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

Percentage Accurate: 99.5% → 99.7%

Time: 8.0s

Alternatives: 14

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-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. Final simplification 99.8%

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

Alternative 2: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.11:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-132}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-56}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.11)
     t_0
     (if (<= z -7.5e-132)
       (* x -3.0)
       (if (<= z -2.1e-198)
         (* y 4.0)
         (if (<= z 6e-289)
           (* x -3.0)
           (if (<= z 3.15e-201)
             (* y 4.0)
             (if (<= z 1.7e-56)
               (* x -3.0)
               (if (<= z 0.58) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.11) {
		tmp = t_0;
	} else if (z <= -7.5e-132) {
		tmp = x * -3.0;
	} else if (z <= -2.1e-198) {
		tmp = y * 4.0;
	} else if (z <= 6e-289) {
		tmp = x * -3.0;
	} else if (z <= 3.15e-201) {
		tmp = y * 4.0;
	} else if (z <= 1.7e-56) {
		tmp = x * -3.0;
	} else if (z <= 0.58) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.11d0)) then
        tmp = t_0
    else if (z <= (-7.5d-132)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.1d-198)) then
        tmp = y * 4.0d0
    else if (z <= 6d-289) then
        tmp = x * (-3.0d0)
    else if (z <= 3.15d-201) then
        tmp = y * 4.0d0
    else if (z <= 1.7d-56) then
        tmp = x * (-3.0d0)
    else if (z <= 0.58d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.11) {
		tmp = t_0;
	} else if (z <= -7.5e-132) {
		tmp = x * -3.0;
	} else if (z <= -2.1e-198) {
		tmp = y * 4.0;
	} else if (z <= 6e-289) {
		tmp = x * -3.0;
	} else if (z <= 3.15e-201) {
		tmp = y * 4.0;
	} else if (z <= 1.7e-56) {
		tmp = x * -3.0;
	} else if (z <= 0.58) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.11:
		tmp = t_0
	elif z <= -7.5e-132:
		tmp = x * -3.0
	elif z <= -2.1e-198:
		tmp = y * 4.0
	elif z <= 6e-289:
		tmp = x * -3.0
	elif z <= 3.15e-201:
		tmp = y * 4.0
	elif z <= 1.7e-56:
		tmp = x * -3.0
	elif z <= 0.58:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.11)
		tmp = t_0;
	elseif (z <= -7.5e-132)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.1e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-289)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.15e-201)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.7e-56)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.58)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.11)
		tmp = t_0;
	elseif (z <= -7.5e-132)
		tmp = x * -3.0;
	elseif (z <= -2.1e-198)
		tmp = y * 4.0;
	elseif (z <= 6e-289)
		tmp = x * -3.0;
	elseif (z <= 3.15e-201)
		tmp = y * 4.0;
	elseif (z <= 1.7e-56)
		tmp = x * -3.0;
	elseif (z <= 0.58)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.11], t$95$0, If[LessEqual[z, -7.5e-132], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.1e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-289], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.15e-201], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.7e-56], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.110000000000000001 or 0.57999999999999996 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.8%

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

   if -0.110000000000000001 < z < -7.49999999999999989e-132 or -2.09999999999999993e-198 < z < 5.9999999999999996e-289 or 3.15e-201 < z < 1.69999999999999991e-56

   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. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. distribute-lft1-in 66.9%

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

      2. metadata-eval 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -7.49999999999999989e-132 < z < -2.09999999999999993e-198 or 5.9999999999999996e-289 < z < 3.15e-201 or 1.69999999999999991e-56 < z < 0.57999999999999996

   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 99.8%

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

      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. Taylor expanded in y around inf 71.1%

