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

Percentage Accurate: 99.5% → 99.8%

Time: 11.9s

Alternatives: 13

Speedup: 1.2×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-281}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+197} \lor \neg \left(z \leq 2.8 \cdot 10^{+270}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1e+65)
     t_0
     (if (<= z -0.66)
       t_1
       (if (<= z -7e-223)
         (* y 4.0)
         (if (<= z -8.2e-281)
           (* x -3.0)
           (if (<= z 1.95e-268)
             (* y 4.0)
             (if (<= z 3.7e-160)
               (* x -3.0)
               (if (<= z 0.086)
                 (* y 4.0)
                 (if (or (<= z 5.2e+197) (not (<= z 2.8e+270)))
                   t_1
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1e+65) {
		tmp = t_0;
	} else if (z <= -0.66) {
		tmp = t_1;
	} else if (z <= -7e-223) {
		tmp = y * 4.0;
	} else if (z <= -8.2e-281) {
		tmp = x * -3.0;
	} else if (z <= 1.95e-268) {
		tmp = y * 4.0;
	} else if (z <= 3.7e-160) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else if ((z <= 5.2e+197) || !(z <= 2.8e+270)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-1d+65)) then
        tmp = t_0
    else if (z <= (-0.66d0)) then
        tmp = t_1
    else if (z <= (-7d-223)) then
        tmp = y * 4.0d0
    else if (z <= (-8.2d-281)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.95d-268) then
        tmp = y * 4.0d0
    else if (z <= 3.7d-160) then
        tmp = x * (-3.0d0)
    else if (z <= 0.086d0) then
        tmp = y * 4.0d0
    else if ((z <= 5.2d+197) .or. (.not. (z <= 2.8d+270))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1e+65) {
		tmp = t_0;
	} else if (z <= -0.66) {
		tmp = t_1;
	} else if (z <= -7e-223) {
		tmp = y * 4.0;
	} else if (z <= -8.2e-281) {
		tmp = x * -3.0;
	} else if (z <= 1.95e-268) {
		tmp = y * 4.0;
	} else if (z <= 3.7e-160) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else if ((z <= 5.2e+197) || !(z <= 2.8e+270)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -1e+65:
		tmp = t_0
	elif z <= -0.66:
		tmp = t_1
	elif z <= -7e-223:
		tmp = y * 4.0
	elif z <= -8.2e-281:
		tmp = x * -3.0
	elif z <= 1.95e-268:
		tmp = y * 4.0
	elif z <= 3.7e-160:
		tmp = x * -3.0
	elif z <= 0.086:
		tmp = y * 4.0
	elif (z <= 5.2e+197) or not (z <= 2.8e+270):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1e+65)
		tmp = t_0;
	elseif (z <= -0.66)
		tmp = t_1;
	elseif (z <= -7e-223)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.2e-281)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.95e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.7e-160)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.086)
		tmp = Float64(y * 4.0);
	elseif ((z <= 5.2e+197) || !(z <= 2.8e+270))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1e+65)
		tmp = t_0;
	elseif (z <= -0.66)
		tmp = t_1;
	elseif (z <= -7e-223)
		tmp = y * 4.0;
	elseif (z <= -8.2e-281)
		tmp = x * -3.0;
	elseif (z <= 1.95e-268)
		tmp = y * 4.0;
	elseif (z <= 3.7e-160)
		tmp = x * -3.0;
	elseif (z <= 0.086)
		tmp = y * 4.0;
	elseif ((z <= 5.2e+197) || ~((z <= 2.8e+270)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+65], t$95$0, If[LessEqual[z, -0.66], t$95$1, If[LessEqual[z, -7e-223], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.2e-281], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.95e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.7e-160], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.086], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 5.2e+197], N[Not[LessEqual[z, 2.8e+270]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.9999999999999999e64 or 5.19999999999999975e197 < z < 2.8000000000000001e270

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. sub-neg 71.2%

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

      2. distribute-rgt-in 71.2%

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

      3. metadata-eval 71.2%

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

      4. metadata-eval 71.2%

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

      5. distribute-lft-neg-in 71.2%

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

      6. associate-+r+ 71.2%

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

      7. metadata-eval 71.2%

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

      8. metadata-eval 71.2%

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

      9. distribute-rgt-neg-in 71.2%

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

      10. metadata-eval 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in z around inf 71.2%

