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

Percentage Accurate: 99.5% → 99.8%

Time: 17.1s

Alternatives: 15

Speedup: 1.2×

• 20.8% 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, 0.9× speedup

Math

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

FPCore

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

C

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

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) * 4.0d0) - ((-6.0d0) * (z * (x - y))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -35:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.2e+212)
   (* -6.0 (* z y))
   (if (<= z -35.0)
     (* 6.0 (* x z))
     (if (<= z 1.45e-180)
       (* y 4.0)
       (if (<= z 0.5) (* x -3.0) (* y (* -6.0 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+212) {
		tmp = -6.0 * (z * y);
	} else if (z <= -35.0) {
		tmp = 6.0 * (x * z);
	} else if (z <= 1.45e-180) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = y * (-6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.2d+212)) then
        tmp = (-6.0d0) * (z * y)
    else if (z <= (-35.0d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= 1.45d-180) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = y * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+212) {
		tmp = -6.0 * (z * y);
	} else if (z <= -35.0) {
		tmp = 6.0 * (x * z);
	} else if (z <= 1.45e-180) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = y * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.2e+212:
		tmp = -6.0 * (z * y)
	elif z <= -35.0:
		tmp = 6.0 * (x * z)
	elif z <= 1.45e-180:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = y * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.2e+212)
		tmp = Float64(-6.0 * Float64(z * y));
	elseif (z <= -35.0)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= 1.45e-180)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.2e+212)
		tmp = -6.0 * (z * y);
	elseif (z <= -35.0)
		tmp = 6.0 * (x * z);
	elseif (z <= 1.45e-180)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = y * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.2e+212], N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -35.0], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-180], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.1999999999999997e212

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. *-commutative 65.7%

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

   8. Simplified 65.7%

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

   9. Taylor expanded in z around inf 65.8%

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

       1. *-commutative 65.8%

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

   11. Simplified 65.8%

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

   if -5.1999999999999997e212 < z < -35

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 64.0%

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

   6. Taylor expanded in z around inf 62.5%

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

   if -35 < z < 1.4499999999999999e-180

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in z around 0 60.4%

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

       1. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if 1.4499999999999999e-180 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 53.9%

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

      1. *-lft-identity 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 54.0%

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

      4. sub-neg 54.0%

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

      5. distribute-rgt-in 54.0%

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

      6. metadata-eval 54.0%

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

      7. neg-mul-1 54.0%

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

      8. associate-*r* 54.0%

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

      9. *-commutative 54.0%

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

      10. metadata-eval 54.0%

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

      11. distribute-lft-in 54.0%

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

      12. distribute-rgt-in 54.0%

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

      13. distribute-lft-in 54.0%

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

      14. metadata-eval 54.0%

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

      15. associate-+r+ 54.0%

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

      16. metadata-eval 54.0%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 54.0%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 87.5%

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

   6. Taylor expanded in z around inf 90.1%

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

   7. Taylor expanded in x around 0 57.4%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -35:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+212}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.15:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -1.15e+212)
     t_0
     (if (<= z -1.15)
       (* 6.0 (* x z))
       (if (<= z 5.5e-178) (* 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 * (z * y);
	double tmp;
	if (z <= -1.15e+212) {
		tmp = t_0;
	} else if (z <= -1.15) {
		tmp = 6.0 * (x * z);
	} else if (z <= 5.5e-178) {
		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) * (z * y)
    if (z <= (-1.15d+212)) then
        tmp = t_0
    else if (z <= (-1.15d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= 5.5d-178) 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 * (z * y);
	double tmp;
	if (z <= -1.15e+212) {
		tmp = t_0;
	} else if (z <= -1.15) {
		tmp = 6.0 * (x * z);
	} else if (z <= 5.5e-178) {
		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 * (z * y)
	tmp = 0
	if z <= -1.15e+212:
		tmp = t_0
	elif z <= -1.15:
		tmp = 6.0 * (x * z)
	elif z <= 5.5e-178:
		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(z * y))
	tmp = 0.0
	if (z <= -1.15e+212)
		tmp = t_0;
	elseif (z <= -1.15)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= 5.5e-178)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -1.15e+212)
		tmp = t_0;
	elseif (z <= -1.15)
		tmp = 6.0 * (x * z);
	elseif (z <= 5.5e-178)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+212], t$95$0, If[LessEqual[z, -1.15], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-178], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1499999999999999e212 or 0.619999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   9. Taylor expanded in z around inf 59.6%