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

   5. Taylor expanded in z around 0 70.6%

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

      1. *-commutative 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.11:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-132}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-56}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.11:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-60}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.11)
     t_0
     (if (<= z -1.42e-129)
       (* x -3.0)
       (if (<= z -7e-198)
         (* y 4.0)
         (if (<= z 1.35e-289)
           (* x -3.0)
           (if (<= z 1.9e-201)
             (* y 4.0)
             (if (<= z 4.7e-60)
               (* x -3.0)
               (if (<= z 0.66) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.11) {
		tmp = t_0;
	} else if (z <= -1.42e-129) {
		tmp = x * -3.0;
	} else if (z <= -7e-198) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-289) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-201) {
		tmp = y * 4.0;
	} else if (z <= 4.7e-60) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.11d0)) then
        tmp = t_0
    else if (z <= (-1.42d-129)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7d-198)) then
        tmp = y * 4.0d0
    else if (z <= 1.35d-289) then
        tmp = x * (-3.0d0)
    else if (z <= 1.9d-201) then
        tmp = y * 4.0d0
    else if (z <= 4.7d-60) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.11) {
		tmp = t_0;
	} else if (z <= -1.42e-129) {
		tmp = x * -3.0;
	} else if (z <= -7e-198) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-289) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-201) {
		tmp = y * 4.0;
	} else if (z <= 4.7e-60) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.11:
		tmp = t_0
	elif z <= -1.42e-129:
		tmp = x * -3.0
	elif z <= -7e-198:
		tmp = y * 4.0
	elif z <= 1.35e-289:
		tmp = x * -3.0
	elif z <= 1.9e-201:
		tmp = y * 4.0
	elif z <= 4.7e-60:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -0.11)
		tmp = t_0;
	elseif (z <= -1.42e-129)
		tmp = Float64(x * -3.0);
	elseif (z <= -7e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.35e-289)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.9e-201)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.7e-60)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -0.11)
		tmp = t_0;
	elseif (z <= -1.42e-129)
		tmp = x * -3.0;
	elseif (z <= -7e-198)
		tmp = y * 4.0;
	elseif (z <= 1.35e-289)
		tmp = x * -3.0;
	elseif (z <= 1.9e-201)
		tmp = y * 4.0;
	elseif (z <= 4.7e-60)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.11], t$95$0, If[LessEqual[z, -1.42e-129], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.35e-289], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.9e-201], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.7e-60], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.110000000000000001 or 0.660000000000000031 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*l* 98.9%

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

   7. Simplified 98.9%

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

   if -0.110000000000000001 < z < -1.42e-129 or -7.0000000000000005e-198 < z < 1.35e-289 or 1.9e-201 < z < 4.7e-60

   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. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. distribute-lft1-in 66.9%

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

      2. metadata-eval 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -1.42e-129 < z < -7.0000000000000005e-198 or 1.35e-289 < z < 1.9e-201 or 4.7e-60 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. +-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 99.8%

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

      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. Taylor expanded in y around inf 71.1%

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

   5. Taylor expanded in z around 0 70.6%

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

      1. *-commutative 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.11:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-60}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.11:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-202}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-56}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 16000000000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.11)
     t_0
     (if (<= z -6e-130)
       (* x -3.0)
       (if (<= z -3e-198)
         (* y 4.0)
         (if (<= z 1.65e-289)
           (* x -3.0)
           (if (<= z 6.6e-202)
             (* y 4.0)
             (if (<= z 1.2e-56)
               (* x -3.0)
               (if (<= z 16000000000.0) (* y (+ 4.0 (* z -6.0))) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.11) {
		tmp = t_0;
	} else if (z <= -6e-130) {
		tmp = x * -3.0;
	} else if (z <= -3e-198) {
		tmp = y * 4.0;
	} else if (z <= 1.65e-289) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-202) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-56) {
		tmp = x * -3.0;
	} else if (z <= 16000000000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.11d0)) then
        tmp = t_0
    else if (z <= (-6d-130)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3d-198)) then
        tmp = y * 4.0d0
    else if (z <= 1.65d-289) then
        tmp = x * (-3.0d0)
    else if (z <= 6.6d-202) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-56) then
        tmp = x * (-3.0d0)
    else if (z <= 16000000000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.11) {
		tmp = t_0;
	} else if (z <= -6e-130) {
		tmp = x * -3.0;
	} else if (z <= -3e-198) {
		tmp = y * 4.0;
	} else if (z <= 1.65e-289) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-202) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-56) {
		tmp = x * -3.0;
	} else if (z <= 16000000000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.11:
		tmp = t_0
	elif z <= -6e-130:
		tmp = x * -3.0
	elif z <= -3e-198:
		tmp = y * 4.0
	elif z <= 1.65e-289:
		tmp = x * -3.0
	elif z <= 6.6e-202:
		tmp = y * 4.0
	elif z <= 1.2e-56:
		tmp = x * -3.0
	elif z <= 16000000000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -0.11)
		tmp = t_0;
	elseif (z <= -6e-130)
		tmp = Float64(x * -3.0);
	elseif (z <= -3e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.65e-289)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.6e-202)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-56)
		tmp = Float64(x * -3.0);
	elseif (z <= 16000000000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -0.11)
		tmp = t_0;
	elseif (z <= -6e-130)
		tmp = x * -3.0;
	elseif (z <= -3e-198)
		tmp = y * 4.0;
	elseif (z <= 1.65e-289)
		tmp = x * -3.0;
	elseif (z <= 6.6e-202)
		tmp = y * 4.0;
	elseif (z <= 1.2e-56)
		tmp = x * -3.0;
	elseif (z <= 16000000000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.11], t$95$0, If[LessEqual[z, -6e-130], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.65e-289], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.6e-202], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-56], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 16000000000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.110000000000000001 or 1.6e10 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l* 99.7%

