

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

      17. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in z around 0 67.1%

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

      1. *-commutative 67.1%

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

   10. Simplified 67.1%

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

   if 0.5 < z < 3.29999999999999995e164

   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 67.1%

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

      1. sub-neg 67.1%

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

      2. distribute-lft-in 67.1%

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

      3. metadata-eval 67.1%

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

      4. metadata-eval 67.1%

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

      5. neg-mul-1 67.1%

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

      6. *-commutative 67.1%

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

      7. associate-*l* 67.1%

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

      8. distribute-rgt-in 67.1%

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

      9. distribute-lft-in 67.1%

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

      10. metadata-eval 67.1%

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

      11. metadata-eval 67.1%

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

      12. associate-+r+ 67.1%

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

      13. metadata-eval 67.1%

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

      14. metadata-eval 67.1%

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

      15. associate-*r* 67.1%

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

      16. metadata-eval 67.1%

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

      17. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in z around inf 62.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.3:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-203}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-300}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-200}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0295:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-203}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-294}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-200}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0295)
     t_1
     (if (<= z -2.25e-203)
       t_0
       (if (<= z -5.5e-299)
         (* x -3.0)
         (if (<= z 1.05e-294)
           t_0
           (if (<= z 3.5e-200)
             (* x -3.0)
             (if (<= z 1.05e-22) t_0 (if (<= z 0.5) (* x -3.0) t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0295) {
		tmp = t_1;
	} else if (z <= -2.25e-203) {
		tmp = t_0;
	} else if (z <= -5.5e-299) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-294) {
		tmp = t_0;
	} else if (z <= 3.5e-200) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-22) {
		tmp = t_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 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0295d0)) then
        tmp = t_1
    else if (z <= (-2.25d-203)) then
        tmp = t_0
    else if (z <= (-5.5d-299)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d-294) then
        tmp = t_0
    else if (z <= 3.5d-200) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d-22) then
        tmp = t_0
    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 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0295) {
		tmp = t_1;
	} else if (z <= -2.25e-203) {
		tmp = t_0;
	} else if (z <= -5.5e-299) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-294) {
		tmp = t_0;
	} else if (z <= 3.5e-200) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-22) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0295:
		tmp = t_1
	elif z <= -2.25e-203:
		tmp = t_0
	elif z <= -5.5e-299:
		tmp = x * -3.0
	elif z <= 1.05e-294:
		tmp = t_0
	elif z <= 3.5e-200:
		tmp = x * -3.0
	elif z <= 1.05e-22:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0295)
		tmp = t_1;
	elseif (z <= -2.25e-203)
		tmp = t_0;
	elseif (z <= -5.5e-299)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05e-294)
		tmp = t_0;
	elseif (z <= 3.5e-200)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05e-22)
		tmp = t_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 = x + (y * 4.0);
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0295)
		tmp = t_1;
	elseif (z <= -2.25e-203)
		tmp = t_0;
	elseif (z <= -5.5e-299)
		tmp = x * -3.0;
	elseif (z <= 1.05e-294)
		tmp = t_0;
	elseif (z <= 3.5e-200)
		tmp = x * -3.0;
	elseif (z <= 1.05e-22)
		tmp = t_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[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0295], t$95$1, If[LessEqual[z, -2.25e-203], t$95$0, If[LessEqual[z, -5.5e-299], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05e-294], t$95$0, If[LessEqual[z, 3.5e-200], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05e-22], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.029499999999999998 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 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 97.2%

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

   if -0.029499999999999998 < z < -2.2500000000000001e-203 or -5.5e-299 < z < 1.04999999999999992e-294 or 3.50000000000000023e-200 < z < 1.05000000000000004e-22

   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 y around inf 65.8%

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

      1. associate-*r* 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if -2.2500000000000001e-203 < z < -5.5e-299 or 1.04999999999999992e-294 < z < 3.50000000000000023e-200 or 1.05000000000000004e-22 < 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 69.2%