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

       1. *-commutative 59.6%

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

   11. Simplified 59.6%

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

   if -1.1499999999999999e212 < z < -1.1499999999999999

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 64.0%

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

   6. Taylor expanded in z around inf 62.5%

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

   if -1.1499999999999999 < z < 5.50000000000000028e-178

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in z around 0 60.4%

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

       1. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if 5.50000000000000028e-178 < z < 0.619999999999999996

   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-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 53.9%

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

      1. *-lft-identity 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 54.0%

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

      4. sub-neg 54.0%

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

      5. distribute-rgt-in 54.0%

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

      6. metadata-eval 54.0%

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

      7. neg-mul-1 54.0%

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

      8. associate-*r* 54.0%

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

      9. *-commutative 54.0%

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

      10. metadata-eval 54.0%

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

      11. distribute-lft-in 54.0%

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

      12. distribute-rgt-in 54.0%

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

      13. distribute-lft-in 54.0%

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

      14. metadata-eval 54.0%

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

      15. associate-+r+ 54.0%

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

      16. metadata-eval 54.0%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 54.0%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

Alternative 4: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.43:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 11:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.43)
     t_0
     (if (<= z 1.18e-182)
       (* y 4.0)
       (if (<= z 11.0) (* x (+ -3.0 (* z 6.0))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.43) {
		tmp = t_0;
	} else if (z <= 1.18e-182) {
		tmp = y * 4.0;
	} else if (z <= 11.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * (y - x))
    if (z <= (-0.43d0)) then
        tmp = t_0
    else if (z <= 1.18d-182) then
        tmp = y * 4.0d0
    else if (z <= 11.0d0) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.43) {
		tmp = t_0;
	} else if (z <= 1.18e-182) {
		tmp = y * 4.0;
	} else if (z <= 11.0) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.43:
		tmp = t_0
	elif z <= 1.18e-182:
		tmp = y * 4.0
	elif z <= 11.0:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.43)
		tmp = t_0;
	elseif (z <= 1.18e-182)
		tmp = Float64(y * 4.0);
	elseif (z <= 11.0)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.43)
		tmp = t_0;
	elseif (z <= 1.18e-182)
		tmp = y * 4.0;
	elseif (z <= 11.0)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.43], t$95$0, If[LessEqual[z, 1.18e-182], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 11.0], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.429999999999999993 or 11 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.0%

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

   6. Taylor expanded in z around inf 98.0%

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

   if -0.429999999999999993 < z < 1.17999999999999997e-182

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in z around 0 60.4%

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

       1. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if 1.17999999999999997e-182 < z < 11

   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-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 53.9%

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

      1. *-lft-identity 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 54.0%

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

      4. sub-neg 54.0%

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

      5. distribute-rgt-in 54.0%

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

      6. metadata-eval 54.0%

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

      7. neg-mul-1 54.0%

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

      8. associate-*r* 54.0%

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

      9. *-commutative 54.0%

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

      10. metadata-eval 54.0%

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

      11. distribute-lft-in 54.0%

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

      12. distribute-rgt-in 54.0%

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

      13. distribute-lft-in 54.0%

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

      14. metadata-eval 54.0%

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

      15. associate-+r+ 54.0%

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

      16. metadata-eval 54.0%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 54.0%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 54.0%

