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

Percentage Accurate: 99.5% → 99.7%

Time: 10.2s

Alternatives: 14

Speedup: 1.2×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * (y - x)) + (x + ((-6.0d0) * ((y - x) * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

2. Taylor expanded in z around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-192}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-217}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.75e+123)
     t_0
     (if (<= z -4.5e+42)
       t_1
       (if (<= z -3.5e+16)
         t_0
         (if (<= z -3.6e-142)
           (* 4.0 y)
           (if (<= z -5.8e-192)
             (* x -3.0)
             (if (<= z -1.76e-217)
               (* 4.0 y)
               (if (<= z -4.8e-241)
                 (* x -3.0)
                 (if (<= z 340000000000.0) (* 4.0 y) t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.75e+123) {
		tmp = t_0;
	} else if (z <= -4.5e+42) {
		tmp = t_1;
	} else if (z <= -3.5e+16) {
		tmp = t_0;
	} else if (z <= -3.6e-142) {
		tmp = 4.0 * y;
	} else if (z <= -5.8e-192) {
		tmp = x * -3.0;
	} else if (z <= -1.76e-217) {
		tmp = 4.0 * y;
	} else if (z <= -4.8e-241) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-1.75d+123)) then
        tmp = t_0
    else if (z <= (-4.5d+42)) then
        tmp = t_1
    else if (z <= (-3.5d+16)) then
        tmp = t_0
    else if (z <= (-3.6d-142)) then
        tmp = 4.0d0 * y
    else if (z <= (-5.8d-192)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.76d-217)) then
        tmp = 4.0d0 * y
    else if (z <= (-4.8d-241)) then
        tmp = x * (-3.0d0)
    else if (z <= 340000000000.0d0) then
        tmp = 4.0d0 * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.75e+123) {
		tmp = t_0;
	} else if (z <= -4.5e+42) {
		tmp = t_1;
	} else if (z <= -3.5e+16) {
		tmp = t_0;
	} else if (z <= -3.6e-142) {
		tmp = 4.0 * y;
	} else if (z <= -5.8e-192) {
		tmp = x * -3.0;
	} else if (z <= -1.76e-217) {
		tmp = 4.0 * y;
	} else if (z <= -4.8e-241) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.75e+123:
		tmp = t_0
	elif z <= -4.5e+42:
		tmp = t_1
	elif z <= -3.5e+16:
		tmp = t_0
	elif z <= -3.6e-142:
		tmp = 4.0 * y
	elif z <= -5.8e-192:
		tmp = x * -3.0
	elif z <= -1.76e-217:
		tmp = 4.0 * y
	elif z <= -4.8e-241:
		tmp = x * -3.0
	elif z <= 340000000000.0:
		tmp = 4.0 * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.75e+123)
		tmp = t_0;
	elseif (z <= -4.5e+42)
		tmp = t_1;
	elseif (z <= -3.5e+16)
		tmp = t_0;
	elseif (z <= -3.6e-142)
		tmp = Float64(4.0 * y);
	elseif (z <= -5.8e-192)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.76e-217)
		tmp = Float64(4.0 * y);
	elseif (z <= -4.8e-241)
		tmp = Float64(x * -3.0);
	elseif (z <= 340000000000.0)
		tmp = Float64(4.0 * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.75e+123)
		tmp = t_0;
	elseif (z <= -4.5e+42)
		tmp = t_1;
	elseif (z <= -3.5e+16)
		tmp = t_0;
	elseif (z <= -3.6e-142)
		tmp = 4.0 * y;
	elseif (z <= -5.8e-192)
		tmp = x * -3.0;
	elseif (z <= -1.76e-217)
		tmp = 4.0 * y;
	elseif (z <= -4.8e-241)
		tmp = x * -3.0;
	elseif (z <= 340000000000.0)
		tmp = 4.0 * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+123], t$95$0, If[LessEqual[z, -4.5e+42], t$95$1, If[LessEqual[z, -3.5e+16], t$95$0, If[LessEqual[z, -3.6e-142], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -5.8e-192], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.76e-217], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -4.8e-241], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 340000000000.0], N[(4.0 * y), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.75e123 or -4.50000000000000012e42 < z < -3.5e16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 66.3%

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

   if -1.75e123 < z < -4.50000000000000012e42 or 3.4e11 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 59.5%

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

   if -3.5e16 < z < -3.6e-142 or -5.80000000000000033e-192 < z < -1.76000000000000006e-217 or -4.8e-241 < z < 3.4e11

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 61.7%

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

   3. Taylor expanded in x around 0 62.3%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -3.6e-142 < z < -5.80000000000000033e-192 or -1.76000000000000006e-217 < z < -4.8e-241