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

   if -9.9999999999999999e64 < z < -0.660000000000000031 or 0.085999999999999993 < z < 5.19999999999999975e197 or 2.8000000000000001e270 < 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. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 69.2%

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

   6. Taylor expanded in z around inf 68.2%

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

      1. *-commutative 68.2%

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

   8. Simplified 68.2%

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

   if -0.660000000000000031 < z < -7.00000000000000018e-223 or -8.1999999999999998e-281 < z < 1.9499999999999999e-268 or 3.69999999999999977e-160 < z < 0.085999999999999993

   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-def 99.9%

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

      4. sub-neg 99.9%

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

      5. 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 61.0%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

   8. Simplified 59.0%

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

   if -7.00000000000000018e-223 < z < -8.1999999999999998e-281 or 1.9499999999999999e-268 < z < 3.69999999999999977e-160

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 70.0%

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

      1. sub-neg 70.0%

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

      2. distribute-rgt-in 70.0%

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

      3. metadata-eval 70.0%

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

      4. metadata-eval 70.0%

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

      5. distribute-lft-neg-in 70.0%

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

      6. associate-+r+ 70.0%

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

      7. metadata-eval 70.0%

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

      8. metadata-eval 70.0%

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

      9. distribute-rgt-neg-in 70.0%

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

      10. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in z around 0 70.0%

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

      1. *-commutative 70.0%

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

   10. Simplified 70.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+65}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-281}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+197} \lor \neg \left(z \leq 2.8 \cdot 10^{+270}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-159}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+264}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* y (* z -6.0))))
   (if (<= z -8.5e+64)
     t_0
     (if (<= z -0.66)
       t_1
       (if (<= z -4.3e-223)
         (* y 4.0)
         (if (<= z -9.8e-281)
           (* x -3.0)
           (if (<= z 1.1e-268)
             (* y 4.0)
             (if (<= z 4.3e-159)
               (* x -3.0)
               (if (<= z 0.086)
                 (* y 4.0)
                 (if (<= z 6e+194)
                   t_1
                   (if (<= z 3.6e+264) t_0 (* -6.0 (* y z)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -8.5e+64) {
		tmp = t_0;
	} else if (z <= -0.66) {
		tmp = t_1;
	} else if (z <= -4.3e-223) {
		tmp = y * 4.0;
	} else if (z <= -9.8e-281) {
		tmp = x * -3.0;
	} else if (z <= 1.1e-268) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-159) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else if (z <= 6e+194) {
		tmp = t_1;
	} else if (z <= 3.6e+264) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = y * (z * (-6.0d0))
    if (z <= (-8.5d+64)) then
        tmp = t_0
    else if (z <= (-0.66d0)) then
        tmp = t_1
    else if (z <= (-4.3d-223)) then
        tmp = y * 4.0d0
    else if (z <= (-9.8d-281)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.1d-268) then
        tmp = y * 4.0d0
    else if (z <= 4.3d-159) then
        tmp = x * (-3.0d0)
    else if (z <= 0.086d0) then
        tmp = y * 4.0d0
    else if (z <= 6d+194) then
        tmp = t_1
    else if (z <= 3.6d+264) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -8.5e+64) {
		tmp = t_0;
	} else if (z <= -0.66) {
		tmp = t_1;
	} else if (z <= -4.3e-223) {
		tmp = y * 4.0;
	} else if (z <= -9.8e-281) {
		tmp = x * -3.0;
	} else if (z <= 1.1e-268) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-159) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else if (z <= 6e+194) {
		tmp = t_1;
	} else if (z <= 3.6e+264) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = y * (z * -6.0)
	tmp = 0
	if z <= -8.5e+64:
		tmp = t_0
	elif z <= -0.66:
		tmp = t_1
	elif z <= -4.3e-223:
		tmp = y * 4.0
	elif z <= -9.8e-281:
		tmp = x * -3.0
	elif z <= 1.1e-268:
		tmp = y * 4.0
	elif z <= 4.3e-159:
		tmp = x * -3.0
	elif z <= 0.086:
		tmp = y * 4.0
	elif z <= 6e+194:
		tmp = t_1
	elif z <= 3.6e+264:
		tmp = t_0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -8.5e+64)
		tmp = t_0;
	elseif (z <= -0.66)
		tmp = t_1;
	elseif (z <= -4.3e-223)
		tmp = Float64(y * 4.0);
	elseif (z <= -9.8e-281)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.1e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.3e-159)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.086)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e+194)
		tmp = t_1;
	elseif (z <= 3.6e+264)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -8.5e+64)
		tmp = t_0;
	elseif (z <= -0.66)
		tmp = t_1;
	elseif (z <= -4.3e-223)
		tmp = y * 4.0;
	elseif (z <= -9.8e-281)
		tmp = x * -3.0;
	elseif (z <= 1.1e-268)
		tmp = y * 4.0;
	elseif (z <= 4.3e-159)
		tmp = x * -3.0;
	elseif (z <= 0.086)
		tmp = y * 4.0;
	elseif (z <= 6e+194)
		tmp = t_1;
	elseif (z <= 3.6e+264)
		tmp = t_0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+64], t$95$0, If[LessEqual[z, -0.66], t$95$1, If[LessEqual[z, -4.3e-223], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -9.8e-281], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.1e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.3e-159], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.086], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e+194], t$95$1, If[LessEqual[z, 3.6e+264], t$95$0, N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.4999999999999998e64 or 6.0000000000000006e194 < z < 3.60000000000000011e264