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

   7. Simplified 54.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.43:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 11:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.43:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-179}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.43)
     t_0
     (if (<= z 3.05e-179) (* 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 * (z * (y - x));
	double tmp;
	if (z <= -0.43) {
		tmp = t_0;
	} else if (z <= 3.05e-179) {
		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) * (z * (y - x))
    if (z <= (-0.43d0)) then
        tmp = t_0
    else if (z <= 3.05d-179) 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 * (z * (y - x));
	double tmp;
	if (z <= -0.43) {
		tmp = t_0;
	} else if (z <= 3.05e-179) {
		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 * (z * (y - x))
	tmp = 0
	if z <= -0.43:
		tmp = t_0
	elif z <= 3.05e-179:
		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(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.43)
		tmp = t_0;
	elseif (z <= 3.05e-179)
		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 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.43)
		tmp = t_0;
	elseif (z <= 3.05e-179)
		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[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.43], t$95$0, If[LessEqual[z, 3.05e-179], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.429999999999999993 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.0%

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

   6. Taylor expanded in z around inf 98.0%

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

   if -0.429999999999999993 < z < 3.04999999999999998e-179

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in z around 0 60.4%

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

       1. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if 3.04999999999999998e-179 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 53.9%

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

      1. *-lft-identity 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 54.0%

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

      4. sub-neg 54.0%

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

      5. distribute-rgt-in 54.0%

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

      6. metadata-eval 54.0%

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

      7. neg-mul-1 54.0%

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

      8. associate-*r* 54.0%

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

      9. *-commutative 54.0%

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

      10. metadata-eval 54.0%

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

      11. distribute-lft-in 54.0%

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

      12. distribute-rgt-in 54.0%

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

      13. distribute-lft-in 54.0%

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

      14. metadata-eval 54.0%

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

      15. associate-+r+ 54.0%

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

      16. metadata-eval 54.0%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 54.0%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

Alternative 6: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-179}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -0.66)
     t_0
     (if (<= z 1.8e-179) (* 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 * (z * y);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= 1.8e-179) {
		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) * (z * y)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= 1.8d-179) 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 * (z * y);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= 1.8e-179) {
		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 * (z * y)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= 1.8e-179:
		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(z * y))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= 1.8e-179)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= 1.8e-179)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, 1.8e-179], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in y around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. *-commutative 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in z around inf 51.7%

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

       1. *-commutative 51.7%

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

   11. Simplified 51.7%

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

   if -0.660000000000000031 < z < 1.80000000000000004e-179

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in z around 0 60.4%

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

       1. *-commutative 60.4%

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

   11. Simplified 60.4%

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

   if 1.80000000000000004e-179 < z < 0.5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 53.9%

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

      1. *-lft-identity 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*r* 54.0%

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

      4. sub-neg 54.0%

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

      5. distribute-rgt-in 54.0%

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

      6. metadata-eval 54.0%

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

      7. neg-mul-1 54.0%

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

      8. associate-*r* 54.0%

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

      9. *-commutative 54.0%

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

      10. metadata-eval 54.0%

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

      11. distribute-lft-in 54.0%

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

      12. distribute-rgt-in 54.0%

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

      13. distribute-lft-in 54.0%

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

      14. metadata-eval 54.0%

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

      15. associate-+r+ 54.0%

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

      16. metadata-eval 54.0%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 54.0%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   10. Simplified 52.6%

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

Alternative 7: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot 6\right) \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.66)
   (+ x (* z (* 6.0 (- x y))))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (+ x (* (* z 6.0) (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + (z * (6.0 * (x - y)));
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + ((z * 6.0) * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.66d0)) then
        tmp = x + (z * (6.0d0 * (x - y)))
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + ((z * 6.0d0) * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.66) {
		tmp = x + (z * (6.0 * (x - y)));
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + ((z * 6.0) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.66:
		tmp = x + (z * (6.0 * (x - y)))
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + ((z * 6.0) * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.66)
		tmp = Float64(x + Float64(z * Float64(6.0 * Float64(x - y))));
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(Float64(z * 6.0) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.66)
		tmp = x + (z * (6.0 * (x - y)));
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + ((z * 6.0) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.66], N[(x + N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * 6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.5%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.5%