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

      1. sub-neg 69.2%

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

      2. distribute-lft-in 69.2%

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

      3. metadata-eval 69.2%

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

      4. metadata-eval 69.2%

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

      5. neg-mul-1 69.2%

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

      6. *-commutative 69.2%

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

      7. associate-*l* 69.2%

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

      8. distribute-rgt-in 69.2%

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

      9. distribute-lft-in 69.2%

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

      10. metadata-eval 69.2%

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

      11. metadata-eval 69.2%

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

      12. associate-+r+ 69.2%

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

      13. metadata-eval 69.2%

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

      14. metadata-eval 69.2%

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

      15. associate-*r* 69.2%

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

      16. metadata-eval 69.2%

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

      17. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in z around 0 67.1%

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

      1. *-commutative 67.1%

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

   10. Simplified 67.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0295:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-203}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-294}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-200}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.008:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-203}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-294}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-198}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1100000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.008)
     t_1
     (if (<= z -8e-203)
       t_0
       (if (<= z -1.2e-299)
         (* x -3.0)
         (if (<= z 2e-294)
           t_0
           (if (<= z 4.9e-198)
             (* x -3.0)
             (if (<= z 1.3e-22)
               t_0
               (if (<= z 1100000.0) (* x (+ -3.0 (* z 6.0))) t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.008) {
		tmp = t_1;
	} else if (z <= -8e-203) {
		tmp = t_0;
	} else if (z <= -1.2e-299) {
		tmp = x * -3.0;
	} else if (z <= 2e-294) {
		tmp = t_0;
	} else if (z <= 4.9e-198) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-22) {
		tmp = t_0;
	} else if (z <= 1100000.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.008d0)) then
        tmp = t_1
    else if (z <= (-8d-203)) then
        tmp = t_0
    else if (z <= (-1.2d-299)) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-294) then
        tmp = t_0
    else if (z <= 4.9d-198) then
        tmp = x * (-3.0d0)
    else if (z <= 1.3d-22) then
        tmp = t_0
    else if (z <= 1100000.0d0) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.008) {
		tmp = t_1;
	} else if (z <= -8e-203) {
		tmp = t_0;
	} else if (z <= -1.2e-299) {
		tmp = x * -3.0;
	} else if (z <= 2e-294) {
		tmp = t_0;
	} else if (z <= 4.9e-198) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-22) {
		tmp = t_0;
	} else if (z <= 1100000.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.008:
		tmp = t_1
	elif z <= -8e-203:
		tmp = t_0
	elif z <= -1.2e-299:
		tmp = x * -3.0
	elif z <= 2e-294:
		tmp = t_0
	elif z <= 4.9e-198:
		tmp = x * -3.0
	elif z <= 1.3e-22:
		tmp = t_0
	elif z <= 1100000.0:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.008)
		tmp = t_1;
	elseif (z <= -8e-203)
		tmp = t_0;
	elseif (z <= -1.2e-299)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-294)
		tmp = t_0;
	elseif (z <= 4.9e-198)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.3e-22)
		tmp = t_0;
	elseif (z <= 1100000.0)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.008)
		tmp = t_1;
	elseif (z <= -8e-203)
		tmp = t_0;
	elseif (z <= -1.2e-299)
		tmp = x * -3.0;
	elseif (z <= 2e-294)
		tmp = t_0;
	elseif (z <= 4.9e-198)
		tmp = x * -3.0;
	elseif (z <= 1.3e-22)
		tmp = t_0;
	elseif (z <= 1100000.0)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.008], t$95$1, If[LessEqual[z, -8e-203], t$95$0, If[LessEqual[z, -1.2e-299], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-294], t$95$0, If[LessEqual[z, 4.9e-198], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.3e-22], t$95$0, If[LessEqual[z, 1100000.0], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0080000000000000002 or 1.1e6 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 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 98.2%

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

   if -0.0080000000000000002 < z < -8.0000000000000003e-203 or -1.2000000000000001e-299 < z < 2.00000000000000003e-294 or 4.9000000000000002e-198 < z < 1.3e-22

   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 y around inf 65.8%

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

      1. associate-*r* 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if -8.0000000000000003e-203 < z < -1.2000000000000001e-299 or 2.00000000000000003e-294 < z < 4.9000000000000002e-198

