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

Percentage Accurate: 99.5% → 99.7%

Time: 13.3s

Alternatives: 15

Speedup: 1.2×

• 21.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Add Preprocessing

Alternative 2: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.33:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.8e+137)
     (* x (* z 6.0))
     (if (<= z -0.33)
       t_1
       (if (<= z -3.8e-42)
         t_0
         (if (<= z -1.06e-216)
           (* x -3.0)
           (if (<= z 4.8e-162) t_0 (if (<= z 0.54) (* 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 * z);
	double tmp;
	if (z <= -1.8e+137) {
		tmp = x * (z * 6.0);
	} else if (z <= -0.33) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -1.06e-216) {
		tmp = x * -3.0;
	} else if (z <= 4.8e-162) {
		tmp = t_0;
	} else if (z <= 0.54) {
		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 * z)
    if (z <= (-1.8d+137)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-0.33d0)) then
        tmp = t_1
    else if (z <= (-3.8d-42)) then
        tmp = t_0
    else if (z <= (-1.06d-216)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.8d-162) then
        tmp = t_0
    else if (z <= 0.54d0) 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 * z);
	double tmp;
	if (z <= -1.8e+137) {
		tmp = x * (z * 6.0);
	} else if (z <= -0.33) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -1.06e-216) {
		tmp = x * -3.0;
	} else if (z <= 4.8e-162) {
		tmp = t_0;
	} else if (z <= 0.54) {
		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 * z)
	tmp = 0
	if z <= -1.8e+137:
		tmp = x * (z * 6.0)
	elif z <= -0.33:
		tmp = t_1
	elif z <= -3.8e-42:
		tmp = t_0
	elif z <= -1.06e-216:
		tmp = x * -3.0
	elif z <= 4.8e-162:
		tmp = t_0
	elif z <= 0.54:
		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(y * z))
	tmp = 0.0
	if (z <= -1.8e+137)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -0.33)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -1.06e-216)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.8e-162)
		tmp = t_0;
	elseif (z <= 0.54)
		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 * z);
	tmp = 0.0;
	if (z <= -1.8e+137)
		tmp = x * (z * 6.0);
	elseif (z <= -0.33)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -1.06e-216)
		tmp = x * -3.0;
	elseif (z <= 4.8e-162)
		tmp = t_0;
	elseif (z <= 0.54)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+137], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.33], t$95$1, If[LessEqual[z, -3.8e-42], t$95$0, If[LessEqual[z, -1.06e-216], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.8e-162], t$95$0, If[LessEqual[z, 0.54], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e137

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. fma-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 0 58.8%

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

      1. *-lft-identity 58.8%

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

      2. *-commutative 58.8%

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

      3. +-commutative 58.8%

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

      4. *-commutative 58.8%

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

      5. fma-define 58.8%

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

      6. associate-*r* 58.8%

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

      7. neg-mul-1 58.8%

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

      8. fma-define 58.8%

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

      9. distribute-neg-in 58.8%

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

      10. distribute-lft-neg-in 58.8%

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

      11. metadata-eval 58.8%

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

      12. metadata-eval 58.8%

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

      13. distribute-rgt-in 58.8%

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

      14. +-commutative 58.8%

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

      15. sub-neg 58.8%

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

      16. distribute-rgt-in 58.8%

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

      17. sub-neg 58.8%

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

      18. distribute-rgt-in 58.8%

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

      19. metadata-eval 58.8%

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

      20. distribute-lft-neg-in 58.8%

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

      21. associate-+r+ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*r* 58.8%

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

   10. Simplified 58.8%

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

   if -1.8e137 < z < -0.330000000000000016 or 0.54000000000000004 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 95.9%

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

   8. Taylor expanded in y around inf 56.2%

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

   if -0.330000000000000016 < z < -3.80000000000000017e-42 or -1.06e-216 < z < 4.8000000000000004e-162

   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. Step-by-step derivation

      1. +-commutative 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

      1. fma-undefine 99.4%

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

   8. Applied egg-rr 99.4%

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

   9. Taylor expanded in z around 0 98.2%

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

   10. Taylor expanded in y around inf 72.5%

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

   if -3.80000000000000017e-42 < z < -1.06e-216 or 4.8000000000000004e-162 < z < 0.54000000000000004

