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

Percentage Accurate: 99.5% → 99.8%

Time: 10.6s

Alternatives: 17

Speedup: 1.2×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.7%

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

   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. +-commutative 99.7%

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

   6. distribute-lft-in 99.8%

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

   7. neg-mul-1 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   8. associate-*r* 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

   9. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   10. fma-def 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.031:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-118}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.031)
     t_0
     (if (<= z -1.35e-122)
       (* x -3.0)
       (if (<= z -4.6e-257)
         (* y 4.0)
         (if (<= z 1.8e-231)
           (* x -3.0)
           (if (<= z 3.6e-118) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.031) {
		tmp = t_0;
	} else if (z <= -1.35e-122) {
		tmp = x * -3.0;
	} else if (z <= -4.6e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-231) {
		tmp = x * -3.0;
	} else if (z <= 3.6e-118) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.031d0)) then
        tmp = t_0
    else if (z <= (-1.35d-122)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.6d-257)) then
        tmp = y * 4.0d0
    else if (z <= 1.8d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 3.6d-118) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.031) {
		tmp = t_0;
	} else if (z <= -1.35e-122) {
		tmp = x * -3.0;
	} else if (z <= -4.6e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-231) {
		tmp = x * -3.0;
	} else if (z <= 3.6e-118) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.031:
		tmp = t_0
	elif z <= -1.35e-122:
		tmp = x * -3.0
	elif z <= -4.6e-257:
		tmp = y * 4.0
	elif z <= 1.8e-231:
		tmp = x * -3.0
	elif z <= 3.6e-118:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.031)
		tmp = t_0;
	elseif (z <= -1.35e-122)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.6e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.8e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.6e-118)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.031)
		tmp = t_0;
	elseif (z <= -1.35e-122)
		tmp = x * -3.0;
	elseif (z <= -4.6e-257)
		tmp = y * 4.0;
	elseif (z <= 1.8e-231)
		tmp = x * -3.0;
	elseif (z <= 3.6e-118)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.031], t$95$0, If[LessEqual[z, -1.35e-122], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.6e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.8e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.6e-118], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.031 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 96.4%

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

   if -0.031 < z < -1.35000000000000005e-122 or -4.6e-257 < z < 1.79999999999999987e-231 or 3.6000000000000002e-118 < 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. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. fma-neg 76.8%

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

      4. metadata-eval 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -1.35000000000000005e-122 < z < -4.6e-257 or 1.79999999999999987e-231 < z < 3.6000000000000002e-118

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.031:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-118}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.006:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.006)
     t_0
     (if (<= z -9.5e-122)
       (* x -3.0)
       (if (<= z -5.6e-257)
         (* y 4.0)
         (if (<= z 9.2e-231)
           (* x -3.0)
           (if (<= z 1.55e-117) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.006) {
		tmp = t_0;
	} else if (z <= -9.5e-122) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-257) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-231) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.006d0)) then
        tmp = t_0
    else if (z <= (-9.5d-122)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.6d-257)) then
        tmp = y * 4.0d0
    else if (z <= 9.2d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 1.55d-117) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.006) {
		tmp = t_0;
	} else if (z <= -9.5e-122) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-257) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-231) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.006:
		tmp = t_0
	elif z <= -9.5e-122:
		tmp = x * -3.0
	elif z <= -5.6e-257:
		tmp = y * 4.0
	elif z <= 9.2e-231:
		tmp = x * -3.0
	elif z <= 1.55e-117:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -0.006)
		tmp = t_0;
	elseif (z <= -9.5e-122)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.6e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.2e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.55e-117)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -0.006)
		tmp = t_0;
	elseif (z <= -9.5e-122)
		tmp = x * -3.0;
	elseif (z <= -5.6e-257)
		tmp = y * 4.0;
	elseif (z <= 9.2e-231)
		tmp = x * -3.0;
	elseif (z <= 1.55e-117)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.006], t$95$0, If[LessEqual[z, -9.5e-122], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.6e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.2e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.55e-117], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0060000000000000001 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-*r* 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*l* 96.5%

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

   5. Simplified 96.5%

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

   if -0.0060000000000000001 < z < -9.5000000000000002e-122 or -5.60000000000000002e-257 < z < 9.2e-231 or 1.55000000000000005e-117 < 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. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. fma-neg 76.8%

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

      4. metadata-eval 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -9.5000000000000002e-122 < z < -5.60000000000000002e-257 or 9.2e-231 < z < 1.55000000000000005e-117