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. sub-neg 71.2%

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

      2. distribute-rgt-in 71.2%

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

      3. metadata-eval 71.2%

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

      4. metadata-eval 71.2%

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

      5. distribute-lft-neg-in 71.2%

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

      6. associate-+r+ 71.2%

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

      7. metadata-eval 71.2%

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

      8. metadata-eval 71.2%

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

      9. distribute-rgt-neg-in 71.2%

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

      10. metadata-eval 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in z around inf 71.2%

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

   if -8.4999999999999998e64 < z < -0.660000000000000031 or 0.085999999999999993 < z < 6.0000000000000006e194

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. 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 inf 67.7%

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

   6. Taylor expanded in z around inf 66.7%

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

   if -0.660000000000000031 < z < -4.2999999999999999e-223 or -9.7999999999999999e-281 < z < 1.10000000000000002e-268 or 4.3e-159 < z < 0.085999999999999993

   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-def 99.9%

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

      4. sub-neg 99.9%

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

      5. 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 61.0%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

   8. Simplified 59.0%

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

   if -4.2999999999999999e-223 < z < -9.7999999999999999e-281 or 1.10000000000000002e-268 < z < 4.3e-159

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 70.0%

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

      1. sub-neg 70.0%

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

      2. distribute-rgt-in 70.0%

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

      3. metadata-eval 70.0%

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

      4. metadata-eval 70.0%

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

      5. distribute-lft-neg-in 70.0%

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

      6. associate-+r+ 70.0%

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

      7. metadata-eval 70.0%

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

      8. metadata-eval 70.0%

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

      9. distribute-rgt-neg-in 70.0%

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

      10. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in z around 0 70.0%

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

      1. *-commutative 70.0%

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

   10. Simplified 70.0%

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

   if 3.60000000000000011e264 < 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. +-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* 100.0%

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

      3. fma-def 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 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 83.3%