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 66.8%

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

      1. *-lft-identity 66.8%

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

      2. *-commutative 66.8%

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

      3. +-commutative 66.8%

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

      4. *-commutative 66.8%

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

      5. fma-define 66.8%

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

      6. associate-*r* 66.8%

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

      7. neg-mul-1 66.8%

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

      8. fma-define 66.8%

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

      9. distribute-neg-in 66.8%

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

      10. distribute-lft-neg-in 66.8%

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

      11. metadata-eval 66.8%

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

      12. metadata-eval 66.8%

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

      13. distribute-rgt-in 66.8%

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

      14. +-commutative 66.8%

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

      15. sub-neg 66.8%

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

      16. distribute-rgt-in 66.8%

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

      17. sub-neg 66.8%

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

      18. distribute-rgt-in 66.8%

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

      19. metadata-eval 66.8%

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

      20. distribute-lft-neg-in 66.8%

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

      21. associate-+r+ 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in z around 0 66.5%

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

      1. *-commutative 66.5%

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

   10. Simplified 66.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.33:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-162}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ t_2 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;z \leq -215000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0))))
        (t_1 (* -6.0 (* (- y x) z)))
        (t_2 (* x (+ -3.0 (* z 6.0)))))
   (if (<= z -215000000.0)
     t_1
     (if (<= z -3.8e-42)
       t_0
       (if (<= z -6.6e-185)
         t_2
         (if (<= z 4.9e-162) t_0 (if (<= z 1000.0) t_2 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double t_2 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -215000000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -6.6e-185) {
		tmp = t_2;
	} else if (z <= 4.9e-162) {
		tmp = t_0;
	} else if (z <= 1000.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    t_1 = (-6.0d0) * ((y - x) * z)
    t_2 = x * ((-3.0d0) + (z * 6.0d0))
    if (z <= (-215000000.0d0)) then
        tmp = t_1
    else if (z <= (-3.8d-42)) then
        tmp = t_0
    else if (z <= (-6.6d-185)) then
        tmp = t_2
    else if (z <= 4.9d-162) then
        tmp = t_0
    else if (z <= 1000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    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 t_1 = -6.0 * ((y - x) * z);
	double t_2 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -215000000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -6.6e-185) {
		tmp = t_2;
	} else if (z <= 4.9e-162) {
		tmp = t_0;
	} else if (z <= 1000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	t_1 = -6.0 * ((y - x) * z)
	t_2 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if z <= -215000000.0:
		tmp = t_1
	elif z <= -3.8e-42:
		tmp = t_0
	elif z <= -6.6e-185:
		tmp = t_2
	elif z <= 4.9e-162:
		tmp = t_0
	elif z <= 1000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	t_2 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (z <= -215000000.0)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -6.6e-185)
		tmp = t_2;
	elseif (z <= 4.9e-162)
		tmp = t_0;
	elseif (z <= 1000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	t_1 = -6.0 * ((y - x) * z);
	t_2 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (z <= -215000000.0)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -6.6e-185)
		tmp = t_2;
	elseif (z <= 4.9e-162)
		tmp = t_0;
	elseif (z <= 1000.0)
		tmp = t_2;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -215000000.0], t$95$1, If[LessEqual[z, -3.8e-42], t$95$0, If[LessEqual[z, -6.6e-185], t$95$2, If[LessEqual[z, 4.9e-162], t$95$0, If[LessEqual[z, 1000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e8 or 1e3 < 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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 98.7%

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

   if -2.15e8 < z < -3.80000000000000017e-42 or -6.5999999999999995e-185 < z < 4.89999999999999976e-162

   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. +-commutative 99.4%

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

      2. associate-*l* 100.0%

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

      3. fma-define 100.0%

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

      4. sub-neg 100.0%

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

      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 72.9%

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

   if -3.80000000000000017e-42 < z < -6.5999999999999995e-185 or 4.89999999999999976e-162 < z < 1e3

   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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 67.4%