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

   7. Simplified 99.7%

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

   if -0.110000000000000001 < z < -5.99999999999999972e-130 or -3.0000000000000001e-198 < z < 1.64999999999999999e-289 or 6.59999999999999979e-202 < z < 1.2e-56

   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. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. distribute-lft1-in 66.9%

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

      2. metadata-eval 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -5.99999999999999972e-130 < z < -3.0000000000000001e-198 or 1.64999999999999999e-289 < z < 6.59999999999999979e-202

   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* 99.9%

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

      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. Taylor expanded in y around inf 74.1%

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

   5. Taylor expanded in z around 0 74.1%

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

      1. *-commutative 74.1%

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

   7. Simplified 74.1%

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

   if 1.2e-56 < z < 1.6e10

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 62.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.11:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-202}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-56}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 16000000000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 5: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.35)
     t_0
     (if (<= z -1.42e-129)
       (* x -3.0)
       (if (<= z -3.05e-198)
         (* y 4.0)
         (if (<= z 3.2e-288)
           (* x -3.0)
           (if (<= z 2.2e-201)
             (* y 4.0)
             (if (<= z 1.35e-57)
               (* x -3.0)
               (if (<= z 0.66) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.35) {
		tmp = t_0;
	} else if (z <= -1.42e-129) {
		tmp = x * -3.0;
	} else if (z <= -3.05e-198) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-288) {
		tmp = x * -3.0;
	} else if (z <= 2.2e-201) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-57) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.35d0)) then
        tmp = t_0
    else if (z <= (-1.42d-129)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.05d-198)) then
        tmp = y * 4.0d0
    else if (z <= 3.2d-288) then
        tmp = x * (-3.0d0)
    else if (z <= 2.2d-201) then
        tmp = y * 4.0d0
    else if (z <= 1.35d-57) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.35) {
		tmp = t_0;
	} else if (z <= -1.42e-129) {
		tmp = x * -3.0;
	} else if (z <= -3.05e-198) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-288) {
		tmp = x * -3.0;
	} else if (z <= 2.2e-201) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-57) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.35:
		tmp = t_0
	elif z <= -1.42e-129:
		tmp = x * -3.0
	elif z <= -3.05e-198:
		tmp = y * 4.0
	elif z <= 3.2e-288:
		tmp = x * -3.0
	elif z <= 2.2e-201:
		tmp = y * 4.0
	elif z <= 1.35e-57:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.35)
		tmp = t_0;
	elseif (z <= -1.42e-129)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.05e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.2e-288)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.2e-201)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.35e-57)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.35)
		tmp = t_0;
	elseif (z <= -1.42e-129)
		tmp = x * -3.0;
	elseif (z <= -3.05e-198)
		tmp = y * 4.0;
	elseif (z <= 3.2e-288)
		tmp = x * -3.0;
	elseif (z <= 2.2e-201)
		tmp = y * 4.0;
	elseif (z <= 1.35e-57)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35], t$95$0, If[LessEqual[z, -1.42e-129], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.05e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.2e-288], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.2e-201], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.35e-57], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001 or 0.660000000000000031 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.8%

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

   6. Taylor expanded in y around inf 45.6%

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

      1. *-commutative 45.6%

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

   8. Simplified 45.6%

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

   if -1.3500000000000001 < z < -1.42e-129 or -3.05e-198 < z < 3.2e-288 or 2.2e-201 < z < 1.3500000000000001e-57

   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. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. distribute-lft1-in 66.9%

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

      2. metadata-eval 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -1.42e-129 < z < -3.05e-198 or 3.2e-288 < z < 2.2e-201 or 1.3500000000000001e-57 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. +-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 99.8%

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

      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. Taylor expanded in y around inf 71.1%