   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 68.9%

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

      1. sub-neg 68.9%

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

      2. distribute-lft-in 68.9%

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

      3. metadata-eval 68.9%

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

      4. metadata-eval 68.9%

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

      5. neg-mul-1 68.9%

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

      6. *-commutative 68.9%

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

      7. associate-*l* 68.9%

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

      8. distribute-rgt-in 68.9%

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

      9. distribute-lft-in 68.9%

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

      10. metadata-eval 68.9%

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

      11. metadata-eval 68.9%

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

      12. associate-+r+ 68.9%

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

      13. metadata-eval 68.9%

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

      14. metadata-eval 68.9%

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

      15. associate-*r* 68.9%

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

      16. metadata-eval 68.9%

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

      17. *-commutative 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in z around 0 68.9%

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

      1. *-commutative 68.9%

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

   10. Simplified 68.9%

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

   if 1.3e-22 < z < 1.1e6

   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 79.6%

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

      1. sub-neg 79.6%

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

      2. distribute-lft-in 79.6%

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

      3. metadata-eval 79.6%

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

      4. metadata-eval 79.6%

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

      5. neg-mul-1 79.6%

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

      6. *-commutative 79.6%

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

      7. associate-*l* 79.6%

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

      8. distribute-rgt-in 79.6%

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

      9. distribute-lft-in 79.6%

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

      10. metadata-eval 79.6%

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

      11. metadata-eval 79.6%

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

      12. associate-+r+ 79.6%

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

      13. metadata-eval 79.6%

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

      14. metadata-eval 79.6%

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

      15. associate-*r* 79.6%

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

      16. metadata-eval 79.6%

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

      17. *-commutative 79.6%

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

   7. Simplified 79.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.008:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-203}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-294}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-198}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 1100000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-49}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-53} \lor \neg \left(y \leq 2.25 \cdot 10^{+34}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= y -1.45e+69)
     t_0
     (if (<= y -3.5e-49)
       (* -6.0 (* (- y x) z))
       (if (or (<= y -8.5e-53) (not (<= y 2.25e+34)))
         t_0
         (* x (+ -3.0 (* z 6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -1.45e+69) {
		tmp = t_0;
	} else if (y <= -3.5e-49) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((y <= -8.5e-53) || !(y <= 2.25e+34)) {
		tmp = t_0;
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    if (y <= (-1.45d+69)) then
        tmp = t_0
    else if (y <= (-3.5d-49)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if ((y <= (-8.5d-53)) .or. (.not. (y <= 2.25d+34))) then
        tmp = t_0
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -1.45e+69) {
		tmp = t_0;
	} else if (y <= -3.5e-49) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((y <= -8.5e-53) || !(y <= 2.25e+34)) {
		tmp = t_0;
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if y <= -1.45e+69:
		tmp = t_0
	elif y <= -3.5e-49:
		tmp = -6.0 * ((y - x) * z)
	elif (y <= -8.5e-53) or not (y <= 2.25e+34):
		tmp = t_0
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -1.45e+69)
		tmp = t_0;
	elseif (y <= -3.5e-49)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif ((y <= -8.5e-53) || !(y <= 2.25e+34))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -1.45e+69)
		tmp = t_0;
	elseif (y <= -3.5e-49)
		tmp = -6.0 * ((y - x) * z);
	elseif ((y <= -8.5e-53) || ~((y <= 2.25e+34)))
		tmp = t_0;
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+69], t$95$0, If[LessEqual[y, -3.5e-49], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.5e-53], N[Not[LessEqual[y, 2.25e+34]], $MachinePrecision]], t$95$0, N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e69 or -3.50000000000000006e-49 < y < -8.50000000000000044e-53 or 2.25e34 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 84.5%

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

   if -1.4499999999999999e69 < y < -3.50000000000000006e-49

   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 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 75.0%