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

      1. *-lft-identity 67.4%

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

      2. *-commutative 67.4%

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

      3. +-commutative 67.4%

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

      4. *-commutative 67.4%

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

      5. fma-define 67.4%

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

      6. associate-*r* 67.4%

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

      7. neg-mul-1 67.4%

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

      8. fma-define 67.4%

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

      9. distribute-neg-in 67.4%

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

      10. distribute-lft-neg-in 67.4%

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

      11. metadata-eval 67.4%

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

      12. metadata-eval 67.4%

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

      13. distribute-rgt-in 67.4%

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

      14. +-commutative 67.4%

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

      15. sub-neg 67.4%

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

      16. distribute-rgt-in 67.4%

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

      17. sub-neg 67.4%

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

      18. distribute-rgt-in 67.4%

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

      19. metadata-eval 67.4%

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

      20. distribute-lft-neg-in 67.4%

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

      21. associate-+r+ 67.4%

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

   7. Simplified 67.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -215000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-162}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ t_2 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;z \leq -195000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1050:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z)))
        (t_2 (* x (+ -3.0 (* z 6.0)))))
   (if (<= z -195000000.0)
     t_1
     (if (<= z -3.8e-42)
       t_0
       (if (<= z -7.2e-185)
         t_2
         (if (<= z 4.6e-162) t_0 (if (<= z 1050.0) t_2 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double t_2 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -195000000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -7.2e-185) {
		tmp = t_2;
	} else if (z <= 4.6e-162) {
		tmp = t_0;
	} else if (z <= 1050.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    t_2 = x * ((-3.0d0) + (z * 6.0d0))
    if (z <= (-195000000.0d0)) then
        tmp = t_1
    else if (z <= (-3.8d-42)) then
        tmp = t_0
    else if (z <= (-7.2d-185)) then
        tmp = t_2
    else if (z <= 4.6d-162) then
        tmp = t_0
    else if (z <= 1050.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double t_2 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -195000000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -7.2e-185) {
		tmp = t_2;
	} else if (z <= 4.6e-162) {
		tmp = t_0;
	} else if (z <= 1050.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	t_2 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if z <= -195000000.0:
		tmp = t_1
	elif z <= -3.8e-42:
		tmp = t_0
	elif z <= -7.2e-185:
		tmp = t_2
	elif z <= 4.6e-162:
		tmp = t_0
	elif z <= 1050.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	t_2 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (z <= -195000000.0)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -7.2e-185)
		tmp = t_2;
	elseif (z <= 4.6e-162)
		tmp = t_0;
	elseif (z <= 1050.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	t_2 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (z <= -195000000.0)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -7.2e-185)
		tmp = t_2;
	elseif (z <= 4.6e-162)
		tmp = t_0;
	elseif (z <= 1050.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -195000000.0], t$95$1, If[LessEqual[z, -3.8e-42], t$95$0, If[LessEqual[z, -7.2e-185], t$95$2, If[LessEqual[z, 4.6e-162], t$95$0, If[LessEqual[z, 1050.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e8 or 1050 < 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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 98.7%

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

   if -1.95e8 < z < -3.80000000000000017e-42 or -7.1999999999999997e-185 < z < 4.5999999999999996e-162

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 78.7%

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

   6. Taylor expanded in x around 0 72.5%

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

   if -3.80000000000000017e-42 < z < -7.1999999999999997e-185 or 4.5999999999999996e-162 < z < 1050

   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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 67.4%