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

   if -0.660000000000000031 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 96.3%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.6%

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

      1. neg-mul-1 97.6%

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

   7. Simplified 97.6%

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

      1. add-sqr-sqrt 54.4%

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

      2. fma-define 54.4%

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

      3. distribute-rgt-neg-out 54.4%

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

      4. add-sqr-sqrt 54.3%

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

      5. sqrt-unprod 43.8%

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

      6. sqr-neg 43.8%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.3%

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

      9. *-commutative 0.3%

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

      10. *-commutative 0.3%

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

      11. fmm-def 0.3%

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

      12. add-sqr-sqrt 0.5%

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

      13. associate-*l* 0.5%

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

      14. add-sqr-sqrt 0.0%

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

      15. sqrt-unprod 77.9%

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

      16. sqr-neg 77.9%

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

      17. sqrt-unprod 97.4%

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

      18. add-sqr-sqrt 97.6%

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

      19. *-commutative 97.6%

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

   9. Applied egg-rr 97.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot 6\right) \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.4%

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

   6. Taylor expanded in z around inf 98.5%

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

   if -0.599999999999999978 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 96.3%

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

   if 0.660000000000000031 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.6%

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

      1. neg-mul-1 97.6%

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

   7. Simplified 97.6%

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

      1. add-sqr-sqrt 54.4%

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

      2. fma-define 54.4%

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

      3. distribute-rgt-neg-out 54.4%

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

      4. add-sqr-sqrt 54.3%

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

      5. sqrt-unprod 43.8%

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

      6. sqr-neg 43.8%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.3%

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

      9. *-commutative 0.3%

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

      10. *-commutative 0.3%

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

      11. fmm-def 0.3%

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

      12. add-sqr-sqrt 0.5%

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

      13. associate-*l* 0.5%

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

      14. add-sqr-sqrt 0.0%

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

      15. sqrt-unprod 77.9%

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

      16. sqr-neg 77.9%

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

      17. sqrt-unprod 97.4%

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

      18. add-sqr-sqrt 97.6%

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

      19. *-commutative 97.6%

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

   9. Applied egg-rr 97.6%

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

4. Final simplification 97.2%

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

Alternative 9: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.58) t_0 (if (<= z 0.66) (+ x (* (- y x) 4.0)) (+ x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + 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) * (z * (y - x))
    if (z <= (-0.58d0)) then
        tmp = t_0
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.58:
		tmp = t_0
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.58], t$95$0, If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.4%

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

   6. Taylor expanded in z around inf 98.5%

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

   if -0.57999999999999996 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 96.3%

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

   if 0.660000000000000031 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 97.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.65)))
   (* -6.0 (* z (- y x)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.65)) {
		tmp = -6.0 * (z * (y - x));
	} 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 <= (-0.6d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    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 <= -0.6) || !(z <= 0.65)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.65):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	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 <= -0.6) || ~((z <= 0.65)))
		tmp = -6.0 * (z * (y - x));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.650000000000000022 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 98.0%

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

   6. Taylor expanded in z around inf 98.0%

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

   if -0.599999999999999978 < 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. Step-by-step derivation

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 96.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-52} \lor \neg \left(y \leq 1.82 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e-52) (not (<= y 1.82e-34)))
   (* y (+ 4.0 (* -6.0 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e-52) || !(y <= 1.82e-34)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (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 ((y <= (-5.5d-52)) .or. (.not. (y <= 1.82d-34))) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e-52) || !(y <= 1.82e-34)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e-52) or not (y <= 1.82e-34):
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e-52) || !(y <= 1.82e-34))
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e-52) || ~((y <= 1.82e-34)))
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e-52], N[Not[LessEqual[y, 1.82e-34]], $MachinePrecision]], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e-52 or 1.82000000000000009e-34 < y

   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-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 83.1%