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-neg 83.8%

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

      3. distribute-lft-in 83.8%

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

      4. metadata-eval 83.8%

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

      5. metadata-eval 83.8%

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

      6. neg-mul-1 83.8%

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

      7. *-commutative 83.8%

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

      8. associate-*l* 83.8%

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

      9. distribute-rgt-in 83.8%

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

      10. distribute-lft-in 83.8%

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

      11. associate-+r+ 83.8%

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

      12. metadata-eval 83.8%

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

      13. metadata-eval 83.8%

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

      14. metadata-eval 83.8%

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

      15. distribute-lft-in 83.8%

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

      16. +-commutative 83.8%

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

      17. distribute-rgt-in 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*l* 83.8%

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

      20. metadata-eval 83.8%

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

      21. metadata-eval 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+123}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-192}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-217}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-217}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-237}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.32e+122)
     t_0
     (if (<= z -4.4e+42)
       t_1
       (if (<= z -3.5e+16)
         t_0
         (if (<= z -5.5e-142)
           (* 4.0 y)
           (if (<= z -3.3e-190)
             (* x -3.0)
             (if (<= z -2.55e-217)
               (* 4.0 y)
               (if (<= z -2.25e-237)
                 (* x -3.0)
                 (if (<= z 340000000000.0) (* 4.0 y) t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.32e+122) {
		tmp = t_0;
	} else if (z <= -4.4e+42) {
		tmp = t_1;
	} else if (z <= -3.5e+16) {
		tmp = t_0;
	} else if (z <= -5.5e-142) {
		tmp = 4.0 * y;
	} else if (z <= -3.3e-190) {
		tmp = x * -3.0;
	} else if (z <= -2.55e-217) {
		tmp = 4.0 * y;
	} else if (z <= -2.25e-237) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-1.32d+122)) then
        tmp = t_0
    else if (z <= (-4.4d+42)) then
        tmp = t_1
    else if (z <= (-3.5d+16)) then
        tmp = t_0
    else if (z <= (-5.5d-142)) then
        tmp = 4.0d0 * y
    else if (z <= (-3.3d-190)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.55d-217)) then
        tmp = 4.0d0 * y
    else if (z <= (-2.25d-237)) then
        tmp = x * (-3.0d0)
    else if (z <= 340000000000.0d0) then
        tmp = 4.0d0 * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.32e+122) {
		tmp = t_0;
	} else if (z <= -4.4e+42) {
		tmp = t_1;
	} else if (z <= -3.5e+16) {
		tmp = t_0;
	} else if (z <= -5.5e-142) {
		tmp = 4.0 * y;
	} else if (z <= -3.3e-190) {
		tmp = x * -3.0;
	} else if (z <= -2.55e-217) {
		tmp = 4.0 * y;
	} else if (z <= -2.25e-237) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.32e+122:
		tmp = t_0
	elif z <= -4.4e+42:
		tmp = t_1
	elif z <= -3.5e+16:
		tmp = t_0
	elif z <= -5.5e-142:
		tmp = 4.0 * y
	elif z <= -3.3e-190:
		tmp = x * -3.0
	elif z <= -2.55e-217:
		tmp = 4.0 * y
	elif z <= -2.25e-237:
		tmp = x * -3.0
	elif z <= 340000000000.0:
		tmp = 4.0 * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.32e+122)
		tmp = t_0;
	elseif (z <= -4.4e+42)
		tmp = t_1;
	elseif (z <= -3.5e+16)
		tmp = t_0;
	elseif (z <= -5.5e-142)
		tmp = Float64(4.0 * y);
	elseif (z <= -3.3e-190)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.55e-217)
		tmp = Float64(4.0 * y);
	elseif (z <= -2.25e-237)
		tmp = Float64(x * -3.0);
	elseif (z <= 340000000000.0)
		tmp = Float64(4.0 * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.32e+122)
		tmp = t_0;
	elseif (z <= -4.4e+42)
		tmp = t_1;
	elseif (z <= -3.5e+16)
		tmp = t_0;
	elseif (z <= -5.5e-142)
		tmp = 4.0 * y;
	elseif (z <= -3.3e-190)
		tmp = x * -3.0;
	elseif (z <= -2.55e-217)
		tmp = 4.0 * y;
	elseif (z <= -2.25e-237)
		tmp = x * -3.0;
	elseif (z <= 340000000000.0)
		tmp = 4.0 * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e+122], t$95$0, If[LessEqual[z, -4.4e+42], t$95$1, If[LessEqual[z, -3.5e+16], t$95$0, If[LessEqual[z, -5.5e-142], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -3.3e-190], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.55e-217], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -2.25e-237], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 340000000000.0], N[(4.0 * y), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.31999999999999992e122 or -4.4000000000000003e42 < z < -3.5e16