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

   6. Taylor expanded in z around inf 83.3%

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

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+64}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-223}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-159}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+264}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -8.3 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-222}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-159}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+202}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+266}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))))
   (if (<= z -8.3e+64)
     (* z (* x 6.0))
     (if (<= z -0.66)
       t_0
       (if (<= z -7.2e-222)
         (* y 4.0)
         (if (<= z -2.2e-279)
           (* x -3.0)
           (if (<= z 1.4e-269)
             (* y 4.0)
             (if (<= z 4.3e-159)
               (* x -3.0)
               (if (<= z 0.086)
                 (* y 4.0)
                 (if (<= z 2.7e+202)
                   t_0
                   (if (<= z 2.6e+266)
                     (* 6.0 (* x z))
                     (* -6.0 (* y z)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -8.3e+64) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -7.2e-222) {
		tmp = y * 4.0;
	} else if (z <= -2.2e-279) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-269) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-159) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else if (z <= 2.7e+202) {
		tmp = t_0;
	} else if (z <= 2.6e+266) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * (-6.0d0))
    if (z <= (-8.3d+64)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-7.2d-222)) then
        tmp = y * 4.0d0
    else if (z <= (-2.2d-279)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.4d-269) then
        tmp = y * 4.0d0
    else if (z <= 4.3d-159) then
        tmp = x * (-3.0d0)
    else if (z <= 0.086d0) then
        tmp = y * 4.0d0
    else if (z <= 2.7d+202) then
        tmp = t_0
    else if (z <= 2.6d+266) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -8.3e+64) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -7.2e-222) {
		tmp = y * 4.0;
	} else if (z <= -2.2e-279) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-269) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-159) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else if (z <= 2.7e+202) {
		tmp = t_0;
	} else if (z <= 2.6e+266) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	tmp = 0
	if z <= -8.3e+64:
		tmp = z * (x * 6.0)
	elif z <= -0.66:
		tmp = t_0
	elif z <= -7.2e-222:
		tmp = y * 4.0
	elif z <= -2.2e-279:
		tmp = x * -3.0
	elif z <= 1.4e-269:
		tmp = y * 4.0
	elif z <= 4.3e-159:
		tmp = x * -3.0
	elif z <= 0.086:
		tmp = y * 4.0
	elif z <= 2.7e+202:
		tmp = t_0
	elif z <= 2.6e+266:
		tmp = 6.0 * (x * z)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -8.3e+64)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -0.66)
		tmp = t_0;
	elseif (z <= -7.2e-222)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.2e-279)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.4e-269)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.3e-159)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.086)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.7e+202)
		tmp = t_0;
	elseif (z <= 2.6e+266)
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -8.3e+64)
		tmp = z * (x * 6.0);
	elseif (z <= -0.66)
		tmp = t_0;
	elseif (z <= -7.2e-222)
		tmp = y * 4.0;
	elseif (z <= -2.2e-279)
		tmp = x * -3.0;
	elseif (z <= 1.4e-269)
		tmp = y * 4.0;
	elseif (z <= 4.3e-159)
		tmp = x * -3.0;
	elseif (z <= 0.086)
		tmp = y * 4.0;
	elseif (z <= 2.7e+202)
		tmp = t_0;
	elseif (z <= 2.6e+266)
		tmp = 6.0 * (x * z);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.3e+64], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -7.2e-222], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.2e-279], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.4e-269], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.3e-159], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.086], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.7e+202], t$95$0, If[LessEqual[z, 2.6e+266], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.3000000000000004e64

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. sub-neg 67.7%

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

      2. distribute-rgt-in 67.7%

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

      3. metadata-eval 67.7%

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

      4. metadata-eval 67.7%

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

      5. distribute-lft-neg-in 67.7%

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

      6. associate-+r+ 67.7%

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

      7. metadata-eval 67.7%

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

      8. metadata-eval 67.7%

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

      9. distribute-rgt-neg-in 67.7%

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

      10. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l* 67.7%

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

      3. *-commutative 67.7%

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

      4. associate-*r* 67.7%

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

   10. Simplified 67.7%

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

   if -8.3000000000000004e64 < z < -0.660000000000000031 or 0.085999999999999993 < z < 2.69999999999999995e202

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. 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 inf 67.7%

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

   6. Taylor expanded in z around inf 66.7%

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

   if -0.660000000000000031 < z < -7.19999999999999948e-222 or -2.2e-279 < z < 1.39999999999999997e-269 or 4.3e-159 < z < 0.085999999999999993

   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-def 99.9%

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

      4. sub-neg 99.9%

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

      5. 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 61.0%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

   8. Simplified 59.0%

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

   if -7.19999999999999948e-222 < z < -2.2e-279 or 1.39999999999999997e-269 < z < 4.3e-159

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 70.0%

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

      1. sub-neg 70.0%

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

      2. distribute-rgt-in 70.0%

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

      3. metadata-eval 70.0%

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

      4. metadata-eval 70.0%

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

      5. distribute-lft-neg-in 70.0%

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

      6. associate-+r+ 70.0%

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

      7. metadata-eval 70.0%

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

      8. metadata-eval 70.0%

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

      9. distribute-rgt-neg-in 70.0%

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

      10. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in z around 0 70.0%

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

      1. *-commutative 70.0%

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

   10. Simplified 70.0%

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

   if 2.69999999999999995e202 < z < 2.60000000000000014e266

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 89.5%

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

      1. sub-neg 89.5%

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

      2. distribute-rgt-in 89.5%

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

      3. metadata-eval 89.5%

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

      4. metadata-eval 89.5%

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

      5. distribute-lft-neg-in 89.5%

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

      6. associate-+r+ 89.5%

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

      7. metadata-eval 89.5%

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

      8. metadata-eval 89.5%

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

      9. distribute-rgt-neg-in 89.5%

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

      10. metadata-eval 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in z around inf 89.6%

