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

Percentage Accurate: 99.5% → 99.8%

Time: 10.2s

Alternatives: 14

Speedup: 1.2×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   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: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.04 \cdot 10^{+93}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1700:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.04e+93)
     (* 6.0 (* x z))
     (if (<= z -1700.0)
       t_0
       (if (<= z -2.75e-186)
         (* x -3.0)
         (if (<= z -5.5e-207) (* y 4.0) (if (<= z 0.55) (* 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 <= -1.04e+93) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1700.0) {
		tmp = t_0;
	} else if (z <= -2.75e-186) {
		tmp = x * -3.0;
	} else if (z <= -5.5e-207) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		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 <= (-1.04d+93)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1700.0d0)) then
        tmp = t_0
    else if (z <= (-2.75d-186)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.5d-207)) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) 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 <= -1.04e+93) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1700.0) {
		tmp = t_0;
	} else if (z <= -2.75e-186) {
		tmp = x * -3.0;
	} else if (z <= -5.5e-207) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		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 <= -1.04e+93:
		tmp = 6.0 * (x * z)
	elif z <= -1700.0:
		tmp = t_0
	elif z <= -2.75e-186:
		tmp = x * -3.0
	elif z <= -5.5e-207:
		tmp = y * 4.0
	elif z <= 0.55:
		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 <= -1.04e+93)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1700.0)
		tmp = t_0;
	elseif (z <= -2.75e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.5e-207)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		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 <= -1.04e+93)
		tmp = 6.0 * (x * z);
	elseif (z <= -1700.0)
		tmp = t_0;
	elseif (z <= -2.75e-186)
		tmp = x * -3.0;
	elseif (z <= -5.5e-207)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		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, -1.04e+93], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1700.0], t$95$0, If[LessEqual[z, -2.75e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.5e-207], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.04e93

   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. associate-*r* 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r* 99.8%

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

      7. fma-def 99.8%

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

      8. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 59.2%

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

   if -1.04e93 < z < -1700 or 0.55000000000000004 < z

   1. Initial program 99.6%

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

      1. +-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* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 58.4%

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

   5. Taylor expanded in z around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if -1700 < z < -2.7500000000000001e-186 or -5.4999999999999997e-207 < z < 0.55000000000000004

   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 96.7%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. distribute-lft1-in 59.2%

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

      2. metadata-eval 59.2%

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

      3. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if -2.7500000000000001e-186 < z < -5.4999999999999997e-207

   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 85.8%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+93}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1700:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 3: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1300:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -6.6e+93)
     (* x (* z 6.0))
     (if (<= z -1300.0)
       t_0
       (if (<= z -2.8e-188)
         (* x -3.0)
         (if (<= z -1.6e-206) (* 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 * z);
	double tmp;
	if (z <= -6.6e+93) {
		tmp = x * (z * 6.0);
	} else if (z <= -1300.0) {
		tmp = t_0;
	} else if (z <= -2.8e-188) {
		tmp = x * -3.0;
	} else if (z <= -1.6e-206) {
		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 * z)
    if (z <= (-6.6d+93)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-1300.0d0)) then
        tmp = t_0
    else if (z <= (-2.8d-188)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.6d-206)) 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 * z);
	double tmp;
	if (z <= -6.6e+93) {
		tmp = x * (z * 6.0);
	} else if (z <= -1300.0) {
		tmp = t_0;
	} else if (z <= -2.8e-188) {
		tmp = x * -3.0;
	} else if (z <= -1.6e-206) {
		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 * z)
	tmp = 0
	if z <= -6.6e+93:
		tmp = x * (z * 6.0)
	elif z <= -1300.0:
		tmp = t_0
	elif z <= -2.8e-188:
		tmp = x * -3.0
	elif z <= -1.6e-206:
		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(y * z))
	tmp = 0.0
	if (z <= -6.6e+93)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -1300.0)
		tmp = t_0;
	elseif (z <= -2.8e-188)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.6e-206)
		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 * z);
	tmp = 0.0;
	if (z <= -6.6e+93)
		tmp = x * (z * 6.0);
	elseif (z <= -1300.0)
		tmp = t_0;
	elseif (z <= -2.8e-188)
		tmp = x * -3.0;
	elseif (z <= -1.6e-206)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+93], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1300.0], t$95$0, If[LessEqual[z, -2.8e-188], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.6e-206], 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 < -6.60000000000000017e93

   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. associate-*r* 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r* 99.8%