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. sub-neg 66.4%

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

      3. distribute-lft-in 66.4%

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

      4. metadata-eval 66.4%

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

      5. metadata-eval 66.4%

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

      6. neg-mul-1 66.4%

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

      7. *-commutative 66.4%

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

      8. associate-*l* 66.4%

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

      9. distribute-rgt-in 66.4%

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

      10. distribute-lft-in 66.4%

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

      11. associate-+r+ 66.4%

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

      12. metadata-eval 66.4%

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

      13. metadata-eval 66.4%

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

      14. metadata-eval 66.4%

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

      15. distribute-lft-in 66.4%

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

      16. +-commutative 66.4%

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

      17. distribute-rgt-in 66.4%

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

      18. *-commutative 66.4%

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

      19. associate-*l* 66.4%

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

      20. metadata-eval 66.4%

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

      21. metadata-eval 66.4%

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

   4. Simplified 66.4%

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

   5. Taylor expanded in z around inf 66.4%

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

   if -1.31999999999999992e122 < z < -4.4000000000000003e42 or 3.4e11 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 59.5%

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

   if -3.5e16 < z < -5.50000000000000023e-142 or -3.30000000000000019e-190 < z < -2.5499999999999998e-217 or -2.25000000000000005e-237 < z < 3.4e11

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 61.7%

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

   3. Taylor expanded in x around 0 62.3%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -5.50000000000000023e-142 < z < -3.30000000000000019e-190 or -2.5499999999999998e-217 < z < -2.25000000000000005e-237

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-neg 83.8%

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

      3. distribute-lft-in 83.8%

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

      4. metadata-eval 83.8%

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

      5. metadata-eval 83.8%

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

      6. neg-mul-1 83.8%

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

      7. *-commutative 83.8%

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

      8. associate-*l* 83.8%

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

      9. distribute-rgt-in 83.8%

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

      10. distribute-lft-in 83.8%

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

      11. associate-+r+ 83.8%

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

      12. metadata-eval 83.8%

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

      13. metadata-eval 83.8%

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

      14. metadata-eval 83.8%

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

      15. distribute-lft-in 83.8%

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

      16. +-commutative 83.8%

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

      17. distribute-rgt-in 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*l* 83.8%

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

      20. metadata-eval 83.8%

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

      21. metadata-eval 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+42}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-217}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-237}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-216}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -7.8e+121)
     (* z (* x 6.0))
     (if (<= z -4.5e+42)
       t_0
       (if (<= z -3.5e+16)
         (* x (* z 6.0))
         (if (<= z -4.9e-142)
           (* 4.0 y)
           (if (<= z -1.25e-190)
             (* x -3.0)
             (if (<= z -2.5e-216)
               (* 4.0 y)
               (if (<= z -1.8e-241)
                 (* x -3.0)
                 (if (<= z 340000000000.0) (* 4.0 y) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -7.8e+121) {
		tmp = z * (x * 6.0);
	} else if (z <= -4.5e+42) {
		tmp = t_0;
	} else if (z <= -3.5e+16) {
		tmp = x * (z * 6.0);
	} else if (z <= -4.9e-142) {
		tmp = 4.0 * y;
	} else if (z <= -1.25e-190) {
		tmp = x * -3.0;
	} else if (z <= -2.5e-216) {
		tmp = 4.0 * y;
	} else if (z <= -1.8e-241) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-7.8d+121)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-4.5d+42)) then
        tmp = t_0
    else if (z <= (-3.5d+16)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-4.9d-142)) then
        tmp = 4.0d0 * y
    else if (z <= (-1.25d-190)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.5d-216)) then
        tmp = 4.0d0 * y
    else if (z <= (-1.8d-241)) then
        tmp = x * (-3.0d0)
    else if (z <= 340000000000.0d0) then
        tmp = 4.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -7.8e+121) {
		tmp = z * (x * 6.0);
	} else if (z <= -4.5e+42) {
		tmp = t_0;
	} else if (z <= -3.5e+16) {
		tmp = x * (z * 6.0);
	} else if (z <= -4.9e-142) {
		tmp = 4.0 * y;
	} else if (z <= -1.25e-190) {
		tmp = x * -3.0;
	} else if (z <= -2.5e-216) {
		tmp = 4.0 * y;
	} else if (z <= -1.8e-241) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -7.8e+121:
		tmp = z * (x * 6.0)
	elif z <= -4.5e+42:
		tmp = t_0
	elif z <= -3.5e+16:
		tmp = x * (z * 6.0)
	elif z <= -4.9e-142:
		tmp = 4.0 * y
	elif z <= -1.25e-190:
		tmp = x * -3.0
	elif z <= -2.5e-216:
		tmp = 4.0 * y
	elif z <= -1.8e-241:
		tmp = x * -3.0
	elif z <= 340000000000.0:
		tmp = 4.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -7.8e+121)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -4.5e+42)
		tmp = t_0;
	elseif (z <= -3.5e+16)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -4.9e-142)
		tmp = Float64(4.0 * y);
	elseif (z <= -1.25e-190)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.5e-216)
		tmp = Float64(4.0 * y);
	elseif (z <= -1.8e-241)
		tmp = Float64(x * -3.0);
	elseif (z <= 340000000000.0)
		tmp = Float64(4.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -7.8e+121)
		tmp = z * (x * 6.0);
	elseif (z <= -4.5e+42)
		tmp = t_0;
	elseif (z <= -3.5e+16)
		tmp = x * (z * 6.0);
	elseif (z <= -4.9e-142)
		tmp = 4.0 * y;
	elseif (z <= -1.25e-190)
		tmp = x * -3.0;
	elseif (z <= -2.5e-216)
		tmp = 4.0 * y;
	elseif (z <= -1.8e-241)
		tmp = x * -3.0;
	elseif (z <= 340000000000.0)
		tmp = 4.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+121], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e+42], t$95$0, If[LessEqual[z, -3.5e+16], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-142], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -1.25e-190], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.5e-216], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -1.8e-241], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 340000000000.0], N[(4.0 * y), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.79999999999999967e121