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.006:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 4: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6 - 3\right)\\ t_1 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -140000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-118}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 700000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- (* z 6.0) 3.0))) (t_1 (* z (* (- y x) -6.0))))
   (if (<= z -140000000.0)
     t_1
     (if (<= z -1.3e-123)
       t_0
       (if (<= z -2e-257)
         (* y 4.0)
         (if (<= z 1.2e-230)
           (* x -3.0)
           (if (<= z 1.55e-118) (* y 4.0) (if (<= z 700000.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * 6.0) - 3.0);
	double t_1 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -140000000.0) {
		tmp = t_1;
	} else if (z <= -1.3e-123) {
		tmp = t_0;
	} else if (z <= -2e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-230) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-118) {
		tmp = y * 4.0;
	} else if (z <= 700000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((z * 6.0d0) - 3.0d0)
    t_1 = z * ((y - x) * (-6.0d0))
    if (z <= (-140000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.3d-123)) then
        tmp = t_0
    else if (z <= (-2d-257)) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 1.55d-118) then
        tmp = y * 4.0d0
    else if (z <= 700000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((z * 6.0) - 3.0);
	double t_1 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -140000000.0) {
		tmp = t_1;
	} else if (z <= -1.3e-123) {
		tmp = t_0;
	} else if (z <= -2e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-230) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-118) {
		tmp = y * 4.0;
	} else if (z <= 700000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * 6.0) - 3.0)
	t_1 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -140000000.0:
		tmp = t_1
	elif z <= -1.3e-123:
		tmp = t_0
	elif z <= -2e-257:
		tmp = y * 4.0
	elif z <= 1.2e-230:
		tmp = x * -3.0
	elif z <= 1.55e-118:
		tmp = y * 4.0
	elif z <= 700000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * 6.0) - 3.0))
	t_1 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -140000000.0)
		tmp = t_1;
	elseif (z <= -1.3e-123)
		tmp = t_0;
	elseif (z <= -2e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.55e-118)
		tmp = Float64(y * 4.0);
	elseif (z <= 700000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * 6.0) - 3.0);
	t_1 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -140000000.0)
		tmp = t_1;
	elseif (z <= -1.3e-123)
		tmp = t_0;
	elseif (z <= -2e-257)
		tmp = y * 4.0;
	elseif (z <= 1.2e-230)
		tmp = x * -3.0;
	elseif (z <= 1.55e-118)
		tmp = y * 4.0;
	elseif (z <= 700000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -140000000.0], t$95$1, If[LessEqual[z, -1.3e-123], t$95$0, If[LessEqual[z, -2e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.55e-118], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 700000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4e8 or 7e5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 98.2%

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

      1. associate-*r* 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*l* 98.3%

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

   5. Simplified 98.3%

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

   if -1.4e8 < z < -1.29999999999999998e-123 or 1.5500000000000001e-118 < z < 7e5

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 73.7%

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

   if -1.29999999999999998e-123 < z < -2e-257 or 1.2000000000000001e-230 < z < 1.5500000000000001e-118

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   if -2e-257 < z < 1.2000000000000001e-230

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 99.5%

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

   3. Taylor expanded in x around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-in 80.1%

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

      3. fma-neg 80.1%

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

      4. metadata-eval 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in z around 0 80.1%

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

      1. *-commutative 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-118}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 700000:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 5: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.115:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-127}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.115)
     t_0
     (if (<= z -6.8e-127)
       (* x -3.0)
       (if (<= z -2e-257)
         (* y 4.0)
         (if (<= z 4.6e-231)
           (* x -3.0)
           (if (<= z 6.8e-117) (* y 4.0) (if (<= z 0.63) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.115) {
		tmp = t_0;
	} else if (z <= -6.8e-127) {
		tmp = x * -3.0;
	} else if (z <= -2e-257) {
		tmp = y * 4.0;
	} else if (z <= 4.6e-231) {
		tmp = x * -3.0;
	} else if (z <= 6.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.63) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.115d0)) then
        tmp = t_0
    else if (z <= (-6.8d-127)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2d-257)) then
        tmp = y * 4.0d0
    else if (z <= 4.6d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 6.8d-117) then
        tmp = y * 4.0d0
    else if (z <= 0.63d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.115) {
		tmp = t_0;
	} else if (z <= -6.8e-127) {
		tmp = x * -3.0;
	} else if (z <= -2e-257) {
		tmp = y * 4.0;
	} else if (z <= 4.6e-231) {
		tmp = x * -3.0;
	} else if (z <= 6.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.63) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.115:
		tmp = t_0
	elif z <= -6.8e-127:
		tmp = x * -3.0
	elif z <= -2e-257:
		tmp = y * 4.0
	elif z <= 4.6e-231:
		tmp = x * -3.0
	elif z <= 6.8e-117:
		tmp = y * 4.0
	elif z <= 0.63:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.115)
		tmp = t_0;
	elseif (z <= -6.8e-127)
		tmp = Float64(x * -3.0);
	elseif (z <= -2e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.6e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.8e-117)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.63)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.115)
		tmp = t_0;
	elseif (z <= -6.8e-127)
		tmp = x * -3.0;
	elseif (z <= -2e-257)
		tmp = y * 4.0;
	elseif (z <= 4.6e-231)
		tmp = x * -3.0;
	elseif (z <= 6.8e-117)
		tmp = y * 4.0;
	elseif (z <= 0.63)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.115], t$95$0, If[LessEqual[z, -6.8e-127], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.6e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.8e-117], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.63], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.115000000000000005 or 0.630000000000000004 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-*r* 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*l* 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in y around inf 56.4%

