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

Percentage Accurate: 99.5% → 99.8%

Time: 12.7s

Alternatives: 18

Speedup: 1.2×

• 21.4% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. sub-neg 99.8%

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

   5. +-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. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-183}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-159}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+279}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -2.1e+158)
     t_0
     (if (<= z -0.6)
       t_1
       (if (<= z -4.2e-81)
         (* x -3.0)
         (if (<= z -5.6e-183)
           (* y 4.0)
           (if (<= z -4.2e-233)
             (* x -3.0)
             (if (<= z -2.7e-250)
               (* y 4.0)
               (if (<= z 9e-260)
                 (* x -3.0)
                 (if (<= z 1.2e-159)
                   (* y 4.0)
                   (if (<= z 0.5)
                     (* x -3.0)
                     (if (<= z 4.4e+279) t_0 t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.1e+158) {
		tmp = t_0;
	} else if (z <= -0.6) {
		tmp = t_1;
	} else if (z <= -4.2e-81) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-183) {
		tmp = y * 4.0;
	} else if (z <= -4.2e-233) {
		tmp = x * -3.0;
	} else if (z <= -2.7e-250) {
		tmp = y * 4.0;
	} else if (z <= 9e-260) {
		tmp = x * -3.0;
	} else if (z <= 1.2e-159) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 4.4e+279) {
		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 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-2.1d+158)) then
        tmp = t_0
    else if (z <= (-0.6d0)) then
        tmp = t_1
    else if (z <= (-4.2d-81)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.6d-183)) then
        tmp = y * 4.0d0
    else if (z <= (-4.2d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.7d-250)) then
        tmp = y * 4.0d0
    else if (z <= 9d-260) then
        tmp = x * (-3.0d0)
    else if (z <= 1.2d-159) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d+279) 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 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.1e+158) {
		tmp = t_0;
	} else if (z <= -0.6) {
		tmp = t_1;
	} else if (z <= -4.2e-81) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-183) {
		tmp = y * 4.0;
	} else if (z <= -4.2e-233) {
		tmp = x * -3.0;
	} else if (z <= -2.7e-250) {
		tmp = y * 4.0;
	} else if (z <= 9e-260) {
		tmp = x * -3.0;
	} else if (z <= 1.2e-159) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 4.4e+279) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.1e+158:
		tmp = t_0
	elif z <= -0.6:
		tmp = t_1
	elif z <= -4.2e-81:
		tmp = x * -3.0
	elif z <= -5.6e-183:
		tmp = y * 4.0
	elif z <= -4.2e-233:
		tmp = x * -3.0
	elif z <= -2.7e-250:
		tmp = y * 4.0
	elif z <= 9e-260:
		tmp = x * -3.0
	elif z <= 1.2e-159:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 4.4e+279:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.1e+158)
		tmp = t_0;
	elseif (z <= -0.6)
		tmp = t_1;
	elseif (z <= -4.2e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.6e-183)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.2e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.7e-250)
		tmp = Float64(y * 4.0);
	elseif (z <= 9e-260)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.2e-159)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e+279)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.1e+158)
		tmp = t_0;
	elseif (z <= -0.6)
		tmp = t_1;
	elseif (z <= -4.2e-81)
		tmp = x * -3.0;
	elseif (z <= -5.6e-183)
		tmp = y * 4.0;
	elseif (z <= -4.2e-233)
		tmp = x * -3.0;
	elseif (z <= -2.7e-250)
		tmp = y * 4.0;
	elseif (z <= 9e-260)
		tmp = x * -3.0;
	elseif (z <= 1.2e-159)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 4.4e+279)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+158], t$95$0, If[LessEqual[z, -0.6], t$95$1, If[LessEqual[z, -4.2e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.6e-183], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.2e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.7e-250], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9e-260], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.2e-159], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e+279], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0999999999999999e158 or 0.5 < z < 4.3999999999999999e279

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.6%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in z around inf 60.7%

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

   if -2.0999999999999999e158 < z < -0.599999999999999978 or 4.3999999999999999e279 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.6%

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

   5. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

   7. Simplified 63.7%

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

   if -0.599999999999999978 < z < -4.1999999999999998e-81 or -5.5999999999999997e-183 < z < -4.1999999999999997e-233 or -2.70000000000000002e-250 < z < 8.9999999999999995e-260 or 1.19999999999999999e-159 < z < 0.5

   1. Initial program 99.3%

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

   2. 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 64.7%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if -4.1999999999999998e-81 < z < -5.5999999999999997e-183 or -4.1999999999999997e-233 < z < -2.70000000000000002e-250 or 8.9999999999999995e-260 < z < 1.19999999999999999e-159