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-*r* 62.6%

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

   8. Simplified 62.6%

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

   if -7.79999999999999967e121 < z < -4.50000000000000012e42 or 3.4e11 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 59.5%

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

   if -4.50000000000000012e42 < z < -3.5e16

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. neg-mul-1 100.0%

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

      7. *-commutative 100.0%

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

      8. associate-*l* 100.0%

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

      9. distribute-rgt-in 100.0%

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

      10. distribute-lft-in 100.0%

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

      11. associate-+r+ 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

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

      15. distribute-lft-in 100.0%

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

      16. +-commutative 100.0%

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

      17. distribute-rgt-in 100.0%

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

      18. *-commutative 100.0%

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

      19. associate-*l* 100.0%

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

      20. metadata-eval 100.0%

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

      21. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   if -3.5e16 < z < -4.9000000000000003e-142 or -1.25000000000000009e-190 < z < -2.5000000000000001e-216 or -1.7999999999999999e-241 < z < 3.4e11

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 61.7%

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

   3. Taylor expanded in x around 0 62.3%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -4.9000000000000003e-142 < z < -1.25000000000000009e-190 or -2.5000000000000001e-216 < z < -1.7999999999999999e-241

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-neg 83.8%

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

      3. distribute-lft-in 83.8%

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

      4. metadata-eval 83.8%

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

      5. metadata-eval 83.8%

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

      6. neg-mul-1 83.8%

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

      7. *-commutative 83.8%

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

      8. associate-*l* 83.8%

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

      9. distribute-rgt-in 83.8%

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

      10. distribute-lft-in 83.8%

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

      11. associate-+r+ 83.8%

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

      12. metadata-eval 83.8%

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

      13. metadata-eval 83.8%

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

      14. metadata-eval 83.8%

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

      15. distribute-lft-in 83.8%

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

      16. +-commutative 83.8%

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

      17. distribute-rgt-in 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*l* 83.8%

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

      20. metadata-eval 83.8%

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

      21. metadata-eval 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

      \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-216}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0265:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-191}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-218}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0265)
     t_0
     (if (<= z -3.8e-142)
       (* 4.0 y)
       (if (<= z -3.7e-191)
         (* x -3.0)
         (if (<= z -1.02e-218)
           (* 4.0 y)
           (if (<= z -3.2e-241)
             (* x -3.0)
             (if (<= z 0.52) (* 4.0 y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0265) {
		tmp = t_0;
	} else if (z <= -3.8e-142) {
		tmp = 4.0 * y;
	} else if (z <= -3.7e-191) {
		tmp = x * -3.0;
	} else if (z <= -1.02e-218) {
		tmp = 4.0 * y;
	} else if (z <= -3.2e-241) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0265d0)) then
        tmp = t_0
    else if (z <= (-3.8d-142)) then
        tmp = 4.0d0 * y
    else if (z <= (-3.7d-191)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.02d-218)) then
        tmp = 4.0d0 * y
    else if (z <= (-3.2d-241)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = 4.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0265) {
		tmp = t_0;
	} else if (z <= -3.8e-142) {
		tmp = 4.0 * y;
	} else if (z <= -3.7e-191) {
		tmp = x * -3.0;
	} else if (z <= -1.02e-218) {
		tmp = 4.0 * y;
	} else if (z <= -3.2e-241) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0265:
		tmp = t_0
	elif z <= -3.8e-142:
		tmp = 4.0 * y
	elif z <= -3.7e-191:
		tmp = x * -3.0
	elif z <= -1.02e-218:
		tmp = 4.0 * y
	elif z <= -3.2e-241:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = 4.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0265)
		tmp = t_0;
	elseif (z <= -3.8e-142)
		tmp = Float64(4.0 * y);
	elseif (z <= -3.7e-191)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.02e-218)
		tmp = Float64(4.0 * y);
	elseif (z <= -3.2e-241)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(4.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0265)
		tmp = t_0;
	elseif (z <= -3.8e-142)
		tmp = 4.0 * y;
	elseif (z <= -3.7e-191)
		tmp = x * -3.0;
	elseif (z <= -1.02e-218)
		tmp = 4.0 * y;
	elseif (z <= -3.2e-241)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = 4.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0265], t$95$0, If[LessEqual[z, -3.8e-142], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -3.7e-191], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.02e-218], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -3.2e-241], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(4.0 * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0264999999999999993 or 0.52000000000000002 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.9%