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

   if 2.60000000000000014e266 < 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. +-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* 100.0%

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

      3. fma-def 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 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 83.3%

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

   6. Taylor expanded in z around inf 83.3%

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

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.66:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-222}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-159}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+266}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-222}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-277}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-272}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-156}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.66)
     t_0
     (if (<= z -5.3e-222)
       (* y 4.0)
       (if (<= z -2.5e-277)
         (* x -3.0)
         (if (<= z 1.45e-272)
           (* y 4.0)
           (if (<= z 3.5e-156)
             (* x -3.0)
             (if (<= z 0.086) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -5.3e-222) {
		tmp = y * 4.0;
	} else if (z <= -2.5e-277) {
		tmp = x * -3.0;
	} else if (z <= 1.45e-272) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-156) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-5.3d-222)) then
        tmp = y * 4.0d0
    else if (z <= (-2.5d-277)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.45d-272) then
        tmp = y * 4.0d0
    else if (z <= 3.5d-156) then
        tmp = x * (-3.0d0)
    else if (z <= 0.086d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -5.3e-222) {
		tmp = y * 4.0;
	} else if (z <= -2.5e-277) {
		tmp = x * -3.0;
	} else if (z <= 1.45e-272) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-156) {
		tmp = x * -3.0;
	} else if (z <= 0.086) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= -5.3e-222:
		tmp = y * 4.0
	elif z <= -2.5e-277:
		tmp = x * -3.0
	elif z <= 1.45e-272:
		tmp = y * 4.0
	elif z <= 3.5e-156:
		tmp = x * -3.0
	elif z <= 0.086:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -5.3e-222)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.5e-277)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.45e-272)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.5e-156)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.086)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -5.3e-222)
		tmp = y * 4.0;
	elseif (z <= -2.5e-277)
		tmp = x * -3.0;
	elseif (z <= 1.45e-272)
		tmp = y * 4.0;
	elseif (z <= 3.5e-156)
		tmp = x * -3.0;
	elseif (z <= 0.086)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -5.3e-222], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.5e-277], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.45e-272], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.5e-156], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.086], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 0.085999999999999993 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. 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 inf 52.3%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

   8. Simplified 51.8%

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

   if -0.660000000000000031 < z < -5.29999999999999981e-222 or -2.5e-277 < z < 1.44999999999999997e-272 or 3.4999999999999999e-156 < z < 0.085999999999999993

   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-def 99.9%

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

      4. sub-neg 99.9%

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

      5. 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 61.0%

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

   6. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

   8. Simplified 59.0%

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

   if -5.29999999999999981e-222 < z < -2.5e-277 or 1.44999999999999997e-272 < z < 3.4999999999999999e-156