   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* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.7%

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

   5. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-183}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-250}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-159}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+279}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+157}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.26:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-249}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-162}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+280}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))) (t_1 (* -6.0 (* y z))))
   (if (<= z -9e+157)
     t_0
     (if (<= z -0.26)
       t_1
       (if (<= z -4.2e-83)
         (* x -3.0)
         (if (<= z -4.1e-181)
           (* y 4.0)
           (if (<= z -5.5e-233)
             (* x -3.0)
             (if (<= z -1.35e-249)
               (* y 4.0)
               (if (<= z 5e-262)
                 (* x -3.0)
                 (if (<= z 4.2e-162)
                   (* y 4.0)
                   (if (<= z 0.5)
                     (* x -3.0)
                     (if (<= z 4.5e+280) t_0 t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -9e+157) {
		tmp = t_0;
	} else if (z <= -0.26) {
		tmp = t_1;
	} else if (z <= -4.2e-83) {
		tmp = x * -3.0;
	} else if (z <= -4.1e-181) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-233) {
		tmp = x * -3.0;
	} else if (z <= -1.35e-249) {
		tmp = y * 4.0;
	} else if (z <= 5e-262) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-162) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 4.5e+280) {
		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 = z * (x * 6.0d0)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-9d+157)) then
        tmp = t_0
    else if (z <= (-0.26d0)) then
        tmp = t_1
    else if (z <= (-4.2d-83)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.1d-181)) then
        tmp = y * 4.0d0
    else if (z <= (-5.5d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.35d-249)) then
        tmp = y * 4.0d0
    else if (z <= 5d-262) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d-162) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d+280) 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 = z * (x * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -9e+157) {
		tmp = t_0;
	} else if (z <= -0.26) {
		tmp = t_1;
	} else if (z <= -4.2e-83) {
		tmp = x * -3.0;
	} else if (z <= -4.1e-181) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-233) {
		tmp = x * -3.0;
	} else if (z <= -1.35e-249) {
		tmp = y * 4.0;
	} else if (z <= 5e-262) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-162) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 4.5e+280) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -9e+157:
		tmp = t_0
	elif z <= -0.26:
		tmp = t_1
	elif z <= -4.2e-83:
		tmp = x * -3.0
	elif z <= -4.1e-181:
		tmp = y * 4.0
	elif z <= -5.5e-233:
		tmp = x * -3.0
	elif z <= -1.35e-249:
		tmp = y * 4.0
	elif z <= 5e-262:
		tmp = x * -3.0
	elif z <= 4.2e-162:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 4.5e+280:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -9e+157)
		tmp = t_0;
	elseif (z <= -0.26)
		tmp = t_1;
	elseif (z <= -4.2e-83)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.1e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.5e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.35e-249)
		tmp = Float64(y * 4.0);
	elseif (z <= 5e-262)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e-162)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e+280)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -9e+157)
		tmp = t_0;
	elseif (z <= -0.26)
		tmp = t_1;
	elseif (z <= -4.2e-83)
		tmp = x * -3.0;
	elseif (z <= -4.1e-181)
		tmp = y * 4.0;
	elseif (z <= -5.5e-233)
		tmp = x * -3.0;
	elseif (z <= -1.35e-249)
		tmp = y * 4.0;
	elseif (z <= 5e-262)
		tmp = x * -3.0;
	elseif (z <= 4.2e-162)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 4.5e+280)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+157], t$95$0, If[LessEqual[z, -0.26], t$95$1, If[LessEqual[z, -4.2e-83], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.1e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.5e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.35e-249], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5e-262], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e-162], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e+280], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999997e157 or 0.5 < z < 4.5000000000000001e280

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.6%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-*l* 60.8%

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

   6. Simplified 60.8%

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

   if -8.9999999999999997e157 < z < -0.26000000000000001 or 4.5000000000000001e280 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.6%

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

   5. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

   7. Simplified 63.7%

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

   if -0.26000000000000001 < z < -4.1999999999999998e-83 or -4.1000000000000001e-181 < z < -5.50000000000000005e-233 or -1.35e-249 < z < 4.99999999999999992e-262 or 4.2e-162 < z < 0.5

   1. Initial program 99.3%

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

   2. 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 64.7%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if -4.1999999999999998e-83 < z < -4.1000000000000001e-181 or -5.50000000000000005e-233 < z < -1.35e-249 or 4.99999999999999992e-262 < z < 4.2e-162

   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* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.7%