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

   if -0.0264999999999999993 < z < -3.79999999999999972e-142 or -3.6999999999999997e-191 < z < -1.02e-218 or -3.2e-241 < z < 0.52000000000000002

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 61.9%

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

   3. Taylor expanded in x around 0 62.8%

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

   4. Taylor expanded in z around 0 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if -3.79999999999999972e-142 < z < -3.6999999999999997e-191 or -1.02e-218 < z < -3.2e-241

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-neg 83.8%

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

      3. distribute-lft-in 83.8%

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

      4. metadata-eval 83.8%

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

      5. metadata-eval 83.8%

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

      6. neg-mul-1 83.8%

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

      7. *-commutative 83.8%

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

      8. associate-*l* 83.8%

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

      9. distribute-rgt-in 83.8%

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

      10. distribute-lft-in 83.8%

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

      11. associate-+r+ 83.8%

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

      12. metadata-eval 83.8%

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

      13. metadata-eval 83.8%

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

      14. metadata-eval 83.8%

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

      15. distribute-lft-in 83.8%

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

      16. +-commutative 83.8%

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

      17. distribute-rgt-in 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*l* 83.8%

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

      20. metadata-eval 83.8%

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

      21. metadata-eval 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0265:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-191}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-218}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-241}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-220}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-236}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -3.5e+16)
     t_1
     (if (<= z -4.6e-142)
       t_0
       (if (<= z -1.08e-190)
         (* x -3.0)
         (if (<= z -7e-220)
           (* 4.0 y)
           (if (<= z -1.8e-236) (* x -3.0) (if (<= z 0.55) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3.5e+16) {
		tmp = t_1;
	} else if (z <= -4.6e-142) {
		tmp = t_0;
	} else if (z <= -1.08e-190) {
		tmp = x * -3.0;
	} else if (z <= -7e-220) {
		tmp = 4.0 * y;
	} else if (z <= -1.8e-236) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-3.5d+16)) then
        tmp = t_1
    else if (z <= (-4.6d-142)) then
        tmp = t_0
    else if (z <= (-1.08d-190)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7d-220)) then
        tmp = 4.0d0 * y
    else if (z <= (-1.8d-236)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.55d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -3.5e+16) {
		tmp = t_1;
	} else if (z <= -4.6e-142) {
		tmp = t_0;
	} else if (z <= -1.08e-190) {
		tmp = x * -3.0;
	} else if (z <= -7e-220) {
		tmp = 4.0 * y;
	} else if (z <= -1.8e-236) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -3.5e+16:
		tmp = t_1
	elif z <= -4.6e-142:
		tmp = t_0
	elif z <= -1.08e-190:
		tmp = x * -3.0
	elif z <= -7e-220:
		tmp = 4.0 * y
	elif z <= -1.8e-236:
		tmp = x * -3.0
	elif z <= 0.55:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -3.5e+16)
		tmp = t_1;
	elseif (z <= -4.6e-142)
		tmp = t_0;
	elseif (z <= -1.08e-190)
		tmp = Float64(x * -3.0);
	elseif (z <= -7e-220)
		tmp = Float64(4.0 * y);
	elseif (z <= -1.8e-236)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.55)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -3.5e+16)
		tmp = t_1;
	elseif (z <= -4.6e-142)
		tmp = t_0;
	elseif (z <= -1.08e-190)
		tmp = x * -3.0;
	elseif (z <= -7e-220)
		tmp = 4.0 * y;
	elseif (z <= -1.8e-236)
		tmp = x * -3.0;
	elseif (z <= 0.55)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+16], t$95$1, If[LessEqual[z, -4.6e-142], t$95$0, If[LessEqual[z, -1.08e-190], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7e-220], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -1.8e-236], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.55], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5e16 or 0.55000000000000004 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.1%

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

   if -3.5e16 < z < -4.60000000000000005e-142 or -1.80000000000000004e-236 < z < 0.55000000000000004

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 61.0%

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

   3. Taylor expanded in x around 0 61.9%

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

   if -4.60000000000000005e-142 < z < -1.08e-190 or -6.99999999999999975e-220 < z < -1.80000000000000004e-236

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-neg 83.8%

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

      3. distribute-lft-in 83.8%

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

      4. metadata-eval 83.8%

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

      5. metadata-eval 83.8%

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

      6. neg-mul-1 83.8%

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

      7. *-commutative 83.8%

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

      8. associate-*l* 83.8%

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

      9. distribute-rgt-in 83.8%

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

      10. distribute-lft-in 83.8%

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

      11. associate-+r+ 83.8%

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

      12. metadata-eval 83.8%

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

      13. metadata-eval 83.8%

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

      14. metadata-eval 83.8%

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

      15. distribute-lft-in 83.8%

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

      16. +-commutative 83.8%

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

      17. distribute-rgt-in 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*l* 83.8%