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

      1. *-lft-identity 67.4%

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

      2. *-commutative 67.4%

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

      3. +-commutative 67.4%

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

      4. *-commutative 67.4%

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

      5. fma-define 67.4%

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

      6. associate-*r* 67.4%

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

      7. neg-mul-1 67.4%

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

      8. fma-define 67.4%

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

      9. distribute-neg-in 67.4%

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

      10. distribute-lft-neg-in 67.4%

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

      11. metadata-eval 67.4%

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

      12. metadata-eval 67.4%

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

      13. distribute-rgt-in 67.4%

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

      14. +-commutative 67.4%

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

      15. sub-neg 67.4%

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

      16. distribute-rgt-in 67.4%

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

      17. sub-neg 67.4%

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

      18. distribute-rgt-in 67.4%

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

      19. metadata-eval 67.4%

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

      20. distribute-lft-neg-in 67.4%

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

      21. associate-+r+ 67.4%

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

   7. Simplified 67.4%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-162}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 1050:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -195000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -195000000.0)
     t_1
     (if (<= z -3.7e-42)
       t_0
       (if (<= z -6.5e-185)
         (* x -3.0)
         (if (<= z 4.6e-162) t_0 (if (<= z 0.5) (* x -3.0) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -195000000.0) {
		tmp = t_1;
	} else if (z <= -3.7e-42) {
		tmp = t_0;
	} else if (z <= -6.5e-185) {
		tmp = x * -3.0;
	} else if (z <= 4.6e-162) {
		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 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-195000000.0d0)) then
        tmp = t_1
    else if (z <= (-3.7d-42)) then
        tmp = t_0
    else if (z <= (-6.5d-185)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.6d-162) 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 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -195000000.0) {
		tmp = t_1;
	} else if (z <= -3.7e-42) {
		tmp = t_0;
	} else if (z <= -6.5e-185) {
		tmp = x * -3.0;
	} else if (z <= 4.6e-162) {
		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 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -195000000.0:
		tmp = t_1
	elif z <= -3.7e-42:
		tmp = t_0
	elif z <= -6.5e-185:
		tmp = x * -3.0
	elif z <= 4.6e-162:
		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(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -195000000.0)
		tmp = t_1;
	elseif (z <= -3.7e-42)
		tmp = t_0;
	elseif (z <= -6.5e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.6e-162)
		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 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -195000000.0)
		tmp = t_1;
	elseif (z <= -3.7e-42)
		tmp = t_0;
	elseif (z <= -6.5e-185)
		tmp = x * -3.0;
	elseif (z <= 4.6e-162)
		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[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -195000000.0], t$95$1, If[LessEqual[z, -3.7e-42], t$95$0, If[LessEqual[z, -6.5e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.6e-162], 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 < -1.95e8 or 0.5 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 97.2%

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

   if -1.95e8 < z < -3.7000000000000002e-42 or -6.49999999999999946e-185 < z < 4.5999999999999996e-162

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 78.7%

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

   6. Taylor expanded in x around 0 72.5%

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

   if -3.7000000000000002e-42 < z < -6.49999999999999946e-185 or 4.5999999999999996e-162 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 68.4%

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

      1. *-lft-identity 68.4%

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

      2. *-commutative 68.4%

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

      3. +-commutative 68.4%

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

      4. *-commutative 68.4%

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

      5. fma-define 68.4%

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

      6. associate-*r* 68.4%

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

      7. neg-mul-1 68.4%

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

      8. fma-define 68.4%

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

      9. distribute-neg-in 68.4%

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

      10. distribute-lft-neg-in 68.4%

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

      11. metadata-eval 68.4%

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

      12. metadata-eval 68.4%

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

      13. distribute-rgt-in 68.4%

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

      14. +-commutative 68.4%

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

      15. sub-neg 68.4%

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

      16. distribute-rgt-in 68.3%

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

      17. sub-neg 68.3%

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

      18. distribute-rgt-in 68.4%

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

      19. metadata-eval 68.4%

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

      20. distribute-lft-neg-in 68.4%

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

      21. associate-+r+ 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in z around 0 68.1%

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

      1. *-commutative 68.1%

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

   10. Simplified 68.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-42}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-162}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.009:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -0.009)
     t_1
     (if (<= z -3.8e-42)
       t_0
       (if (<= z -3.4e-216)
         (* x -3.0)
         (if (<= z 5e-162) 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 <= -0.009) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -3.4e-216) {
		tmp = x * -3.0;
	} else if (z <= 5e-162) {
		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 <= (-0.009d0)) then
        tmp = t_1
    else if (z <= (-3.8d-42)) then
        tmp = t_0
    else if (z <= (-3.4d-216)) then
        tmp = x * (-3.0d0)
    else if (z <= 5d-162) 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 <= -0.009) {
		tmp = t_1;
	} else if (z <= -3.8e-42) {
		tmp = t_0;
	} else if (z <= -3.4e-216) {
		tmp = x * -3.0;
	} else if (z <= 5e-162) {
		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 <= -0.009:
		tmp = t_1
	elif z <= -3.8e-42:
		tmp = t_0
	elif z <= -3.4e-216:
		tmp = x * -3.0
	elif z <= 5e-162:
		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 <= -0.009)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -3.4e-216)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e-162)
		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 <= -0.009)
		tmp = t_1;
	elseif (z <= -3.8e-42)
		tmp = t_0;
	elseif (z <= -3.4e-216)
		tmp = x * -3.0;
	elseif (z <= 5e-162)
		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, -0.009], t$95$1, If[LessEqual[z, -3.8e-42], t$95$0, If[LessEqual[z, -3.4e-216], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e-162], 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 < -0.00899999999999999932 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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 97.0%