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 70.0%

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

      1. sub-neg 70.0%

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

      2. distribute-rgt-in 70.0%

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

      3. metadata-eval 70.0%

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

      4. metadata-eval 70.0%

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

      5. distribute-lft-neg-in 70.0%

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

      6. associate-+r+ 70.0%

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

      7. metadata-eval 70.0%

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

      8. metadata-eval 70.0%

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

      9. distribute-rgt-neg-in 70.0%

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

      10. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in z around 0 70.0%

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

      1. *-commutative 70.0%

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

   10. Simplified 70.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-222}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-277}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-272}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-156}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.086:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+213}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))))
   (if (<= x -1.25e+229)
     (* x -3.0)
     (if (<= x -2.7e+93)
       t_0
       (if (<= x 1.55e+66)
         (* 6.0 (* y (- 0.6666666666666666 z)))
         (if (<= x 7.5e+213) t_0 (* x -3.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (x <= -1.25e+229) {
		tmp = x * -3.0;
	} else if (x <= -2.7e+93) {
		tmp = t_0;
	} else if (x <= 1.55e+66) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (x <= 7.5e+213) {
		tmp = t_0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * 6.0d0)
    if (x <= (-1.25d+229)) then
        tmp = x * (-3.0d0)
    else if (x <= (-2.7d+93)) then
        tmp = t_0
    else if (x <= 1.55d+66) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (x <= 7.5d+213) then
        tmp = t_0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (x <= -1.25e+229) {
		tmp = x * -3.0;
	} else if (x <= -2.7e+93) {
		tmp = t_0;
	} else if (x <= 1.55e+66) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (x <= 7.5e+213) {
		tmp = t_0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	tmp = 0
	if x <= -1.25e+229:
		tmp = x * -3.0
	elif x <= -2.7e+93:
		tmp = t_0
	elif x <= 1.55e+66:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif x <= 7.5e+213:
		tmp = t_0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (x <= -1.25e+229)
		tmp = Float64(x * -3.0);
	elseif (x <= -2.7e+93)
		tmp = t_0;
	elseif (x <= 1.55e+66)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (x <= 7.5e+213)
		tmp = t_0;
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	tmp = 0.0;
	if (x <= -1.25e+229)
		tmp = x * -3.0;
	elseif (x <= -2.7e+93)
		tmp = t_0;
	elseif (x <= 1.55e+66)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (x <= 7.5e+213)
		tmp = t_0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+229], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, -2.7e+93], t$95$0, If[LessEqual[x, 1.55e+66], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+213], t$95$0, N[(x * -3.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000012e229 or 7.5000000000000003e213 < x

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 91.6%

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

      1. sub-neg 91.6%

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

      2. distribute-rgt-in 91.6%

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

      3. metadata-eval 91.6%

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

      4. metadata-eval 91.6%

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

      5. distribute-lft-neg-in 91.6%

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

      6. associate-+r+ 91.6%

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

      7. metadata-eval 91.6%

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

      8. metadata-eval 91.6%

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

      9. distribute-rgt-neg-in 91.6%

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

      10. metadata-eval 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   10. Simplified 63.0%

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

   if -1.25000000000000012e229 < x < -2.6999999999999999e93 or 1.55000000000000009e66 < x < 7.5000000000000003e213

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 83.9%

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

      1. sub-neg 83.9%

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

      2. distribute-rgt-in 83.9%

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

      3. metadata-eval 83.9%

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

      4. metadata-eval 83.9%

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

      5. distribute-lft-neg-in 83.9%

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

      6. associate-+r+ 83.9%

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

      7. metadata-eval 83.9%

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

      8. metadata-eval 83.9%

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

      9. distribute-rgt-neg-in 83.9%

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

      10. metadata-eval 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in z around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-*l* 52.9%

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

      3. *-commutative 52.9%

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

      4. associate-*r* 52.9%

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

   10. Simplified 52.9%

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

   if -2.6999999999999999e93 < x < 1.55000000000000009e66

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.53\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.53)))
   (* z (+ (* y -6.0) (* x 6.0)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.53)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} 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 <= (-0.58d0)) .or. (.not. (z <= 0.53d0))) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    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 <= -0.58) || !(z <= 0.53)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.53):
		tmp = z * ((y * -6.0) + (x * 6.0))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.53))
		tmp = Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0)));
	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 <= -0.58) || ~((z <= 0.53)))
		tmp = z * ((y * -6.0) + (x * 6.0));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.53]], $MachinePrecision]], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.53000000000000003 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 96.3%

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

   6. Taylor expanded in z around inf 99.2%

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

   if -0.57999999999999996 < z < 0.53000000000000003

   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 96.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.53\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* z (+ (* y -6.0) (* x 6.0)))
   (if (<= z 0.55) (+ x (* (- y x) 4.0)) (+ x (* -6.0 (* (- y x) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else if (z <= 0.55) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    else if (z <= 0.55d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + ((-6.0d0) * ((y - x) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else if (z <= 0.55) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = z * ((y * -6.0) + (x * 6.0))
	elif z <= 0.55:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + (-6.0 * ((y - x) * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0)));
	elseif (z <= 0.55)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = z * ((y * -6.0) + (x * 6.0));
	elseif (z <= 0.55)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + (-6.0 * ((y - x) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 96.6%

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

   6. Taylor expanded in z around inf 98.7%

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

   if -0.57999999999999996 < z < 0.55000000000000004

   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 96.4%

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

   if 0.55000000000000004 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -410000 \lor \neg \left(x \leq 2.7 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -410000.0) (not (<= x 2.7e+42)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -410000.0) || !(x <= 2.7e+42)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-410000.0d0)) .or. (.not. (x <= 2.7d+42))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -410000.0) || !(x <= 2.7e+42)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -410000.0) or not (x <= 2.7e+42):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -410000.0) || !(x <= 2.7e+42))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -410000.0) || ~((x <= 2.7e+42)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -410000.0], N[Not[LessEqual[x, 2.7e+42]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1e5 or 2.7000000000000001e42 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 81.7%