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

   5. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.26:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-249}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-162}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+280}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+159}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.215:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-252}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-261}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-157}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+280}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))))
   (if (<= z -4.2e+159)
     t_0
     (if (<= z -0.215)
       (* y (* z -6.0))
       (if (<= z -3.4e-81)
         (* x -3.0)
         (if (<= z -1.65e-181)
           (* y 4.0)
           (if (<= z -3.8e-233)
             (* x -3.0)
             (if (<= z -1e-252)
               (* y 4.0)
               (if (<= z 1.25e-261)
                 (* x -3.0)
                 (if (<= z 2.1e-157)
                   (* y 4.0)
                   (if (<= z 0.5)
                     (* x -3.0)
                     (if (<= z 1.45e+280) t_0 (* -6.0 (* y z))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -4.2e+159) {
		tmp = t_0;
	} else if (z <= -0.215) {
		tmp = y * (z * -6.0);
	} else if (z <= -3.4e-81) {
		tmp = x * -3.0;
	} else if (z <= -1.65e-181) {
		tmp = y * 4.0;
	} else if (z <= -3.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -1e-252) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-261) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-157) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 1.45e+280) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * 6.0d0)
    if (z <= (-4.2d+159)) then
        tmp = t_0
    else if (z <= (-0.215d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-3.4d-81)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.65d-181)) then
        tmp = y * 4.0d0
    else if (z <= (-3.8d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1d-252)) then
        tmp = y * 4.0d0
    else if (z <= 1.25d-261) then
        tmp = x * (-3.0d0)
    else if (z <= 2.1d-157) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.45d+280) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -4.2e+159) {
		tmp = t_0;
	} else if (z <= -0.215) {
		tmp = y * (z * -6.0);
	} else if (z <= -3.4e-81) {
		tmp = x * -3.0;
	} else if (z <= -1.65e-181) {
		tmp = y * 4.0;
	} else if (z <= -3.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -1e-252) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-261) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-157) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 1.45e+280) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	tmp = 0
	if z <= -4.2e+159:
		tmp = t_0
	elif z <= -0.215:
		tmp = y * (z * -6.0)
	elif z <= -3.4e-81:
		tmp = x * -3.0
	elif z <= -1.65e-181:
		tmp = y * 4.0
	elif z <= -3.8e-233:
		tmp = x * -3.0
	elif z <= -1e-252:
		tmp = y * 4.0
	elif z <= 1.25e-261:
		tmp = x * -3.0
	elif z <= 2.1e-157:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 1.45e+280:
		tmp = t_0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -4.2e+159)
		tmp = t_0;
	elseif (z <= -0.215)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -3.4e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.65e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.8e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -1e-252)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.25e-261)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.1e-157)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.45e+280)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -4.2e+159)
		tmp = t_0;
	elseif (z <= -0.215)
		tmp = y * (z * -6.0);
	elseif (z <= -3.4e-81)
		tmp = x * -3.0;
	elseif (z <= -1.65e-181)
		tmp = y * 4.0;
	elseif (z <= -3.8e-233)
		tmp = x * -3.0;
	elseif (z <= -1e-252)
		tmp = y * 4.0;
	elseif (z <= 1.25e-261)
		tmp = x * -3.0;
	elseif (z <= 2.1e-157)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 1.45e+280)
		tmp = t_0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+159], t$95$0, If[LessEqual[z, -0.215], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.65e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.8e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1e-252], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.25e-261], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.1e-157], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.45e+280], t$95$0, N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.19999999999999978e159 or 0.5 < z < 1.44999999999999993e280

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.6%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-*l* 60.8%

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

   6. Simplified 60.8%

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

   if -4.19999999999999978e159 < z < -0.214999999999999997

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-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 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 58.7%

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

   5. Taylor expanded in z around inf 57.7%

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

   if -0.214999999999999997 < z < -3.3999999999999999e-81 or -1.65000000000000004e-181 < z < -3.8e-233 or -9.99999999999999943e-253 < z < 1.24999999999999995e-261 or 2.1e-157 < z < 0.5

   1. Initial program 99.3%

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

   2. 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 64.7%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if -3.3999999999999999e-81 < z < -1.65000000000000004e-181 or -3.8e-233 < z < -9.99999999999999943e-253 or 1.24999999999999995e-261 < z < 2.1e-157

   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* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.7%