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

   if -8.50000000000000044e-53 < y < 2.25e34

   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 76.6%

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

      1. sub-neg 76.6%

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

      2. distribute-lft-in 76.6%

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

      3. metadata-eval 76.6%

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

      4. metadata-eval 76.6%

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

      5. neg-mul-1 76.6%

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

      6. *-commutative 76.6%

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

      7. associate-*l* 76.6%

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

      8. distribute-rgt-in 76.6%

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

      9. distribute-lft-in 76.6%

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

      10. metadata-eval 76.6%

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

      11. metadata-eval 76.6%

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

      12. associate-+r+ 76.6%

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

      13. metadata-eval 76.6%

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

      14. metadata-eval 76.6%

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

      15. associate-*r* 76.6%

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

      16. metadata-eval 76.6%

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

      17. *-commutative 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-49}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-53} \lor \neg \left(y \leq 2.25 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1360000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+164}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1360000000.0)
     t_0
     (if (<= z 0.5) (* x -3.0) (if (<= z 7.6e+164) (* 6.0 (* x z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1360000000.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 7.6e+164) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1360000000.0d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 7.6d+164) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1360000000.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 7.6e+164) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1360000000.0:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 7.6e+164:
		tmp = 6.0 * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1360000000.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.6e+164)
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1360000000.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 7.6e+164)
		tmp = 6.0 * (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1360000000.0], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.6e+164], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36e9 or 7.60000000000000042e164 < 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 99.8%

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

   6. Taylor expanded in z around inf 99.7%

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

   7. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

   9. Simplified 62.0%

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

   if -1.36e9 < 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 48.8%

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

      1. sub-neg 48.8%

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

      2. distribute-lft-in 48.8%

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

      3. metadata-eval 48.8%

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

      4. metadata-eval 48.8%

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

      5. neg-mul-1 48.8%

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

      6. *-commutative 48.8%

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

      7. associate-*l* 48.8%

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

      8. distribute-rgt-in 48.8%

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

      9. distribute-lft-in 48.8%

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

      10. metadata-eval 48.8%

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

      11. metadata-eval 48.8%

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

      12. associate-+r+ 48.8%

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

      13. metadata-eval 48.8%

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

      14. metadata-eval 48.8%

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

      15. associate-*r* 48.8%

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

      16. metadata-eval 48.8%

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

      17. *-commutative 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in z around 0 46.0%

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

      1. *-commutative 46.0%

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

   10. Simplified 46.0%

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

   if 0.5 < z < 7.60000000000000042e164

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.4%

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

   6. Taylor expanded in z around inf 94.4%

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

   7. Taylor expanded in y around 0 62.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1360000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+164}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1360000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1360000000.0)
     t_0
     (if (<= z 0.5) (* x -3.0) (if (<= z 6.2e+166) (* x (* z 6.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1360000000.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.2e+166) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1360000000.0d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 6.2d+166) then
        tmp = x * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1360000000.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.2e+166) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1360000000.0:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 6.2e+166:
		tmp = x * (z * 6.0)
	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 <= -1360000000.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.2e+166)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1360000000.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 6.2e+166)
		tmp = x * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1360000000.0], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.2e+166], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36e9 or 6.19999999999999966e166 < 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 99.8%

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

   6. Taylor expanded in z around inf 99.7%

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

   7. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

   9. Simplified 62.0%

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

   if -1.36e9 < 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 48.8%

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

      1. sub-neg 48.8%

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

      2. distribute-lft-in 48.8%

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

      3. metadata-eval 48.8%

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

      4. metadata-eval 48.8%

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

      5. neg-mul-1 48.8%

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

      6. *-commutative 48.8%

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

      7. associate-*l* 48.8%

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

      8. distribute-rgt-in 48.8%

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

      9. distribute-lft-in 48.8%

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

      10. metadata-eval 48.8%

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

      11. metadata-eval 48.8%

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

      12. associate-+r+ 48.8%

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

      13. metadata-eval 48.8%

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

      14. metadata-eval 48.8%

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

      15. associate-*r* 48.8%

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

      16. metadata-eval 48.8%

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

      17. *-commutative 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in z around 0 46.0%