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

   if -0.115000000000000005 < z < -6.7999999999999997e-127 or -2e-257 < z < 4.6e-231 or 6.80000000000000069e-117 < z < 0.630000000000000004

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. fma-neg 76.8%

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

      4. metadata-eval 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -6.7999999999999997e-127 < z < -2e-257 or 4.6e-231 < z < 6.80000000000000069e-117

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.115:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-127}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.63:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* 6.0 (* x z))
   (if (<= z -3.5e-121)
     (* x -3.0)
     (if (<= z -2.7e-257)
       (* y 4.0)
       (if (<= z 9e-231)
         (* x -3.0)
         (if (<= z 5.8e-117)
           (* y 4.0)
           (if (<= z 0.5) (* x -3.0) (* -6.0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3.5e-121) {
		tmp = x * -3.0;
	} else if (z <= -2.7e-257) {
		tmp = y * 4.0;
	} else if (z <= 9e-231) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.5d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-3.5d-121)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.7d-257)) then
        tmp = y * 4.0d0
    else if (z <= 9d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 5.8d-117) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * 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 = 6.0 * (x * z);
	} else if (z <= -3.5e-121) {
		tmp = x * -3.0;
	} else if (z <= -2.7e-257) {
		tmp = y * 4.0;
	} else if (z <= 9e-231) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = 6.0 * (x * z)
	elif z <= -3.5e-121:
		tmp = x * -3.0
	elif z <= -2.7e-257:
		tmp = y * 4.0
	elif z <= 9e-231:
		tmp = x * -3.0
	elif z <= 5.8e-117:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -3.5e-121)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.7e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 9e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.8e-117)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = 6.0 * (x * z);
	elseif (z <= -3.5e-121)
		tmp = x * -3.0;
	elseif (z <= -2.7e-257)
		tmp = y * 4.0;
	elseif (z <= 9e-231)
		tmp = x * -3.0;
	elseif (z <= 5.8e-117)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-121], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.7e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.8e-117], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.5%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around 0 55.5%

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

   if -0.5 < z < -3.49999999999999993e-121 or -2.6999999999999999e-257 < z < 8.9999999999999996e-231 or 5.8000000000000001e-117 < 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. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. fma-neg 76.8%

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

      4. metadata-eval 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -3.49999999999999993e-121 < z < -2.6999999999999999e-257 or 8.9999999999999996e-231 < z < 5.8000000000000001e-117

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   if 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. associate-*r* 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*l* 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in y around inf 65.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 7: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* 6.0 (* x z))
   (if (<= z -3.5e-122)
     (* x -3.0)
     (if (<= z -9.8e-257)
       (* y 4.0)
       (if (<= z 1.3e-230)
         (* x -3.0)
         (if (<= z 4.4e-119)
           (* y 4.0)
           (if (<= z 0.6) (* x -3.0) (* z (* y -6.0)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3.5e-122) {
		tmp = x * -3.0;
	} else if (z <= -9.8e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-230) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-119) {
		tmp = y * 4.0;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else {
		tmp = z * (y * -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 <= (-0.5d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-3.5d-122)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9.8d-257)) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d-119) then
        tmp = y * 4.0d0
    else if (z <= 0.6d0) then
        tmp = x * (-3.0d0)
    else
        tmp = z * (y * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3.5e-122) {
		tmp = x * -3.0;
	} else if (z <= -9.8e-257) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-230) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-119) {
		tmp = y * 4.0;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = 6.0 * (x * z)
	elif z <= -3.5e-122:
		tmp = x * -3.0
	elif z <= -9.8e-257:
		tmp = y * 4.0
	elif z <= 1.3e-230:
		tmp = x * -3.0
	elif z <= 4.4e-119:
		tmp = y * 4.0
	elif z <= 0.6:
		tmp = x * -3.0
	else:
		tmp = z * (y * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -3.5e-122)
		tmp = Float64(x * -3.0);
	elseif (z <= -9.8e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e-119)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.6)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(z * Float64(y * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = 6.0 * (x * z);
	elseif (z <= -3.5e-122)
		tmp = x * -3.0;
	elseif (z <= -9.8e-257)
		tmp = y * 4.0;
	elseif (z <= 1.3e-230)
		tmp = x * -3.0;
	elseif (z <= 4.4e-119)
		tmp = y * 4.0;
	elseif (z <= 0.6)
		tmp = x * -3.0;
	else
		tmp = z * (y * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-122], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9.8e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e-119], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.6], N[(x * -3.0), $MachinePrecision], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.5%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around 0 55.5%