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

      7. fma-def 99.8%

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

      8. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 59.2%

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

      1. associate-*r* 59.2%

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

      2. *-commutative 59.2%

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

      3. *-commutative 59.2%

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

   7. Simplified 59.2%

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

   if -6.60000000000000017e93 < z < -1300 or 0.5 < z

   1. Initial program 99.6%

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

      1. +-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* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 58.4%

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

   5. Taylor expanded in z around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if -1300 < z < -2.8000000000000001e-188 or -1.59999999999999988e-206 < 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 96.7%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. distribute-lft1-in 59.2%

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

      2. metadata-eval 59.2%

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

      3. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if -2.8000000000000001e-188 < z < -1.59999999999999988e-206

   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 85.8%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1300:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1300:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+91)
   (* x (* z 6.0))
   (if (<= z -1300.0)
     (* -6.0 (* y z))
     (if (<= z -1.95e-188)
       (* x -3.0)
       (if (<= z -1.2e-206)
         (* y 4.0)
         (if (<= z 0.65) (* x -3.0) (* y (* z -6.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+91) {
		tmp = x * (z * 6.0);
	} else if (z <= -1300.0) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.95e-188) {
		tmp = x * -3.0;
	} else if (z <= -1.2e-206) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9d+91)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-1300.0d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-1.95d-188)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.2d-206)) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    else
        tmp = y * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+91) {
		tmp = x * (z * 6.0);
	} else if (z <= -1300.0) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.95e-188) {
		tmp = x * -3.0;
	} else if (z <= -1.2e-206) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+91:
		tmp = x * (z * 6.0)
	elif z <= -1300.0:
		tmp = -6.0 * (y * z)
	elif z <= -1.95e-188:
		tmp = x * -3.0
	elif z <= -1.2e-206:
		tmp = y * 4.0
	elif z <= 0.65:
		tmp = x * -3.0
	else:
		tmp = y * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+91)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -1300.0)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -1.95e-188)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.2e-206)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+91)
		tmp = x * (z * 6.0);
	elseif (z <= -1300.0)
		tmp = -6.0 * (y * z);
	elseif (z <= -1.95e-188)
		tmp = x * -3.0;
	elseif (z <= -1.2e-206)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	else
		tmp = y * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+91], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1300.0], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-188], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.2e-206], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9e91

   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. associate-*r* 99.9%

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

      2. metadata-eval 99.9%

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

      3. +-commutative 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*r* 99.8%

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

      7. fma-def 99.8%

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

      8. metadata-eval 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in y around 0 59.2%

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

      1. associate-*r* 59.2%

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

      2. *-commutative 59.2%

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

      3. *-commutative 59.2%

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

   7. Simplified 59.2%

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

   if -9e91 < z < -1300

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.6%

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

      3. fma-def 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-lft-in 99.6%

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

      7. neg-mul-1 99.6%

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

      8. associate-*r* 99.6%

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

      9. *-commutative 99.6%

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

      10. fma-def 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 71.8%

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

   5. Taylor expanded in z around inf 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   if -1300 < z < -1.94999999999999988e-188 or -1.2e-206 < z < 0.650000000000000022

   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 96.7%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. distribute-lft1-in 59.2%

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

      2. metadata-eval 59.2%

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

      3. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if -1.94999999999999988e-188 < z < -1.2e-206

   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 85.8%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

   if 0.650000000000000022 < z

   1. Initial program 99.6%

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

      1. +-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* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 56.1%

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

   5. Taylor expanded in z around inf 55.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1300:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 5: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.00062:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.00062)
     t_0
     (if (<= z -3.7e-188)
       (* x -3.0)
       (if (<= z -6.6e-207) (* 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 <= -0.00062) {
		tmp = t_0;
	} else if (z <= -3.7e-188) {
		tmp = x * -3.0;
	} else if (z <= -6.6e-207) {
		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 <= (-0.00062d0)) then
        tmp = t_0
    else if (z <= (-3.7d-188)) then
        tmp = x * (-3.0d0)
    else if (z <= (-6.6d-207)) 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 <= -0.00062) {
		tmp = t_0;
	} else if (z <= -3.7e-188) {
		tmp = x * -3.0;
	} else if (z <= -6.6e-207) {
		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 <= -0.00062:
		tmp = t_0
	elif z <= -3.7e-188:
		tmp = x * -3.0
	elif z <= -6.6e-207:
		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 <= -0.00062)
		tmp = t_0;
	elseif (z <= -3.7e-188)
		tmp = Float64(x * -3.0);
	elseif (z <= -6.6e-207)
		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 <= -0.00062)
		tmp = t_0;
	elseif (z <= -3.7e-188)
		tmp = x * -3.0;
	elseif (z <= -6.6e-207)
		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, -0.00062], t$95$0, If[LessEqual[z, -3.7e-188], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -6.6e-207], 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 < -6.2e-4 or 0.5 < z