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

   if -5.5e-52 < y < 1.82000000000000009e-34

   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* 98.9%

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

      3. fma-define 98.9%

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

      4. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around 0 78.8%

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

      1. *-lft-identity 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 78.1%

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

      4. sub-neg 78.1%

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

      5. distribute-rgt-in 78.1%

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

      6. metadata-eval 78.1%

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

      7. neg-mul-1 78.1%

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

      8. associate-*r* 78.1%

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

      9. *-commutative 78.1%

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

      10. metadata-eval 78.1%

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

      11. distribute-lft-in 78.1%

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

      12. distribute-rgt-in 78.1%

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

      13. distribute-lft-in 78.1%

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

      14. metadata-eval 78.1%

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

      15. associate-+r+ 78.1%

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

      16. metadata-eval 78.1%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 78.1%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-52} \lor \neg \left(y \leq 1.82 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-16} \lor \neg \left(y \leq 2.55 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e-16) (not (<= y 2.55e-35))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e-16) || !(y <= 2.55e-35)) {
		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 ((y <= (-2.1d-16)) .or. (.not. (y <= 2.55d-35))) 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 ((y <= -2.1e-16) || !(y <= 2.55e-35)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e-16) or not (y <= 2.55e-35):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e-16) || !(y <= 2.55e-35))
		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 ((y <= -2.1e-16) || ~((y <= 2.55e-35)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e-16], N[Not[LessEqual[y, 2.55e-35]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e-16 or 2.54999999999999993e-35 < y

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around inf 84.0%

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

      1. +-commutative 84.0%

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

      2. *-commutative 84.0%

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

   8. Simplified 84.0%

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

   9. Taylor expanded in z around 0 42.1%

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

       1. *-commutative 42.1%

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

   11. Simplified 42.1%

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

   if -2.1000000000000001e-16 < y < 2.54999999999999993e-35

   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* 98.9%

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

      3. fma-define 98.9%

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

      4. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in y around 0 77.4%

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

      1. *-lft-identity 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 76.7%

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

      4. sub-neg 76.7%

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

      5. distribute-rgt-in 76.7%

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

      6. metadata-eval 76.7%

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

      7. neg-mul-1 76.7%

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

      8. associate-*r* 76.7%

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

      9. *-commutative 76.7%

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

      10. metadata-eval 76.7%

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

      11. distribute-lft-in 76.7%

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

      12. distribute-rgt-in 76.7%

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

      13. distribute-lft-in 76.7%

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

      14. metadata-eval 76.7%

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

      15. associate-+r+ 76.7%

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

      16. metadata-eval 76.7%

          \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      17. associate-*r* 76.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      18. metadata-eval 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in z around 0 39.4%

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

      1. *-commutative 39.4%

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

   10. Simplified 39.4%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-16} \lor \neg \left(y \leq 2.55 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

Alternative 14: 26.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. 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* 99.4%

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

   3. fma-define 99.4%

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

   4. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in y around 0 48.1%

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

   1. *-lft-identity 48.1%

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

   2. *-commutative 48.1%

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

   3. associate-*r* 48.2%

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

   4. sub-neg 48.2%

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

   5. distribute-rgt-in 48.2%

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

   6. metadata-eval 48.2%

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

   7. neg-mul-1 48.2%

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

   8. associate-*r* 48.2%

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

   9. *-commutative 48.2%

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

   10. metadata-eval 48.2%

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

   11. distribute-lft-in 48.2%

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

   12. distribute-rgt-in 48.2%

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

   13. distribute-lft-in 48.2%

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

   14. metadata-eval 48.2%

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

   15. associate-+r+ 48.2%

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

   16. metadata-eval 48.2%

       \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   17. associate-*r* 48.2%

       \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

   18. metadata-eval 48.2%

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

7. Simplified 48.2%

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

8. Taylor expanded in z around 0 23.1%

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

   1. *-commutative 23.1%

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

10. Simplified 23.1%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 15: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around inf 51.2%

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

6. Taylor expanded in z around 0 2.4%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(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))))