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

   5. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

   7. Simplified 75.7%

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

   if 1.44999999999999993e280 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+159}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.215:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-252}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-261}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-157}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+280}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.002:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.002)
     t_0
     (if (<= z -1.1e-82)
       (* x -3.0)
       (if (<= z -8.6e-182)
         (* y 4.0)
         (if (<= z -4.8e-233)
           (* x -3.0)
           (if (<= z -2.8e-253)
             (* y 4.0)
             (if (<= z 1.3e-262)
               (* x -3.0)
               (if (<= z 3.9e-161)
                 (* 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 <= -0.002) {
		tmp = t_0;
	} else if (z <= -1.1e-82) {
		tmp = x * -3.0;
	} else if (z <= -8.6e-182) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-253) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-262) {
		tmp = x * -3.0;
	} else if (z <= 3.9e-161) {
		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 <= (-0.002d0)) then
        tmp = t_0
    else if (z <= (-1.1d-82)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8.6d-182)) then
        tmp = y * 4.0d0
    else if (z <= (-4.8d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.8d-253)) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-262) then
        tmp = x * (-3.0d0)
    else if (z <= 3.9d-161) 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 <= -0.002) {
		tmp = t_0;
	} else if (z <= -1.1e-82) {
		tmp = x * -3.0;
	} else if (z <= -8.6e-182) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-253) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-262) {
		tmp = x * -3.0;
	} else if (z <= 3.9e-161) {
		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 <= -0.002:
		tmp = t_0
	elif z <= -1.1e-82:
		tmp = x * -3.0
	elif z <= -8.6e-182:
		tmp = y * 4.0
	elif z <= -4.8e-233:
		tmp = x * -3.0
	elif z <= -2.8e-253:
		tmp = y * 4.0
	elif z <= 1.3e-262:
		tmp = x * -3.0
	elif z <= 3.9e-161:
		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 <= -0.002)
		tmp = t_0;
	elseif (z <= -1.1e-82)
		tmp = Float64(x * -3.0);
	elseif (z <= -8.6e-182)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.8e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.8e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-262)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.9e-161)
		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 <= -0.002)
		tmp = t_0;
	elseif (z <= -1.1e-82)
		tmp = x * -3.0;
	elseif (z <= -8.6e-182)
		tmp = y * 4.0;
	elseif (z <= -4.8e-233)
		tmp = x * -3.0;
	elseif (z <= -2.8e-253)
		tmp = y * 4.0;
	elseif (z <= 1.3e-262)
		tmp = x * -3.0;
	elseif (z <= 3.9e-161)
		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, -0.002], t$95$0, If[LessEqual[z, -1.1e-82], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8.6e-182], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.8e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.8e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-262], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.9e-161], 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 < -2e-3 or 0.5 < z

   1. Initial program 99.9%

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

      1. associate-*r* 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. +-commutative 99.7%

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

      4. flip-+ 27.7%

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

      5. pow2 27.7%

         \[\leadsto \frac{\color{blue}{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) - x} \]

      6. metadata-eval 27.7%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) - x} \]

      7. associate-*r* 27.6%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} - x} \]

      8. fma-neg 27.6%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \frac{2}{3} - z, -x\right)}} \]

      9. metadata-eval 27.6%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \color{blue}{0.6666666666666666} - z, -x\right)} \]

   3. Applied egg-rr 27.6%

      \[\leadsto \color{blue}{\frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, 0.6666666666666666 - z, -x\right)}} \]

   4. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) - 4 \cdot \left(y - x\right)} \]
   5. Step-by-step derivation

      1. sub-neg 98.2%

         \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-4 \cdot \left(y - x\right)\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-\color{blue}{\left(y - x\right) \cdot 4}\right) \]

      3. associate-+r+ 98.2%

         \[\leadsto \color{blue}{\left(\left(8 \cdot \left(y - x\right) + -6 \cdot \left(z \cdot \left(y - x\right)\right)\right) + x\right)} + \left(-\left(y - x\right) \cdot 4\right) \]

      4. associate-*r* 98.1%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      5. *-commutative 98.1%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right)\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      6. distribute-rgt-out 99.8%

         \[\leadsto \left(\color{blue}{\left(y - x\right) \cdot \left(8 + z \cdot -6\right)} + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + \color{blue}{-6 \cdot z}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      8. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \color{blue}{\left(y - x\right) \cdot \left(-4\right)} \]

      9. metadata-eval 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot \color{blue}{-4} \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot -4} \]

   7. Taylor expanded in z around inf 97.5%

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

   if -2e-3 < z < -1.09999999999999993e-82 or -8.6e-182 < z < -4.7999999999999998e-233 or -2.80000000000000006e-253 < z < 1.2999999999999999e-262 or 3.89999999999999973e-161 < z < 0.5

   1. Initial program 99.3%

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

   2. 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 64.7%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if -1.09999999999999993e-82 < z < -8.6e-182 or -4.7999999999999998e-233 < z < -2.80000000000000006e-253 or 1.2999999999999999e-262 < z < 3.89999999999999973e-161