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

      20. metadata-eval 83.8%

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

      21. metadata-eval 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

   if -1.08e-190 < z < -6.99999999999999975e-220

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 85.3%

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

   3. Taylor expanded in x around 0 85.4%

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

   4. Taylor expanded in z around 0 85.9%

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

      1. *-commutative 85.9%

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

   6. Simplified 85.9%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-142}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-190}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-220}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-236}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-192}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-218}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-236}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.65)
     t_0
     (if (<= z -4.5e-142)
       (* 4.0 y)
       (if (<= z -2.3e-192)
         (* x -3.0)
         (if (<= z -8.2e-218)
           (* 4.0 y)
           (if (<= z -3.3e-236)
             (* x -3.0)
             (if (<= z 340000000000.0) (* 4.0 y) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -4.5e-142) {
		tmp = 4.0 * y;
	} else if (z <= -2.3e-192) {
		tmp = x * -3.0;
	} else if (z <= -8.2e-218) {
		tmp = 4.0 * y;
	} else if (z <= -3.3e-236) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-4.5d-142)) then
        tmp = 4.0d0 * y
    else if (z <= (-2.3d-192)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8.2d-218)) then
        tmp = 4.0d0 * y
    else if (z <= (-3.3d-236)) then
        tmp = x * (-3.0d0)
    else if (z <= 340000000000.0d0) then
        tmp = 4.0d0 * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -4.5e-142) {
		tmp = 4.0 * y;
	} else if (z <= -2.3e-192) {
		tmp = x * -3.0;
	} else if (z <= -8.2e-218) {
		tmp = 4.0 * y;
	} else if (z <= -3.3e-236) {
		tmp = x * -3.0;
	} else if (z <= 340000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.65:
		tmp = t_0
	elif z <= -4.5e-142:
		tmp = 4.0 * y
	elif z <= -2.3e-192:
		tmp = x * -3.0
	elif z <= -8.2e-218:
		tmp = 4.0 * y
	elif z <= -3.3e-236:
		tmp = x * -3.0
	elif z <= 340000000000.0:
		tmp = 4.0 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -4.5e-142)
		tmp = Float64(4.0 * y);
	elseif (z <= -2.3e-192)
		tmp = Float64(x * -3.0);
	elseif (z <= -8.2e-218)
		tmp = Float64(4.0 * y);
	elseif (z <= -3.3e-236)
		tmp = Float64(x * -3.0);
	elseif (z <= 340000000000.0)
		tmp = Float64(4.0 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -4.5e-142)
		tmp = 4.0 * y;
	elseif (z <= -2.3e-192)
		tmp = x * -3.0;
	elseif (z <= -8.2e-218)
		tmp = 4.0 * y;
	elseif (z <= -3.3e-236)
		tmp = x * -3.0;
	elseif (z <= 340000000000.0)
		tmp = 4.0 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.65], t$95$0, If[LessEqual[z, -4.5e-142], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -2.3e-192], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8.2e-218], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -3.3e-236], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 340000000000.0], N[(4.0 * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022 or 3.4e11 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l* 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in y around inf 53.9%

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

   if -0.650000000000000022 < z < -4.50000000000000019e-142 or -2.30000000000000018e-192 < z < -8.1999999999999995e-218 or -3.3000000000000001e-236 < z < 3.4e11

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 61.0%

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

   3. Taylor expanded in x around 0 61.6%

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

   4. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -4.50000000000000019e-142 < z < -2.30000000000000018e-192 or -8.1999999999999995e-218 < z < -3.3000000000000001e-236

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. *-commutative 83.8%

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

      2. sub-neg 83.8%

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

      3. distribute-lft-in 83.8%

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

      4. metadata-eval 83.8%

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

      5. metadata-eval 83.8%

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

      6. neg-mul-1 83.8%

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

      7. *-commutative 83.8%

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

      8. associate-*l* 83.8%

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

      9. distribute-rgt-in 83.8%

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

      10. distribute-lft-in 83.8%

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

      11. associate-+r+ 83.8%

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

      12. metadata-eval 83.8%

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

      13. metadata-eval 83.8%

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

      14. metadata-eval 83.8%

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

      15. distribute-lft-in 83.8%

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

      16. +-commutative 83.8%

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

      17. distribute-rgt-in 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*l* 83.8%