   1. Initial program 99.6%

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

      1. 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. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-*r* 99.7%

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

      7. fma-def 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 95.9%

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

   if -6.2e-4 < z < -3.69999999999999972e-188 or -6.5999999999999996e-207 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 98.7%

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

   3. Taylor expanded in y around 0 60.4%

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

      1. distribute-lft1-in 60.4%

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

      2. metadata-eval 60.4%

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

      3. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if -3.69999999999999972e-188 < z < -6.5999999999999996e-207

   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 85.8%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00062:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 260000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -3000000.0)
     t_1
     (if (<= z -1.6e-187)
       t_0
       (if (<= z -1.3e-206) (* y 4.0) (if (<= z 260000000.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3000000.0) {
		tmp = t_1;
	} else if (z <= -1.6e-187) {
		tmp = t_0;
	} else if (z <= -1.3e-206) {
		tmp = y * 4.0;
	} else if (z <= 260000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-3000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.6d-187)) then
        tmp = t_0
    else if (z <= (-1.3d-206)) then
        tmp = y * 4.0d0
    else if (z <= 260000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3000000.0) {
		tmp = t_1;
	} else if (z <= -1.6e-187) {
		tmp = t_0;
	} else if (z <= -1.3e-206) {
		tmp = y * 4.0;
	} else if (z <= 260000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -3000000.0:
		tmp = t_1
	elif z <= -1.6e-187:
		tmp = t_0
	elif z <= -1.3e-206:
		tmp = y * 4.0
	elif z <= 260000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -3000000.0)
		tmp = t_1;
	elseif (z <= -1.6e-187)
		tmp = t_0;
	elseif (z <= -1.3e-206)
		tmp = Float64(y * 4.0);
	elseif (z <= 260000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -3000000.0)
		tmp = t_1;
	elseif (z <= -1.6e-187)
		tmp = t_0;
	elseif (z <= -1.3e-206)
		tmp = y * 4.0;
	elseif (z <= 260000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3000000.0], t$95$1, If[LessEqual[z, -1.6e-187], t$95$0, If[LessEqual[z, -1.3e-206], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 260000000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e6 or 2.6e8 < z

   1. Initial program 99.7%

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

      1. 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. metadata-eval 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.7%

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

      7. fma-def 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 99.2%

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

   if -3e6 < z < -1.5999999999999999e-187 or -1.3e-206 < z < 2.6e8

   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 y around 0 62.3%

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

   3. Taylor expanded in z around 0 62.6%

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

      1. +-commutative 62.6%

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

      2. distribute-lft1-in 62.6%

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

      3. metadata-eval 62.6%

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

      4. associate-*r* 62.6%

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

      5. distribute-rgt-out 62.6%

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

      6. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if -1.5999999999999999e-187 < z < -1.3e-206

   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 85.8%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 260000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1300:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1300.0)
     t_0
     (if (<= z -2.7e-188)
       (* x -3.0)
       (if (<= z -1.3e-206) (* y 4.0) (if (<= z 0.62) (* 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 <= -1300.0) {
		tmp = t_0;
	} else if (z <= -2.7e-188) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-206) {
		tmp = y * 4.0;
	} else if (z <= 0.62) {
		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 <= (-1300.0d0)) then
        tmp = t_0
    else if (z <= (-2.7d-188)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.3d-206)) then
        tmp = y * 4.0d0
    else if (z <= 0.62d0) 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 <= -1300.0) {
		tmp = t_0;
	} else if (z <= -2.7e-188) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-206) {
		tmp = y * 4.0;
	} else if (z <= 0.62) {
		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 <= -1300.0:
		tmp = t_0
	elif z <= -2.7e-188:
		tmp = x * -3.0
	elif z <= -1.3e-206:
		tmp = y * 4.0
	elif z <= 0.62:
		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 <= -1300.0)
		tmp = t_0;
	elseif (z <= -2.7e-188)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.3e-206)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.62)
		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 <= -1300.0)
		tmp = t_0;
	elseif (z <= -2.7e-188)
		tmp = x * -3.0;
	elseif (z <= -1.3e-206)
		tmp = y * 4.0;
	elseif (z <= 0.62)
		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, -1300.0], t$95$0, If[LessEqual[z, -2.7e-188], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.3e-206], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1300 or 0.619999999999999996 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-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 54.1%