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

   5. Taylor expanded in z around 0 70.6%

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

      1. *-commutative 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -0.5)
     t_0
     (if (<= z -4e-130)
       (* x -3.0)
       (if (<= z -5e-198)
         (* y 4.0)
         (if (<= z 2.95e-288)
           (* x -3.0)
           (if (<= z 7.8e-201)
             (* y 4.0)
             (if (<= z 7e-57) (* x -3.0) (if (<= z 0.66) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -4e-130) {
		tmp = x * -3.0;
	} else if (z <= -5e-198) {
		tmp = y * 4.0;
	} else if (z <= 2.95e-288) {
		tmp = x * -3.0;
	} else if (z <= 7.8e-201) {
		tmp = y * 4.0;
	} else if (z <= 7e-57) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-4d-130)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5d-198)) then
        tmp = y * 4.0d0
    else if (z <= 2.95d-288) then
        tmp = x * (-3.0d0)
    else if (z <= 7.8d-201) then
        tmp = y * 4.0d0
    else if (z <= 7d-57) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -4e-130) {
		tmp = x * -3.0;
	} else if (z <= -5e-198) {
		tmp = y * 4.0;
	} else if (z <= 2.95e-288) {
		tmp = x * -3.0;
	} else if (z <= 7.8e-201) {
		tmp = y * 4.0;
	} else if (z <= 7e-57) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -4e-130:
		tmp = x * -3.0
	elif z <= -5e-198:
		tmp = y * 4.0
	elif z <= 2.95e-288:
		tmp = x * -3.0
	elif z <= 7.8e-201:
		tmp = y * 4.0
	elif z <= 7e-57:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -4e-130)
		tmp = Float64(x * -3.0);
	elseif (z <= -5e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.95e-288)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.8e-201)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-57)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -4e-130)
		tmp = x * -3.0;
	elseif (z <= -5e-198)
		tmp = y * 4.0;
	elseif (z <= 2.95e-288)
		tmp = x * -3.0;
	elseif (z <= 7.8e-201)
		tmp = y * 4.0;
	elseif (z <= 7e-57)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -4e-130], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.95e-288], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.8e-201], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-57], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.660000000000000031 < 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 54.8%

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

   6. Taylor expanded in z around inf 54.2%

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

   if -0.5 < z < -4.0000000000000003e-130 or -4.9999999999999999e-198 < z < 2.95000000000000007e-288 or 7.8000000000000006e-201 < z < 6.99999999999999983e-57

   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. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. distribute-lft1-in 66.9%

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

      2. metadata-eval 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -4.0000000000000003e-130 < z < -4.9999999999999999e-198 or 2.95000000000000007e-288 < z < 7.8000000000000006e-201 or 6.99999999999999983e-57 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. +-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 99.8%

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

      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. Taylor expanded in y around inf 71.1%

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

   5. Taylor expanded in z around 0 70.6%

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

      1. *-commutative 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-288}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-132}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-287}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* x (* z 6.0))
   (if (<= z -4.2e-132)
     (* x -3.0)
     (if (<= z -3.6e-198)
       (* y 4.0)
       (if (<= z 2.2e-287)
         (* x -3.0)
         (if (<= z 1.12e-201)
           (* y 4.0)
           (if (<= z 9.5e-63)
             (* x -3.0)
             (if (<= z 0.5) (* y 4.0) (* 6.0 (* x z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -4.2e-132) {
		tmp = x * -3.0;
	} else if (z <= -3.6e-198) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-287) {
		tmp = x * -3.0;
	} else if (z <= 1.12e-201) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-63) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = 6.0 * (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 <= (-0.5d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-4.2d-132)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.6d-198)) then
        tmp = y * 4.0d0
    else if (z <= 2.2d-287) then
        tmp = x * (-3.0d0)
    else if (z <= 1.12d-201) then
        tmp = y * 4.0d0
    else if (z <= 9.5d-63) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -4.2e-132) {
		tmp = x * -3.0;
	} else if (z <= -3.6e-198) {
		tmp = y * 4.0;
	} else if (z <= 2.2e-287) {
		tmp = x * -3.0;
	} else if (z <= 1.12e-201) {
		tmp = y * 4.0;
	} else if (z <= 9.5e-63) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = x * (z * 6.0)
	elif z <= -4.2e-132:
		tmp = x * -3.0
	elif z <= -3.6e-198:
		tmp = y * 4.0
	elif z <= 2.2e-287:
		tmp = x * -3.0
	elif z <= 1.12e-201:
		tmp = y * 4.0
	elif z <= 9.5e-63:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -4.2e-132)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.6e-198)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.2e-287)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.12e-201)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e-63)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = x * (z * 6.0);
	elseif (z <= -4.2e-132)
		tmp = x * -3.0;
	elseif (z <= -3.6e-198)
		tmp = y * 4.0;
	elseif (z <= 2.2e-287)
		tmp = x * -3.0;
	elseif (z <= 1.12e-201)
		tmp = y * 4.0;
	elseif (z <= 9.5e-63)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-132], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.6e-198], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.2e-287], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.12e-201], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e-63], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around inf 57.1%