   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* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.7%

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

   5. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.002:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-262}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-161}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-254}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-157}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.88)
     t_0
     (if (<= z -4.7e-81)
       (* x -3.0)
       (if (<= z -1.3e-181)
         (* y 4.0)
         (if (<= z -5.8e-233)
           (* x -3.0)
           (if (<= z -9.6e-254)
             (* y 4.0)
             (if (<= z 6e-260)
               (* x -3.0)
               (if (<= z 1.7e-157)
                 (* y 4.0)
                 (if (<= z 0.54) (* 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 <= -0.88) {
		tmp = t_0;
	} else if (z <= -4.7e-81) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-181) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -9.6e-254) {
		tmp = y * 4.0;
	} else if (z <= 6e-260) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-157) {
		tmp = y * 4.0;
	} else if (z <= 0.54) {
		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 <= (-0.88d0)) then
        tmp = t_0
    else if (z <= (-4.7d-81)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.3d-181)) then
        tmp = y * 4.0d0
    else if (z <= (-5.8d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9.6d-254)) then
        tmp = y * 4.0d0
    else if (z <= 6d-260) then
        tmp = x * (-3.0d0)
    else if (z <= 1.7d-157) then
        tmp = y * 4.0d0
    else if (z <= 0.54d0) 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 <= -0.88) {
		tmp = t_0;
	} else if (z <= -4.7e-81) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-181) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -9.6e-254) {
		tmp = y * 4.0;
	} else if (z <= 6e-260) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-157) {
		tmp = y * 4.0;
	} else if (z <= 0.54) {
		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 <= -0.88:
		tmp = t_0
	elif z <= -4.7e-81:
		tmp = x * -3.0
	elif z <= -1.3e-181:
		tmp = y * 4.0
	elif z <= -5.8e-233:
		tmp = x * -3.0
	elif z <= -9.6e-254:
		tmp = y * 4.0
	elif z <= 6e-260:
		tmp = x * -3.0
	elif z <= 1.7e-157:
		tmp = y * 4.0
	elif z <= 0.54:
		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 <= -0.88)
		tmp = t_0;
	elseif (z <= -4.7e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.3e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.8e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -9.6e-254)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-260)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.7e-157)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.54)
		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 <= -0.88)
		tmp = t_0;
	elseif (z <= -4.7e-81)
		tmp = x * -3.0;
	elseif (z <= -1.3e-181)
		tmp = y * 4.0;
	elseif (z <= -5.8e-233)
		tmp = x * -3.0;
	elseif (z <= -9.6e-254)
		tmp = y * 4.0;
	elseif (z <= 6e-260)
		tmp = x * -3.0;
	elseif (z <= 1.7e-157)
		tmp = y * 4.0;
	elseif (z <= 0.54)
		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, -0.88], t$95$0, If[LessEqual[z, -4.7e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.3e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.8e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9.6e-254], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-260], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.7e-157], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.54], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.880000000000000004 or 0.54000000000000004 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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 99.8%

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

      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 46.9%

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

   5. Taylor expanded in z around inf 45.0%

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

      1. *-commutative 45.0%

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

   7. Simplified 45.0%

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

   if -0.880000000000000004 < z < -4.70000000000000029e-81 or -1.29999999999999999e-181 < z < -5.79999999999999964e-233 or -9.60000000000000007e-254 < z < 6.0000000000000001e-260 or 1.69999999999999989e-157 < z < 0.54000000000000004

   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 64.7%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if -4.70000000000000029e-81 < z < -1.29999999999999999e-181 or -5.79999999999999964e-233 < z < -9.60000000000000007e-254 or 6.0000000000000001e-260 < z < 1.69999999999999989e-157

   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* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.7%