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

      1. *-commutative 46.0%

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

   10. Simplified 46.0%

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

   if 0.5 < z < 6.19999999999999966e166

   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 67.1%

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

      1. sub-neg 67.1%

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

      2. distribute-lft-in 67.1%

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

      3. metadata-eval 67.1%

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

      4. metadata-eval 67.1%

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

      5. neg-mul-1 67.1%

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

      6. *-commutative 67.1%

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

      7. associate-*l* 67.1%

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

      8. distribute-rgt-in 67.1%

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

      9. distribute-lft-in 67.1%

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

      10. metadata-eval 67.1%

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

      11. metadata-eval 67.1%

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

      12. associate-+r+ 67.1%

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

      13. metadata-eval 67.1%

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

      14. metadata-eval 67.1%

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

      15. associate-*r* 67.1%

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

      16. metadata-eval 67.1%

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

      17. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in z around inf 62.8%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1360000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.59 \lor \neg \left(z \leq 0.66\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - 4 \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.59) (not (<= z 0.66)))
   (* -6.0 (* (- y x) z))
   (- x (* 4.0 (- x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.59) || !(z <= 0.66)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x - (4.0 * (x - y));
	}
	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 <= (-0.59d0)) .or. (.not. (z <= 0.66d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = x - (4.0d0 * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.59) || !(z <= 0.66)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x - (4.0 * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.59) or not (z <= 0.66):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = x - (4.0 * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.59) || !(z <= 0.66))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x - Float64(4.0 * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.59) || ~((z <= 0.66)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = x - (4.0 * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.59], N[Not[LessEqual[z, 0.66]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.589999999999999969 or 0.660000000000000031 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 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 97.8%

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

   if -0.589999999999999969 < z < 0.660000000000000031

   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 z around 0 97.7%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.59 \lor \neg \left(z \leq 0.66\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - 4 \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1360000000 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1360000000.0) (not (<= z 0.65))) (* -6.0 (* y z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1360000000.0) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1360000000.0d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1360000000.0) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1360000000.0) or not (z <= 0.65):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1360000000.0) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1360000000.0) || ~((z <= 0.65)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1360000000.0], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.36e9 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 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 98.5%

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

   7. Taylor expanded in y around inf 56.3%

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

      1. *-commutative 56.3%

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

   9. Simplified 56.3%

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

   if -1.36e9 < z < 0.650000000000000022

   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 48.8%

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

      1. sub-neg 48.8%

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

      2. distribute-lft-in 48.8%

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

      3. metadata-eval 48.8%

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

      4. metadata-eval 48.8%

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

      5. neg-mul-1 48.8%

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

      6. *-commutative 48.8%

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

      7. associate-*l* 48.8%

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

      8. distribute-rgt-in 48.8%

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

      9. distribute-lft-in 48.8%

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

      10. metadata-eval 48.8%

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

      11. metadata-eval 48.8%

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

      12. associate-+r+ 48.8%

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

      13. metadata-eval 48.8%

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

      14. metadata-eval 48.8%

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

      15. associate-*r* 48.8%

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

      16. metadata-eval 48.8%

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

      17. *-commutative 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in z around 0 46.0%

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

      1. *-commutative 46.0%

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

   10. Simplified 46.0%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1360000000 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in z around 0 99.8%

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

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 11: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 12: 25.7% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf 49.8%

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

   1. sub-neg 49.8%

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

   2. distribute-lft-in 49.8%

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

   3. metadata-eval 49.8%

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

   4. metadata-eval 49.8%

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

   5. neg-mul-1 49.8%

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

   6. *-commutative 49.8%

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

   7. associate-*l* 49.8%

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

   8. distribute-rgt-in 49.8%

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

   9. distribute-lft-in 49.8%

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

   10. metadata-eval 49.8%

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

   11. metadata-eval 49.8%

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

   12. associate-+r+ 49.8%

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

   13. metadata-eval 49.8%

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

   14. metadata-eval 49.8%

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

   15. associate-*r* 49.8%

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

   16. metadata-eval 49.8%

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

   17. *-commutative 49.8%

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

7. Simplified 49.8%

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

8. Taylor expanded in z around 0 24.7%

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

   1. *-commutative 24.7%

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

10. Simplified 24.7%

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

11. Final simplification 24.7%

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

Alternative 13: 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around inf 54.3%

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

   1. associate-*r* 54.3%

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

7. Simplified 54.3%

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

8. Taylor expanded in x around inf 2.6%

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

9. Final simplification 2.6%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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))))