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

   6. Taylor expanded in z around inf 57.1%

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

   if -0.5 < z < -4.2000000000000002e-132 or -3.59999999999999998e-198 < z < 2.2e-287 or 1.12e-201 < z < 9.50000000000000016e-63

   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. Taylor expanded in y around 0 68.7%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. distribute-lft1-in 66.9%

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

      2. metadata-eval 66.9%

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

      3. *-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -4.2000000000000002e-132 < z < -3.59999999999999998e-198 or 2.2e-287 < z < 1.12e-201 or 9.50000000000000016e-63 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-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. Taylor expanded in y around inf 71.1%

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

   5. Taylor expanded in z around 0 70.6%

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

      1. *-commutative 70.6%

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

   7. Simplified 70.6%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in x around inf 52.5%

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

   6. Taylor expanded in z around inf 51.3%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-132}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-198}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-287}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-201}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 8: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ t_1 := x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-142}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+109}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))) (t_1 (* x (- (* z 6.0) 3.0))))
   (if (<= x -7e-13)
     t_1
     (if (<= x -2.6e-103)
       t_0
       (if (<= x -1e-142)
         (* -6.0 (* (- y x) z))
         (if (<= x 1.05e-65)
           t_0
           (if (<= x 5.2e-8)
             (* z (* (- y x) -6.0))
             (if (<= x 1.62e+109) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = x * ((z * 6.0) - 3.0);
	double tmp;
	if (x <= -7e-13) {
		tmp = t_1;
	} else if (x <= -2.6e-103) {
		tmp = t_0;
	} else if (x <= -1e-142) {
		tmp = -6.0 * ((y - x) * z);
	} else if (x <= 1.05e-65) {
		tmp = t_0;
	} else if (x <= 5.2e-8) {
		tmp = z * ((y - x) * -6.0);
	} else if (x <= 1.62e+109) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    t_1 = x * ((z * 6.0d0) - 3.0d0)
    if (x <= (-7d-13)) then
        tmp = t_1
    else if (x <= (-2.6d-103)) then
        tmp = t_0
    else if (x <= (-1d-142)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (x <= 1.05d-65) then
        tmp = t_0
    else if (x <= 5.2d-8) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (x <= 1.62d+109) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = x * ((z * 6.0) - 3.0);
	double tmp;
	if (x <= -7e-13) {
		tmp = t_1;
	} else if (x <= -2.6e-103) {
		tmp = t_0;
	} else if (x <= -1e-142) {
		tmp = -6.0 * ((y - x) * z);
	} else if (x <= 1.05e-65) {
		tmp = t_0;
	} else if (x <= 5.2e-8) {
		tmp = z * ((y - x) * -6.0);
	} else if (x <= 1.62e+109) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	t_1 = x * ((z * 6.0) - 3.0)
	tmp = 0
	if x <= -7e-13:
		tmp = t_1
	elif x <= -2.6e-103:
		tmp = t_0
	elif x <= -1e-142:
		tmp = -6.0 * ((y - x) * z)
	elif x <= 1.05e-65:
		tmp = t_0
	elif x <= 5.2e-8:
		tmp = z * ((y - x) * -6.0)
	elif x <= 1.62e+109:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	t_1 = Float64(x * Float64(Float64(z * 6.0) - 3.0))
	tmp = 0.0
	if (x <= -7e-13)
		tmp = t_1;
	elseif (x <= -2.6e-103)
		tmp = t_0;
	elseif (x <= -1e-142)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (x <= 1.05e-65)
		tmp = t_0;
	elseif (x <= 5.2e-8)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (x <= 1.62e+109)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	t_1 = x * ((z * 6.0) - 3.0);
	tmp = 0.0;
	if (x <= -7e-13)
		tmp = t_1;
	elseif (x <= -2.6e-103)
		tmp = t_0;
	elseif (x <= -1e-142)
		tmp = -6.0 * ((y - x) * z);
	elseif (x <= 1.05e-65)
		tmp = t_0;
	elseif (x <= 5.2e-8)
		tmp = z * ((y - x) * -6.0);
	elseif (x <= 1.62e+109)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-13], t$95$1, If[LessEqual[x, -2.6e-103], t$95$0, If[LessEqual[x, -1e-142], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-65], t$95$0, If[LessEqual[x, 5.2e-8], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.62e+109], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.0000000000000005e-13 or 1.62e109 < 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. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around inf 88.1%