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

      20. metadata-eval 83.8%

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

      21. metadata-eval 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-192}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-218}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-236}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 340000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -1150000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-99}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-108} \lor \neg \left(y \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -1150000000.0)
     t_0
     (if (<= y -5.5e-99)
       (* -6.0 (* (- y x) z))
       (if (or (<= y -1e-108) (not (<= y 5.5e-17)))
         t_0
         (* x (+ -3.0 (* z 6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -1150000000.0) {
		tmp = t_0;
	} else if (y <= -5.5e-99) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((y <= -1e-108) || !(y <= 5.5e-17)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    if (y <= (-1150000000.0d0)) then
        tmp = t_0
    else if (y <= (-5.5d-99)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if ((y <= (-1d-108)) .or. (.not. (y <= 5.5d-17))) then
        tmp = t_0
    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 t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -1150000000.0) {
		tmp = t_0;
	} else if (y <= -5.5e-99) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((y <= -1e-108) || !(y <= 5.5e-17)) {
		tmp = t_0;
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	tmp = 0
	if y <= -1150000000.0:
		tmp = t_0
	elif y <= -5.5e-99:
		tmp = -6.0 * ((y - x) * z)
	elif (y <= -1e-108) or not (y <= 5.5e-17):
		tmp = t_0
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	tmp = 0.0
	if (y <= -1150000000.0)
		tmp = t_0;
	elseif (y <= -5.5e-99)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif ((y <= -1e-108) || !(y <= 5.5e-17))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	tmp = 0.0;
	if (y <= -1150000000.0)
		tmp = t_0;
	elseif (y <= -5.5e-99)
		tmp = -6.0 * ((y - x) * z);
	elseif ((y <= -1e-108) || ~((y <= 5.5e-17)))
		tmp = t_0;
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1150000000.0], t$95$0, If[LessEqual[y, -5.5e-99], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1e-108], N[Not[LessEqual[y, 5.5e-17]], $MachinePrecision]], t$95$0, N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e9 or -5.49999999999999991e-99 < y < -1.00000000000000004e-108 or 5.50000000000000001e-17 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 81.9%

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

   3. Taylor expanded in x around 0 82.1%

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

   if -1.15e9 < y < -5.49999999999999991e-99

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 71.9%

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

   if -1.00000000000000004e-108 < y < 5.50000000000000001e-17

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. sub-neg 82.5%

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

      3. distribute-lft-in 82.5%

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

      4. metadata-eval 82.5%

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

      5. metadata-eval 82.5%

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

      6. neg-mul-1 82.5%

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

      7. *-commutative 82.5%

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

      8. associate-*l* 82.5%

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

      9. distribute-rgt-in 82.5%

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

      10. distribute-lft-in 82.5%

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

      11. associate-+r+ 82.5%

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

      12. metadata-eval 82.5%

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

      13. metadata-eval 82.5%

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

      14. metadata-eval 82.5%

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

      15. distribute-lft-in 82.5%

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

      16. +-commutative 82.5%

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

      17. distribute-rgt-in 82.5%

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

      18. *-commutative 82.5%

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

      19. associate-*l* 82.5%

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

      20. metadata-eval 82.5%

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

      21. metadata-eval 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1150000000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-99}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-108} \lor \neg \left(y \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 9: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{if}\;y \leq -145000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-99}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-108} \lor \neg \left(y \leq 5.6 \cdot 10^{-17}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* -6.0 z)))))
   (if (<= y -145000000.0)
     t_0
     (if (<= y -4.6e-99)
       (* -6.0 (* (- y x) z))
       (if (or (<= y -1.02e-108) (not (<= y 5.6e-17)))
         t_0
         (* x (+ -3.0 (* z 6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (-6.0 * z));
	double tmp;
	if (y <= -145000000.0) {
		tmp = t_0;
	} else if (y <= -4.6e-99) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((y <= -1.02e-108) || !(y <= 5.6e-17)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * (4.0d0 + ((-6.0d0) * z))
    if (y <= (-145000000.0d0)) then
        tmp = t_0
    else if (y <= (-4.6d-99)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if ((y <= (-1.02d-108)) .or. (.not. (y <= 5.6d-17))) then
        tmp = t_0
    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 t_0 = y * (4.0 + (-6.0 * z));
	double tmp;
	if (y <= -145000000.0) {
		tmp = t_0;
	} else if (y <= -4.6e-99) {
		tmp = -6.0 * ((y - x) * z);
	} else if ((y <= -1.02e-108) || !(y <= 5.6e-17)) {
		tmp = t_0;
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (-6.0 * z))
	tmp = 0
	if y <= -145000000.0:
		tmp = t_0
	elif y <= -4.6e-99:
		tmp = -6.0 * ((y - x) * z)
	elif (y <= -1.02e-108) or not (y <= 5.6e-17):
		tmp = t_0
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(-6.0 * z)))
	tmp = 0.0
	if (y <= -145000000.0)
		tmp = t_0;
	elseif (y <= -4.6e-99)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif ((y <= -1.02e-108) || !(y <= 5.6e-17))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (-6.0 * z));
	tmp = 0.0;
	if (y <= -145000000.0)
		tmp = t_0;
	elseif (y <= -4.6e-99)
		tmp = -6.0 * ((y - x) * z);
	elseif ((y <= -1.02e-108) || ~((y <= 5.6e-17)))
		tmp = t_0;
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -145000000.0], t$95$0, If[LessEqual[y, -4.6e-99], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.02e-108], N[Not[LessEqual[y, 5.6e-17]], $MachinePrecision]], t$95$0, N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e8 or -4.5999999999999997e-99 < y < -1.02000000000000008e-108 or 5.5999999999999998e-17 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. fma-def 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.3%