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

   5. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-254}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-157}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -6200000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-261}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -6200000000.0)
     t_0
     (if (<= z -7.5e-181)
       (* y (+ 4.0 (* z -6.0)))
       (if (<= z -3.8e-233)
         (* x -3.0)
         (if (<= z -5e-253)
           (* y 4.0)
           (if (<= z 1.2e-261)
             (* x -3.0)
             (if (<= z 1.4e-152)
               (* 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 <= -6200000000.0) {
		tmp = t_0;
	} else if (z <= -7.5e-181) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (z <= -3.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -5e-253) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-261) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-152) {
		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 <= (-6200000000.0d0)) then
        tmp = t_0
    else if (z <= (-7.5d-181)) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else if (z <= (-3.8d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5d-253)) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-261) then
        tmp = x * (-3.0d0)
    else if (z <= 1.4d-152) 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 <= -6200000000.0) {
		tmp = t_0;
	} else if (z <= -7.5e-181) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (z <= -3.8e-233) {
		tmp = x * -3.0;
	} else if (z <= -5e-253) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-261) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-152) {
		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 <= -6200000000.0:
		tmp = t_0
	elif z <= -7.5e-181:
		tmp = y * (4.0 + (z * -6.0))
	elif z <= -3.8e-233:
		tmp = x * -3.0
	elif z <= -5e-253:
		tmp = y * 4.0
	elif z <= 1.2e-261:
		tmp = x * -3.0
	elif z <= 1.4e-152:
		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 <= -6200000000.0)
		tmp = t_0;
	elseif (z <= -7.5e-181)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	elseif (z <= -3.8e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -5e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-261)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.4e-152)
		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 <= -6200000000.0)
		tmp = t_0;
	elseif (z <= -7.5e-181)
		tmp = y * (4.0 + (z * -6.0));
	elseif (z <= -3.8e-233)
		tmp = x * -3.0;
	elseif (z <= -5e-253)
		tmp = y * 4.0;
	elseif (z <= 1.2e-261)
		tmp = x * -3.0;
	elseif (z <= 1.4e-152)
		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, -6200000000.0], t$95$0, If[LessEqual[z, -7.5e-181], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-261], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.4e-152], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2e9 or 0.5 < z

   1. Initial program 99.9%

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

      1. associate-*r* 99.8%

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

      2. metadata-eval 99.8%

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

      3. +-commutative 99.8%

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

      4. flip-+ 27.1%

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

      5. pow2 27.1%

         \[\leadsto \frac{\color{blue}{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) - x} \]

      6. metadata-eval 27.1%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) - x} \]

      7. associate-*r* 27.0%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} - x} \]

      8. fma-neg 27.0%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \frac{2}{3} - z, -x\right)}} \]

      9. metadata-eval 27.0%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \color{blue}{0.6666666666666666} - z, -x\right)} \]

   3. Applied egg-rr 27.0%

      \[\leadsto \color{blue}{\frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, 0.6666666666666666 - z, -x\right)}} \]

   4. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) - 4 \cdot \left(y - x\right)} \]
   5. Step-by-step derivation

      1. sub-neg 98.2%

         \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-4 \cdot \left(y - x\right)\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-\color{blue}{\left(y - x\right) \cdot 4}\right) \]

      3. associate-+r+ 98.2%

         \[\leadsto \color{blue}{\left(\left(8 \cdot \left(y - x\right) + -6 \cdot \left(z \cdot \left(y - x\right)\right)\right) + x\right)} + \left(-\left(y - x\right) \cdot 4\right) \]

      4. associate-*r* 98.1%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      5. *-commutative 98.1%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right)\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      6. distribute-rgt-out 99.8%

         \[\leadsto \left(\color{blue}{\left(y - x\right) \cdot \left(8 + z \cdot -6\right)} + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + \color{blue}{-6 \cdot z}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      8. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \color{blue}{\left(y - x\right) \cdot \left(-4\right)} \]

      9. metadata-eval 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot \color{blue}{-4} \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot -4} \]

   7. Taylor expanded in z around inf 97.7%

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

   if -6.2e9 < z < -7.5000000000000002e-181

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      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 58.7%

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

   if -7.5000000000000002e-181 < z < -3.8e-233 or -4.99999999999999971e-253 < z < 1.20000000000000007e-261 or 1.39999999999999992e-152 < z < 0.5

   1. Initial program 99.3%

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

   2. 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 64.2%

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

   4. Taylor expanded in z around 0 62.3%

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

      1. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if -3.8e-233 < z < -4.99999999999999971e-253 or 1.20000000000000007e-261 < z < 1.39999999999999992e-152

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 83.4%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. *-commutative 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-261}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 9: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.66)
   (+ x (* (- y x) (* z -6.0)))
   (if (<= z 0.54) (+ (* x -3.0) (* y 4.0)) (+ x (* z (* 6.0 (- x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.54) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.66d0)) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else if (z <= 0.54d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = x + (z * (6.0d0 * (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.54) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.66:
		tmp = x + ((y - x) * (z * -6.0))
	elif z <= 0.54:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = x + (z * (6.0 * (x - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.66)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	elseif (z <= 0.54)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.66)
		tmp = x + ((y - x) * (z * -6.0));
	elseif (z <= 0.54)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = x + (z * (6.0 * (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.66], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.54], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.3%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