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

   if -7.0000000000000005e-13 < x < -2.59999999999999996e-103 or -1e-142 < x < 1.05000000000000001e-65 or 5.2000000000000002e-8 < x < 1.62e109

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 76.7%

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

   if -2.59999999999999996e-103 < x < -1e-142

   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. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   if 1.05000000000000001e-65 < x < 5.2000000000000002e-8

   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. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in z around inf 91.4%

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

      1. associate-*r* 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l* 91.5%

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

   7. Simplified 91.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-142}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \end{array} \]

Alternative 9: 99.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((y - x) * 4.0) + (x + (-6.0 * ((y - x) * 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 = ((y - x) * 4.0d0) + (x + ((-6.0d0) * ((y - x) * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision] + N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $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. Taylor expanded in z around 0 99.8%

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

5. Final simplification 99.8%

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

Alternative 10: 97.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.55) (not (<= z 0.5)))
   (* z (* (- y x) -6.0))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.55) || !(z <= 0.5)) {
		tmp = z * ((y - x) * -6.0);
	} else {
		tmp = (x * -3.0) + (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 ((z <= (-0.55d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = z * ((y - x) * (-6.0d0))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.55) || !(z <= 0.5)) {
		tmp = z * ((y - x) * -6.0);
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.55) or not (z <= 0.5):
		tmp = z * ((y - x) * -6.0)
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.55) || !(z <= 0.5))
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.55) || ~((z <= 0.5)))
		tmp = z * ((y - x) * -6.0);
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.55], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.55000000000000004 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*l* 98.9%

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

   7. Simplified 98.9%

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

   if -0.55000000000000004 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.5%

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

   5. Taylor expanded in z around 0 97.3%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 11: 97.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.68)
   (+ x (* (- y x) (* z -6.0)))
   (if (<= z 0.55) (+ (* x -3.0) (* y 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.55) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.68d0)) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else if (z <= 0.55d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.55) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.68:
		tmp = x + ((y - x) * (z * -6.0))
	elif z <= 0.55:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	elseif (z <= 0.55)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.68)
		tmp = x + ((y - x) * (z * -6.0));
	elseif (z <= 0.55)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.68], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.680000000000000049

   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. Taylor expanded in z around inf 99.6%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   if -0.680000000000000049 < 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. Taylor expanded in x around 0 99.5%

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

   5. Taylor expanded in z around 0 97.3%

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

   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. Taylor expanded in z around 0 99.6%

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

   5. Taylor expanded in z around inf 98.0%

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

      1. associate-*r* 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l* 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

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. Final simplification 99.6%

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

Alternative 13: 37.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -340000000000:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -340000000000.0)
   (* x -3.0)
   (if (<= x 7.6e+107) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -340000000000.0) {
		tmp = x * -3.0;
	} else if (x <= 7.6e+107) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-340000000000.0d0)) then
        tmp = x * (-3.0d0)
    else if (x <= 7.6d+107) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -340000000000.0) {
		tmp = x * -3.0;
	} else if (x <= 7.6e+107) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -340000000000.0:
		tmp = x * -3.0
	elif x <= 7.6e+107:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -340000000000.0)
		tmp = Float64(x * -3.0);
	elseif (x <= 7.6e+107)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -340000000000.0)
		tmp = x * -3.0;
	elseif (x <= 7.6e+107)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -340000000000.0], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 7.6e+107], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e11 or 7.5999999999999996e107 < 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. Taylor expanded in y around 0 87.5%

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

   5. Taylor expanded in z around 0 45.7%

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

      1. distribute-lft1-in 45.7%

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

      2. metadata-eval 45.7%

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

      3. *-commutative 45.7%

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

   7. Simplified 45.7%

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

   if -3.4e11 < x < 7.5999999999999996e107

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 71.0%

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

   5. Taylor expanded in z around 0 37.9%

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

      1. *-commutative 37.9%

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

   7. Simplified 37.9%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -340000000000:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 14: 27.0% 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. Taylor expanded in y around 0 54.1%

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

5. Taylor expanded in z around 0 27.5%

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

   1. distribute-lft1-in 27.5%

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

   2. metadata-eval 27.5%

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

   3. *-commutative 27.5%

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

7. Simplified 27.5%

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

8. Final simplification 27.5%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023268 
(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))))