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

      1. sub-neg 81.7%

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

      2. distribute-rgt-in 81.7%

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

      3. metadata-eval 81.7%

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

      4. metadata-eval 81.7%

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

      5. distribute-lft-neg-in 81.7%

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

      6. associate-+r+ 81.7%

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

      7. metadata-eval 81.7%

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

      8. metadata-eval 81.7%

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

      9. distribute-rgt-neg-in 81.7%

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

      10. metadata-eval 81.7%

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

   7. Simplified 81.7%

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

   if -4.1e5 < x < 2.7000000000000001e42

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 81.9%

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

      1. *-commutative 81.9%

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

   8. Simplified 81.9%

      \[\leadsto \color{blue}{6 \cdot \left(\left(0.6666666666666666 - z\right) \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -410000 \lor \neg \left(x \leq 2.7 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -59000 \lor \neg \left(x \leq 3.5 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -59000.0) (not (<= x 3.5e+42)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -59000.0) || !(x <= 3.5e+42)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-59000.0d0)) .or. (.not. (x <= 3.5d+42))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -59000.0) || !(x <= 3.5e+42)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -59000.0) or not (x <= 3.5e+42):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -59000.0) || !(x <= 3.5e+42))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -59000.0) || ~((x <= 3.5e+42)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -59000.0], N[Not[LessEqual[x, 3.5e+42]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -59000 or 3.50000000000000023e42 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 81.7%

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

      1. sub-neg 81.7%

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

      2. distribute-rgt-in 81.7%

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

      3. metadata-eval 81.7%

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

      4. metadata-eval 81.7%

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

      5. distribute-lft-neg-in 81.7%

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

      6. associate-+r+ 81.7%

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

      7. metadata-eval 81.7%

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

      8. metadata-eval 81.7%

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

      9. distribute-rgt-neg-in 81.7%

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

      10. metadata-eval 81.7%

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

   7. Simplified 81.7%

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

   if -59000 < x < 3.50000000000000023e42

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 82.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -59000 \lor \neg \left(x \leq 3.5 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.23 \lor \neg \left(x \leq 10^{-18}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.23) (not (<= x 1e-18))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.23) || !(x <= 1e-18)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.23d0)) .or. (.not. (x <= 1d-18))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.23) || !(x <= 1e-18)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.23) or not (x <= 1e-18):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.23) || !(x <= 1e-18))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.23) || ~((x <= 1e-18)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.23], N[Not[LessEqual[x, 1e-18]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.23000000000000001 or 1.0000000000000001e-18 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 77.5%

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

      1. sub-neg 77.5%

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

      2. distribute-rgt-in 77.5%

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

      3. metadata-eval 77.5%

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

      4. metadata-eval 77.5%

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

      5. distribute-lft-neg-in 77.5%

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

      6. associate-+r+ 77.5%

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

      7. metadata-eval 77.5%

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

      8. metadata-eval 77.5%

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

      9. distribute-rgt-neg-in 77.5%

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

      10. metadata-eval 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in z around 0 40.7%

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

      1. *-commutative 40.7%

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

   10. Simplified 40.7%

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

   if -0.23000000000000001 < x < 1.0000000000000001e-18

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 82.8%

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

   6. Taylor expanded in z around 0 47.0%

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

      1. *-commutative 47.0%

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

   8. Simplified 47.0%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.23 \lor \neg \left(x \leq 10^{-18}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 13: 26.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 50.1%

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

   1. sub-neg 50.1%

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

   2. distribute-rgt-in 50.1%

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

   3. metadata-eval 50.1%

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

   4. metadata-eval 50.1%

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

   5. distribute-lft-neg-in 50.1%

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

   6. associate-+r+ 50.1%

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

   7. metadata-eval 50.1%

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

   8. metadata-eval 50.1%

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

   9. distribute-rgt-neg-in 50.1%

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

   10. metadata-eval 50.1%

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

7. Simplified 50.1%

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

8. Taylor expanded in z around 0 26.6%

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

   1. *-commutative 26.6%

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

10. Simplified 26.6%

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

11. Final simplification 26.6%

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

Reproduce

herbie shell --seed 2024041 
(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))))