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

   if -0.00899999999999999932 < z < -3.80000000000000017e-42 or -3.3999999999999998e-216 < z < 5.00000000000000014e-162

   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. Step-by-step derivation

      1. +-commutative 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

      1. fma-undefine 99.4%

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

   8. Applied egg-rr 99.4%

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

   9. Taylor expanded in z around 0 98.2%

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

   10. Taylor expanded in y around inf 72.5%

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

   if -3.80000000000000017e-42 < z < -3.3999999999999998e-216 or 5.00000000000000014e-162 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 66.8%

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

      1. *-lft-identity 66.8%

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

      2. *-commutative 66.8%

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

      3. +-commutative 66.8%

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

      4. *-commutative 66.8%

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

      5. fma-define 66.8%

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

      6. associate-*r* 66.8%

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

      7. neg-mul-1 66.8%

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

      8. fma-define 66.8%

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

      9. distribute-neg-in 66.8%

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

      10. distribute-lft-neg-in 66.8%

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

      11. metadata-eval 66.8%

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

      12. metadata-eval 66.8%

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

      13. distribute-rgt-in 66.8%

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

      14. +-commutative 66.8%

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

      15. sub-neg 66.8%

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

      16. distribute-rgt-in 66.8%

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

      17. sub-neg 66.8%

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

      18. distribute-rgt-in 66.8%

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

      19. metadata-eval 66.8%

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

      20. distribute-lft-neg-in 66.8%

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

      21. associate-+r+ 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in z around 0 66.5%

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

      1. *-commutative 66.5%

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

   10. Simplified 66.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.009:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-216}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-162}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.6e+136)
   (* x (* z 6.0))
   (if (or (<= z -2.8e-17) (not (<= z 0.5))) (* -6.0 (* y z)) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e+136) {
		tmp = x * (z * 6.0);
	} else if ((z <= -2.8e-17) || !(z <= 0.5)) {
		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 <= (-2.6d+136)) then
        tmp = x * (z * 6.0d0)
    else if ((z <= (-2.8d-17)) .or. (.not. (z <= 0.5d0))) 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 <= -2.6e+136) {
		tmp = x * (z * 6.0);
	} else if ((z <= -2.8e-17) || !(z <= 0.5)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.6e+136:
		tmp = x * (z * 6.0)
	elif (z <= -2.8e-17) or not (z <= 0.5):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.6e+136)
		tmp = Float64(x * Float64(z * 6.0));
	elseif ((z <= -2.8e-17) || !(z <= 0.5))
		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 <= -2.6e+136)
		tmp = x * (z * 6.0);
	elseif ((z <= -2.8e-17) || ~((z <= 0.5)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.6e+136], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.8e-17], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000001e136

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. fma-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 0 58.8%

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

      1. *-lft-identity 58.8%

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

      2. *-commutative 58.8%

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

      3. +-commutative 58.8%

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

      4. *-commutative 58.8%

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

      5. fma-define 58.8%

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

      6. associate-*r* 58.8%

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

      7. neg-mul-1 58.8%

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

      8. fma-define 58.8%

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

      9. distribute-neg-in 58.8%

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

      10. distribute-lft-neg-in 58.8%

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

      11. metadata-eval 58.8%

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

      12. metadata-eval 58.8%

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

      13. distribute-rgt-in 58.8%

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

      14. +-commutative 58.8%

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

      15. sub-neg 58.8%

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

      16. distribute-rgt-in 58.8%

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

      17. sub-neg 58.8%

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

      18. distribute-rgt-in 58.8%

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

      19. metadata-eval 58.8%

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

      20. distribute-lft-neg-in 58.8%

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

      21. associate-+r+ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*r* 58.8%

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

   10. Simplified 58.8%

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

   if -2.6000000000000001e136 < z < -2.7999999999999999e-17 or 0.5 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 92.8%