   4. Simplified 99.3%

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

   if -0.660000000000000031 < z < 0.54000000000000004

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 98.5%

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

   3. Taylor expanded in x around 0 98.5%

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

   if 0.54000000000000004 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   4. Simplified 96.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]

Alternative 10: 76.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+39} \lor \neg \left(y \leq 1.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.85e+39) (not (<= y 1.2e-18)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (- (* z 6.0) 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e+39) || !(y <= 1.2e-18)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * ((z * 6.0) - 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 ((y <= (-1.85d+39)) .or. (.not. (y <= 1.2d-18))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((z * 6.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e+39) || !(y <= 1.2e-18)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * ((z * 6.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.85e+39) or not (y <= 1.2e-18):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * ((z * 6.0) - 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.85e+39) || !(y <= 1.2e-18))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.85e+39) || ~((y <= 1.2e-18)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * ((z * 6.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.85e+39], N[Not[LessEqual[y, 1.2e-18]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000006e39 or 1.19999999999999997e-18 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. fma-def 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -1.85000000000000006e39 < y < 1.19999999999999997e-18

   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 z around 0 99.0%

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

   3. Taylor expanded in x around inf 79.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+39} \lor \neg \left(y \leq 1.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \end{array} \]

Alternative 11: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.6)))
   (* -6.0 (* (- y x) z))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.6)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.58d0)) .or. (.not. (z <= 0.6d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.6)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.6):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.6))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.6)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.599999999999999978 < z

   1. Initial program 99.9%

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

      1. associate-*r* 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. +-commutative 99.7%

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

      4. flip-+ 27.7%

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

      5. pow2 27.7%

         \[\leadsto \frac{\color{blue}{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) - x} \]

      6. metadata-eval 27.7%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) - x} \]

      7. associate-*r* 27.6%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} - x} \]

      8. fma-neg 27.6%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \frac{2}{3} - z, -x\right)}} \]

      9. metadata-eval 27.6%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \color{blue}{0.6666666666666666} - z, -x\right)} \]

   3. Applied egg-rr 27.6%

      \[\leadsto \color{blue}{\frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, 0.6666666666666666 - z, -x\right)}} \]

   4. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) - 4 \cdot \left(y - x\right)} \]
   5. Step-by-step derivation

      1. sub-neg 98.2%

         \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-4 \cdot \left(y - x\right)\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-\color{blue}{\left(y - x\right) \cdot 4}\right) \]

      3. associate-+r+ 98.2%

         \[\leadsto \color{blue}{\left(\left(8 \cdot \left(y - x\right) + -6 \cdot \left(z \cdot \left(y - x\right)\right)\right) + x\right)} + \left(-\left(y - x\right) \cdot 4\right) \]

      4. associate-*r* 98.1%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      5. *-commutative 98.1%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right)\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      6. distribute-rgt-out 99.8%

         \[\leadsto \left(\color{blue}{\left(y - x\right) \cdot \left(8 + z \cdot -6\right)} + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      7. *-commutative 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + \color{blue}{-6 \cdot z}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      8. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \color{blue}{\left(y - x\right) \cdot \left(-4\right)} \]

      9. metadata-eval 99.8%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot \color{blue}{-4} \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot -4} \]

   7. Taylor expanded in z around inf 97.5%

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

   if -0.57999999999999996 < 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 98.5%

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

   3. Taylor expanded in x around 0 98.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.66)
   (+ x (* (- y x) (* z -6.0)))
   (if (<= z 0.6) (+ (* x -3.0) (* y 4.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.6) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.66d0)) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else if (z <= 0.6d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + ((y - x) * (z * -6.0));
	} else if (z <= 0.6) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.66:
		tmp = x + ((y - x) * (z * -6.0))
	elif z <= 0.6:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.66)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	elseif (z <= 0.6)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.66)
		tmp = x + ((y - x) * (z * -6.0));
	elseif (z <= 0.6)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.66], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.3%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

   4. Simplified 99.3%

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

   if -0.660000000000000031 < 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 98.5%

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

   3. Taylor expanded in x around 0 98.5%

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

   if 0.599999999999999978 < z

   1. Initial program 99.9%

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

      1. associate-*r* 99.6%

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

      2. metadata-eval 99.6%

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

      3. +-commutative 99.6%

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

      4. flip-+ 32.5%

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

      5. pow2 32.5%

         \[\leadsto \frac{\color{blue}{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) - x} \]

      6. metadata-eval 32.5%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\left(y - x\right) \cdot \left(6 \cdot \left(\color{blue}{\frac{2}{3}} - z\right)\right) - x} \]

      7. associate-*r* 32.4%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} - x} \]