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

   if -0.5 < z < -3.5000000000000001e-122 or -9.80000000000000022e-257 < z < 1.3000000000000001e-230 or 4.4000000000000001e-119 < z < 0.599999999999999978

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. fma-neg 76.8%

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

      4. metadata-eval 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -3.5000000000000001e-122 < z < -9.80000000000000022e-257 or 1.3000000000000001e-230 < z < 4.4000000000000001e-119

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   if 0.599999999999999978 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. associate-*r* 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*l* 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in y around inf 65.5%

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

      1. associate-*r* 65.6%

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

   8. Simplified 65.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]

Alternative 8: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* 6.0 (* x z))
   (if (<= z -1.35e-120)
     (* x -3.0)
     (if (<= z -9.5e-257)
       (* y 4.0)
       (if (<= z 4.5e-231)
         (* x -3.0)
         (if (<= z 7.8e-117)
           (* y 4.0)
           (if (<= z 0.58) (* x -3.0) (* y (* z -6.0)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.35e-120) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-257) {
		tmp = y * 4.0;
	} else if (z <= 4.5e-231) {
		tmp = x * -3.0;
	} else if (z <= 7.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.5d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.35d-120)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9.5d-257)) then
        tmp = y * 4.0d0
    else if (z <= 4.5d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 7.8d-117) then
        tmp = y * 4.0d0
    else if (z <= 0.58d0) then
        tmp = x * (-3.0d0)
    else
        tmp = y * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.35e-120) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-257) {
		tmp = y * 4.0;
	} else if (z <= 4.5e-231) {
		tmp = x * -3.0;
	} else if (z <= 7.8e-117) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = 6.0 * (x * z)
	elif z <= -1.35e-120:
		tmp = x * -3.0
	elif z <= -9.5e-257:
		tmp = y * 4.0
	elif z <= 4.5e-231:
		tmp = x * -3.0
	elif z <= 7.8e-117:
		tmp = y * 4.0
	elif z <= 0.58:
		tmp = x * -3.0
	else:
		tmp = y * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.35e-120)
		tmp = Float64(x * -3.0);
	elseif (z <= -9.5e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.5e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.8e-117)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.58)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.35e-120)
		tmp = x * -3.0;
	elseif (z <= -9.5e-257)
		tmp = y * 4.0;
	elseif (z <= 4.5e-231)
		tmp = x * -3.0;
	elseif (z <= 7.8e-117)
		tmp = y * 4.0;
	elseif (z <= 0.58)
		tmp = x * -3.0;
	else
		tmp = y * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-120], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9.5e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.5e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.8e-117], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(x * -3.0), $MachinePrecision], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.5%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around 0 55.5%

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

   if -0.5 < z < -1.3499999999999999e-120 or -9.49999999999999941e-257 < z < 4.4999999999999998e-231 or 7.79999999999999984e-117 < 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. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. fma-neg 76.8%

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

      4. metadata-eval 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   if -1.3499999999999999e-120 < z < -9.49999999999999941e-257 or 4.4999999999999998e-231 < z < 7.79999999999999984e-117

   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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 65.6%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   if 0.57999999999999996 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      3. fma-def 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-lft-in 99.7%

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

      7. neg-mul-1 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in z around inf 65.6%

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

      1. *-commutative 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]