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

   8. Taylor expanded in y around inf 54.5%

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

   if -2.7999999999999999e-17 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 52.8%

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

      1. *-lft-identity 52.8%

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

      2. *-commutative 52.8%

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

      3. +-commutative 52.8%

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

      4. *-commutative 52.8%

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

      5. fma-define 52.8%

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

      6. associate-*r* 52.8%

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

      7. neg-mul-1 52.8%

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

      8. fma-define 52.8%

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

      9. distribute-neg-in 52.8%

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

      10. distribute-lft-neg-in 52.8%

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

      11. metadata-eval 52.8%

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

      12. metadata-eval 52.8%

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

      13. distribute-rgt-in 52.8%

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

      14. +-commutative 52.8%

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

      15. sub-neg 52.8%

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

      16. distribute-rgt-in 52.8%

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

      17. sub-neg 52.8%

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

      18. distribute-rgt-in 52.8%

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

      19. metadata-eval 52.8%

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

      20. distribute-lft-neg-in 52.8%

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

      21. associate-+r+ 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+136}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4e+136)
   (* 6.0 (* x z))
   (if (or (<= z -2.8e-17) (not (<= z 0.6))) (* -6.0 (* y z)) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4e+136) {
		tmp = 6.0 * (x * z);
	} else if ((z <= -2.8e-17) || !(z <= 0.6)) {
		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 <= (-4d+136)) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= (-2.8d-17)) .or. (.not. (z <= 0.6d0))) 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 <= -4e+136) {
		tmp = 6.0 * (x * z);
	} else if ((z <= -2.8e-17) || !(z <= 0.6)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4e+136:
		tmp = 6.0 * (x * z)
	elif (z <= -2.8e-17) or not (z <= 0.6):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4e+136)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= -2.8e-17) || !(z <= 0.6))
		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 <= -4e+136)
		tmp = 6.0 * (x * z);
	elseif ((z <= -2.8e-17) || ~((z <= 0.6)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4e+136], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.8e-17], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000023e136

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. fma-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 0 58.8%

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

      1. *-lft-identity 58.8%

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

      2. *-commutative 58.8%

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

      3. +-commutative 58.8%

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

      4. *-commutative 58.8%

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

      5. fma-define 58.8%

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

      6. associate-*r* 58.8%

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

      7. neg-mul-1 58.8%

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

      8. fma-define 58.8%

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

      9. distribute-neg-in 58.8%

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

      10. distribute-lft-neg-in 58.8%

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

      11. metadata-eval 58.8%

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

      12. metadata-eval 58.8%

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

      13. distribute-rgt-in 58.8%

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

      14. +-commutative 58.8%

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

      15. sub-neg 58.8%

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

      16. distribute-rgt-in 58.8%

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

      17. sub-neg 58.8%

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

      18. distribute-rgt-in 58.8%

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

      19. metadata-eval 58.8%

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

      20. distribute-lft-neg-in 58.8%

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

      21. associate-+r+ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 58.8%

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

   if -4.00000000000000023e136 < z < -2.7999999999999999e-17 or 0.599999999999999978 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 92.8%

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

   8. Taylor expanded in y around inf 54.5%

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

   if -2.7999999999999999e-17 < z < 0.599999999999999978

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 52.8%

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

      1. *-lft-identity 52.8%

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

      2. *-commutative 52.8%

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

      3. +-commutative 52.8%

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

      4. *-commutative 52.8%

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

      5. fma-define 52.8%

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

      6. associate-*r* 52.8%

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

      7. neg-mul-1 52.8%

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

      8. fma-define 52.8%

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

      9. distribute-neg-in 52.8%

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

      10. distribute-lft-neg-in 52.8%

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

      11. metadata-eval 52.8%

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

      12. metadata-eval 52.8%

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

      13. distribute-rgt-in 52.8%

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

      14. +-commutative 52.8%

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

      15. sub-neg 52.8%

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

      16. distribute-rgt-in 52.8%

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

      17. sub-neg 52.8%

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

      18. distribute-rgt-in 52.8%

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

      19. metadata-eval 52.8%

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

      20. distribute-lft-neg-in 52.8%

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

      21. associate-+r+ 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+136}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.63\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.63)))
   (* -6.0 (* (- y x) z))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.63)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (y * 4.0) + (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 <= (-0.6d0)) .or. (.not. (z <= 0.63d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.63)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.63):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.63))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.63)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.63]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.630000000000000004 < 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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 97.0%