      8. fma-neg 32.5%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \frac{2}{3} - z, -x\right)}} \]

      9. metadata-eval 32.5%

         \[\leadsto \frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, \color{blue}{0.6666666666666666} - z, -x\right)} \]

   3. Applied egg-rr 32.5%

      \[\leadsto \color{blue}{\frac{{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2} - x \cdot x}{\mathsf{fma}\left(\left(y - x\right) \cdot 6, 0.6666666666666666 - z, -x\right)}} \]

   4. Taylor expanded in z around inf 96.7%

      \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) - 4 \cdot \left(y - x\right)} \]
   5. Step-by-step derivation

      1. sub-neg 96.7%

         \[\leadsto \color{blue}{\left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-4 \cdot \left(y - x\right)\right)} \]

      2. *-commutative 96.7%

         \[\leadsto \left(8 \cdot \left(y - x\right) + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x\right)\right) + \left(-\color{blue}{\left(y - x\right) \cdot 4}\right) \]

      3. associate-+r+ 96.7%

         \[\leadsto \color{blue}{\left(\left(8 \cdot \left(y - x\right) + -6 \cdot \left(z \cdot \left(y - x\right)\right)\right) + x\right)} + \left(-\left(y - x\right) \cdot 4\right) \]

      4. associate-*r* 96.6%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      5. *-commutative 96.6%

         \[\leadsto \left(\left(8 \cdot \left(y - x\right) + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right)\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      6. distribute-rgt-out 99.7%

         \[\leadsto \left(\color{blue}{\left(y - x\right) \cdot \left(8 + z \cdot -6\right)} + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + \color{blue}{-6 \cdot z}\right) + x\right) + \left(-\left(y - x\right) \cdot 4\right) \]

      8. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \color{blue}{\left(y - x\right) \cdot \left(-4\right)} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot \color{blue}{-4} \]

   6. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(8 + -6 \cdot z\right) + x\right) + \left(y - x\right) \cdot -4} \]

   7. Taylor expanded in z around inf 95.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

2. Taylor expanded in z around 0 99.6%

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

   1. neg-mul-1 99.6%

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

   2. +-commutative 99.6%

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

   3. sub-neg 99.6%

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

4. Simplified 99.6%

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

5. Taylor expanded in z around 0 99.4%

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

   1. associate-*r* 99.4%

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

   2. distribute-rgt-out 99.8%

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

   3. metadata-eval 99.8%

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

   4. metadata-eval 99.8%

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

   5. associate-*r* 99.8%

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

   6. neg-mul-1 99.8%

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

   7. distribute-lft-in 99.8%

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

   8. sub-neg 99.8%

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

   9. *-commutative 99.8%

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

   10. associate-*l* 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 14: 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 99.6%

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

2. Taylor expanded in z around 0 99.6%

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

   1. neg-mul-1 99.6%

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

   2. +-commutative 99.6%

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

   3. sub-neg 99.6%

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

4. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 15: 99.7% 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 99.6%

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

   1. associate-*l* 99.8%

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

   2. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 16: 37.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e+85) (* x -3.0) (if (<= x 1.15e-32) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e+85) {
		tmp = x * -3.0;
	} else if (x <= 1.15e-32) {
		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 <= (-2.5d+85)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.15d-32) 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 <= -2.5e+85) {
		tmp = x * -3.0;
	} else if (x <= 1.15e-32) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e+85:
		tmp = x * -3.0
	elif x <= 1.15e-32:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e+85)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.15e-32)
		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 <= -2.5e+85)
		tmp = x * -3.0;
	elseif (x <= 1.15e-32)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e+85], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.15e-32], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e85 or 1.15e-32 < x

   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 99.1%

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

   3. Taylor expanded in x around inf 76.3%

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

   4. Taylor expanded in z around 0 38.7%

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

      1. *-commutative 38.7%

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

   6. Simplified 38.7%

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

   if -2.5e85 < x < 1.15e-32

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      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 74.2%

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

   5. Taylor expanded in z around 0 43.3%

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

      1. *-commutative 43.3%

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

   7. Simplified 43.3%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 17: 25.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

2. Taylor expanded in z around 0 99.4%

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

3. Taylor expanded in x around inf 51.5%

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

4. Taylor expanded in z around 0 26.2%

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

   1. *-commutative 26.2%

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

6. Simplified 26.2%

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

7. Final simplification 26.2%

   \[\leadsto x \cdot -3 \]

Alternative 18: 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 99.6%

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

2. Taylor expanded in y around inf 48.6%

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

3. Taylor expanded in x around inf 2.7%

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

4. Final simplification 2.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(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))))