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 99.5%

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

2. Taylor expanded in z around 0 99.7%

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

3. Final simplification 99.7%

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

Alternative 10: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.56)
   (* z (* (- y x) -6.0))
   (if (<= z 0.65) (+ x (* (- y x) 4.0)) (* z (+ (* x 6.0) (* y -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((x * 6.0) + (y * -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 <= (-0.56d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.65d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((x * 6.0d0) + (y * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((x * 6.0) + (y * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.56:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.65:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((x * 6.0) + (y * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.56)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.65)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(x * 6.0) + Float64(y * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.56)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.65)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((x * 6.0) + (y * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.56], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * 6.0), $MachinePrecision] + N[(y * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.56000000000000005

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.5%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.6%

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

   5. Simplified 97.6%

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

   if -0.56000000000000005 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 96.1%

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

   if 0.650000000000000022 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. associate-*r* 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*l* 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in y around 0 95.5%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \end{array} \]

Alternative 11: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.65)
   (+ x (* (- y x) (* z -6.0)))
   (if (<= z 0.66) (+ x (* (- y x) 4.0)) (* z (+ (* x 6.0) (* y -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((x * 6.0) + (y * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.65d0)) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((x * 6.0d0) + (y * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((x * 6.0) + (y * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.65:
		tmp = x + ((y - x) * (z * -6.0))
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((x * 6.0) + (y * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.65)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(x * 6.0) + Float64(y * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.65)
		tmp = x + ((y - x) * (z * -6.0));
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((x * 6.0) + (y * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.65], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * 6.0), $MachinePrecision] + N[(y * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 97.5%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   if -0.650000000000000022 < 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. Taylor expanded in z around 0 96.1%

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

   if 0.660000000000000031 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. associate-*r* 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*l* 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in y around 0 95.5%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.55) (not (<= z 0.6)))
   (* z (* (- y x) -6.0))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.55) || !(z <= 0.6)) {
		tmp = z * ((y - x) * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.55d0)) .or. (.not. (z <= 0.6d0))) then
        tmp = z * ((y - x) * (-6.0d0))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.55) || !(z <= 0.6)) {
		tmp = z * ((y - x) * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.55) or not (z <= 0.6):
		tmp = z * ((y - x) * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.55) || !(z <= 0.6))
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.55) || ~((z <= 0.6)))
		tmp = z * ((y - x) * -6.0);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.55], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.55000000000000004 or 0.599999999999999978 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-*r* 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*l* 96.5%

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

   5. Simplified 96.5%

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

   if -0.55000000000000004 < z < 0.599999999999999978

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 96.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.5%

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

   1. neg-mul-1 99.5%

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

   2. +-commutative 99.5%

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

   3. sub-neg 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 14: 99.8% accurate, 1.2× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate-*l* 99.7%

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

   2. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 15: 38.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.06e-70) (* x -3.0) (if (<= x 3.9e-27) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e-70) {
		tmp = x * -3.0;
	} else if (x <= 3.9e-27) {
		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 <= (-1.06d-70)) then
        tmp = x * (-3.0d0)
    else if (x <= 3.9d-27) 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 <= -1.06e-70) {
		tmp = x * -3.0;
	} else if (x <= 3.9e-27) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.06e-70:
		tmp = x * -3.0
	elif x <= 3.9e-27:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.06e-70)
		tmp = Float64(x * -3.0);
	elseif (x <= 3.9e-27)
		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 <= -1.06e-70)
		tmp = x * -3.0;
	elseif (x <= 3.9e-27)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.06e-70], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 3.9e-27], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e-70 or 3.89999999999999972e-27 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 99.6%

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

   3. Taylor expanded in x around -inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. distribute-rgt-neg-in 77.7%

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

      3. fma-neg 77.7%

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

      4. metadata-eval 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around 0 46.4%

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

      1. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if -1.06e-70 < x < 3.89999999999999972e-27

   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. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. neg-mul-1 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.7%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 76.1%

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

   5. Taylor expanded in z around 0 35.9%

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

      1. *-commutative 35.9%

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

   7. Simplified 35.9%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 16: 25.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in y around 0 99.5%

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

3. Taylor expanded in x around -inf 54.6%

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

   1. mul-1-neg 54.6%

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

   2. distribute-rgt-neg-in 54.6%

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

   3. fma-neg 54.6%

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

   4. metadata-eval 54.6%

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

5. Simplified 54.6%

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

6. Taylor expanded in z around 0 32.6%

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

   1. *-commutative 32.6%

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

8. Simplified 32.6%

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

9. Final simplification 32.6%

   \[\leadsto x \cdot -3 \]

Alternative 17: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in y around 0 99.5%

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

3. Taylor expanded in z around inf 46.1%

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

   1. neg-mul-1 46.1%

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

5. Simplified 46.1%

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

6. Taylor expanded in z around 0 2.5%

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

7. Final simplification 2.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023174 
(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))))