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

   if -1.45e8 < y < -4.5999999999999997e-99

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 71.9%

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

   if -1.02000000000000008e-108 < y < 5.5999999999999998e-17

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. sub-neg 82.5%

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

      3. distribute-lft-in 82.5%

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

      4. metadata-eval 82.5%

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

      5. metadata-eval 82.5%

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

      6. neg-mul-1 82.5%

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

      7. *-commutative 82.5%

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

      8. associate-*l* 82.5%

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

      9. distribute-rgt-in 82.5%

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

      10. distribute-lft-in 82.5%

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

      11. associate-+r+ 82.5%

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

      12. metadata-eval 82.5%

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

      13. metadata-eval 82.5%

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

      14. metadata-eval 82.5%

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

      15. distribute-lft-in 82.5%

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

      16. +-commutative 82.5%

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

      17. distribute-rgt-in 82.5%

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

      18. *-commutative 82.5%

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

      19. associate-*l* 82.5%

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

      20. metadata-eval 82.5%

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

      21. metadata-eval 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -145000000:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-99}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-108} \lor \neg \left(y \leq 5.6 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 10: 97.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.4%

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

   5. Simplified 99.4%

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

   if -0.55000000000000004 < z < 0.55000000000000004

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 98.0%

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

   3. Taylor expanded in x around 0 98.5%

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

   if 0.55000000000000004 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in z around inf 98.5%

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

4. Final simplification 98.8%

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

Alternative 11: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

2. Taylor expanded in z around 0 99.6%

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

   1. neg-mul-1 99.6%

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

   2. +-commutative 99.6%

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

   3. sub-neg 99.6%

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

4. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 12: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. associate-*l* 99.8%

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

   2. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 13: 37.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-44}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3e-44) (* x -3.0) (if (<= x 1.02e-32) (* 4.0 y) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3e-44) {
		tmp = x * -3.0;
	} else if (x <= 1.02e-32) {
		tmp = 4.0 * y;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3d-44)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.02d-32) then
        tmp = 4.0d0 * y
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3e-44) {
		tmp = x * -3.0;
	} else if (x <= 1.02e-32) {
		tmp = 4.0 * y;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3e-44:
		tmp = x * -3.0
	elif x <= 1.02e-32:
		tmp = 4.0 * y
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3e-44)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.02e-32)
		tmp = Float64(4.0 * y);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3e-44)
		tmp = x * -3.0;
	elseif (x <= 1.02e-32)
		tmp = 4.0 * y;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3e-44], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.02e-32], N[(4.0 * y), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000002e-44 or 1.02000000000000002e-32 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. sub-neg 75.1%

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

      3. distribute-lft-in 75.2%

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

      4. metadata-eval 75.2%

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

      5. metadata-eval 75.2%

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

      6. neg-mul-1 75.2%

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

      7. *-commutative 75.2%

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

      8. associate-*l* 75.2%

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

      9. distribute-rgt-in 75.2%

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

      10. distribute-lft-in 75.2%

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

      11. associate-+r+ 75.2%

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

      12. metadata-eval 75.2%

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

      13. metadata-eval 75.2%

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

      14. metadata-eval 75.2%

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

      15. distribute-lft-in 75.2%

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

      16. +-commutative 75.2%

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

      17. distribute-rgt-in 75.2%

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

      18. *-commutative 75.2%

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

      19. associate-*l* 75.2%

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

      20. metadata-eval 75.2%

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

      21. metadata-eval 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in z around 0 32.3%

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

      1. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   if -3.0000000000000002e-44 < x < 1.02000000000000002e-32

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 82.7%

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

   3. Taylor expanded in x around 0 82.9%

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

   4. Taylor expanded in z around 0 43.9%

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

      1. *-commutative 43.9%

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

   6. Simplified 43.9%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-44}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 14: 25.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

2. Taylor expanded in x around inf 49.8%

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

   1. *-commutative 49.8%

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

   2. sub-neg 49.8%

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

   3. distribute-lft-in 49.8%

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

   4. metadata-eval 49.8%

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

   5. metadata-eval 49.8%

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

   6. neg-mul-1 49.8%

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

   7. *-commutative 49.8%

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

   8. associate-*l* 49.8%

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

   9. distribute-rgt-in 49.8%

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

   10. distribute-lft-in 49.8%

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

   11. associate-+r+ 49.8%

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

   12. metadata-eval 49.8%

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

   13. metadata-eval 49.8%

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

   14. metadata-eval 49.8%

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

   15. distribute-lft-in 49.8%

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

   16. +-commutative 49.8%

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

   17. distribute-rgt-in 49.8%

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

   18. *-commutative 49.8%

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

   19. associate-*l* 49.8%

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

   20. metadata-eval 49.8%

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

   21. metadata-eval 49.8%

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

4. Simplified 49.8%

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

5. Taylor expanded in z around 0 22.1%

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

   1. *-commutative 22.1%

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

7. Simplified 22.1%

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

8. Final simplification 22.1%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023199 
(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))))