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

   5. Taylor expanded in z around inf 53.7%

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

      1. *-commutative 53.7%

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

   7. Simplified 53.7%

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

   if -1300 < z < -2.7000000000000001e-188 or -1.3e-206 < z < 0.619999999999999996

   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 96.7%

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

   3. Taylor expanded in y around 0 59.2%

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

      1. distribute-lft1-in 59.2%

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

      2. metadata-eval 59.2%

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

      3. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if -2.7000000000000001e-188 < z < -1.3e-206

   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 85.8%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-188}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-206}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 75.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-34} \lor \neg \left(x \leq 2.9 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-34) (not (<= x 2.9e+24)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-34) || !(x <= 2.9e+24)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7d-34)) .or. (.not. (x <= 2.9d+24))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7e-34) || !(x <= 2.9e+24)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7e-34) or not (x <= 2.9e+24):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7e-34) || !(x <= 2.9e+24))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7e-34) || ~((x <= 2.9e+24)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7e-34], N[Not[LessEqual[x, 2.9e+24]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7e-34 or 2.89999999999999979e24 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 84.3%

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

   3. Taylor expanded in z around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. distribute-lft1-in 84.5%

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

      3. metadata-eval 84.5%

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

      4. associate-*r* 84.5%

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

      5. distribute-rgt-out 84.5%

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

      6. *-commutative 84.5%

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

   5. Simplified 84.5%

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

   if -7e-34 < x < 2.89999999999999979e24

   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 80.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-34} \lor \neg \left(x \leq 2.9 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.65)))
   (* (- y x) (* z -6.0))
   (+ x (* (- y x) 4.0))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.56d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.56) or not (z <= 0.65):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.56], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.650000000000000022 < z

   1. Initial program 99.6%

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

      1. 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. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-*r* 99.7%

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

      7. fma-def 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 97.1%

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

      1. associate-*r* 97.2%

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

      2. *-commutative 97.2%

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

      3. *-commutative 97.2%

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

      4. *-commutative 97.2%

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

   6. Simplified 97.2%

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

   if -0.56000000000000005 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 97.6%

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

4. Final simplification 97.4%

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

Alternative 10: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.5%

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

   1. neg-mul-1 99.5%

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

   2. +-commutative 99.5%

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

   3. sub-neg 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 11: 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 99.5%

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

   1. associate-*l* 99.8%

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

   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 12: 38.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 0.000225:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.7e-35) (* x -3.0) (if (<= x 0.000225) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.7e-35) {
		tmp = x * -3.0;
	} else if (x <= 0.000225) {
		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 <= (-4.7d-35)) then
        tmp = x * (-3.0d0)
    else if (x <= 0.000225d0) 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 <= -4.7e-35) {
		tmp = x * -3.0;
	} else if (x <= 0.000225) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.7e-35:
		tmp = x * -3.0
	elif x <= 0.000225:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.7e-35)
		tmp = Float64(x * -3.0);
	elseif (x <= 0.000225)
		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 <= -4.7e-35)
		tmp = x * -3.0;
	elseif (x <= 0.000225)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.7e-35], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 0.000225], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7e-35 or 2.2499999999999999e-4 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 54.1%

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

   3. Taylor expanded in y around 0 45.1%

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

      1. distribute-lft1-in 45.1%

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

      2. metadata-eval 45.1%

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

      3. *-commutative 45.1%

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

   5. Simplified 45.1%

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

   if -4.7e-35 < x < 2.2499999999999999e-4

   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 81.3%

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

   5. Taylor expanded in z around 0 34.9%

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

      1. *-commutative 34.9%

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

   7. Simplified 34.9%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 0.000225:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 13: 26.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 48.5%

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

3. Taylor expanded in y around 0 28.9%

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

   1. distribute-lft1-in 28.9%

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

   2. metadata-eval 28.9%

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

   3. *-commutative 28.9%

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

5. Simplified 28.9%

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

6. Final simplification 28.9%

   \[\leadsto x \cdot -3 \]

Alternative 14: 2.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around inf 51.5%

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

3. Taylor expanded in z around 0 2.7%

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

4. Final simplification 2.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023187 
(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))))