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

   if -0.599999999999999978 < z < 0.630000000000000004

   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. Step-by-step derivation

      1. +-commutative 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.2%

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

   6. Applied egg-rr 99.2%

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

      1. fma-undefine 99.4%

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

   8. Applied egg-rr 99.4%

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

   9. Taylor expanded in z around 0 98.5%

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

   10. Taylor expanded in x around 0 98.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.63\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.63\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.63)))
   (* -6.0 (* (- y x) z))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.63)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.63d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.63)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.63):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.63))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.63)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.63]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.630000000000000004 < 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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 97.0%

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

   if -0.599999999999999978 < z < 0.630000000000000004

   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 98.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.63\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e-17) (not (<= z 0.5))) (* -6.0 (* y z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-17) || !(z <= 0.5)) {
		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 <= (-2.8d-17)) .or. (.not. (z <= 0.5d0))) 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 <= -2.8e-17) || !(z <= 0.5)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e-17) or not (z <= 0.5):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e-17) || !(z <= 0.5))
		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 <= -2.8e-17) || ~((z <= 0.5)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e-17], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e-17 or 0.5 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 94.6%

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

   8. Taylor expanded in y around inf 51.5%

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

   if -2.7999999999999999e-17 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 52.8%

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

      1. *-lft-identity 52.8%

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

      2. *-commutative 52.8%

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

      3. +-commutative 52.8%

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

      4. *-commutative 52.8%

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

      5. fma-define 52.8%

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

      6. associate-*r* 52.8%

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

      7. neg-mul-1 52.8%

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

      8. fma-define 52.8%

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

      9. distribute-neg-in 52.8%

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

      10. distribute-lft-neg-in 52.8%

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

      11. metadata-eval 52.8%

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

      12. metadata-eval 52.8%

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

      13. distribute-rgt-in 52.8%

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

      14. +-commutative 52.8%

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

      15. sub-neg 52.8%

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

      16. distribute-rgt-in 52.8%

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

      17. sub-neg 52.8%

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

      18. distribute-rgt-in 52.8%

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

      19. metadata-eval 52.8%

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

      20. distribute-lft-neg-in 52.8%

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

      21. associate-+r+ 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. +-commutative 99.5%

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

   2. *-commutative 99.5%

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

   3. associate-*r* 99.6%

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

   4. fma-define 99.6%

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

6. Applied egg-rr 99.6%

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

   1. fma-undefine 99.6%

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

8. Applied egg-rr 99.6%

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

9. Final simplification 99.6%

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

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 14: 26.2% 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. +-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. Taylor expanded in y around 0 51.3%

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

   1. *-lft-identity 51.3%

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

   2. *-commutative 51.3%

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

   3. +-commutative 51.3%

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

   4. *-commutative 51.3%

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

   5. fma-define 51.3%

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

   6. associate-*r* 51.3%

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

   7. neg-mul-1 51.3%

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

   8. fma-define 51.3%

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

   9. distribute-neg-in 51.3%

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

   10. distribute-lft-neg-in 51.3%

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

   11. metadata-eval 51.3%

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

   12. metadata-eval 51.3%

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

   13. distribute-rgt-in 51.3%

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

   14. +-commutative 51.3%

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

   15. sub-neg 51.3%

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

   16. distribute-rgt-in 51.3%

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

   17. sub-neg 51.3%

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

   18. distribute-rgt-in 51.3%

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

   19. metadata-eval 51.3%

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

   20. distribute-lft-neg-in 51.3%

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

   21. associate-+r+ 51.3%

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

7. Simplified 51.3%

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

8. Taylor expanded in z around 0 24.0%

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

   1. *-commutative 24.0%

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

10. Simplified 24.0%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 15: 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 z around inf 55.2%

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

6. Taylor expanded in z around 0 2.6%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024132 
(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))))