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

Percentage Accurate: 99.5% → 99.8%

Time: 9.7s

Alternatives: 14

Speedup: 1.2×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.9× speedup

Math

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

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: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+113} \lor \neg \left(z \leq 7 \cdot 10^{+206}\right) \land z \leq 7.4 \cdot 10^{+245}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3.7e-5)
     t_0
     (if (<= z -3.6e-119)
       (* 4.0 y)
       (if (<= z -1.5e-181)
         (* x -3.0)
         (if (<= z -3.2e-275)
           (* 4.0 y)
           (if (<= z 4.9e-269)
             (* x -3.0)
             (if (<= z 0.66)
               (* 4.0 y)
               (if (or (<= z 2.35e+113)
                       (and (not (<= z 7e+206)) (<= z 7.4e+245)))
                 t_0
                 (* 6.0 (* x z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -3.7e-5) {
		tmp = t_0;
	} else if (z <= -3.6e-119) {
		tmp = 4.0 * y;
	} else if (z <= -1.5e-181) {
		tmp = x * -3.0;
	} else if (z <= -3.2e-275) {
		tmp = 4.0 * y;
	} else if (z <= 4.9e-269) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if ((z <= 2.35e+113) || (!(z <= 7e+206) && (z <= 7.4e+245))) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (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) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-3.7d-5)) then
        tmp = t_0
    else if (z <= (-3.6d-119)) then
        tmp = 4.0d0 * y
    else if (z <= (-1.5d-181)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.2d-275)) then
        tmp = 4.0d0 * y
    else if (z <= 4.9d-269) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = 4.0d0 * y
    else if ((z <= 2.35d+113) .or. (.not. (z <= 7d+206)) .and. (z <= 7.4d+245)) then
        tmp = t_0
    else
        tmp = 6.0d0 * (x * z)
    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 <= -3.7e-5) {
		tmp = t_0;
	} else if (z <= -3.6e-119) {
		tmp = 4.0 * y;
	} else if (z <= -1.5e-181) {
		tmp = x * -3.0;
	} else if (z <= -3.2e-275) {
		tmp = 4.0 * y;
	} else if (z <= 4.9e-269) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if ((z <= 2.35e+113) || (!(z <= 7e+206) && (z <= 7.4e+245))) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -3.7e-5:
		tmp = t_0
	elif z <= -3.6e-119:
		tmp = 4.0 * y
	elif z <= -1.5e-181:
		tmp = x * -3.0
	elif z <= -3.2e-275:
		tmp = 4.0 * y
	elif z <= 4.9e-269:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = 4.0 * y
	elif (z <= 2.35e+113) or (not (z <= 7e+206) and (z <= 7.4e+245)):
		tmp = t_0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.7e-5)
		tmp = t_0;
	elseif (z <= -3.6e-119)
		tmp = Float64(4.0 * y);
	elseif (z <= -1.5e-181)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.2e-275)
		tmp = Float64(4.0 * y);
	elseif (z <= 4.9e-269)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(4.0 * y);
	elseif ((z <= 2.35e+113) || (!(z <= 7e+206) && (z <= 7.4e+245)))
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.7e-5)
		tmp = t_0;
	elseif (z <= -3.6e-119)
		tmp = 4.0 * y;
	elseif (z <= -1.5e-181)
		tmp = x * -3.0;
	elseif (z <= -3.2e-275)
		tmp = 4.0 * y;
	elseif (z <= 4.9e-269)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = 4.0 * y;
	elseif ((z <= 2.35e+113) || (~((z <= 7e+206)) && (z <= 7.4e+245)))
		tmp = t_0;
	else
		tmp = 6.0 * (x * z);
	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, -3.7e-5], t$95$0, If[LessEqual[z, -3.6e-119], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -1.5e-181], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.2e-275], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 4.9e-269], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], If[Or[LessEqual[z, 2.35e+113], And[N[Not[LessEqual[z, 7e+206]], $MachinePrecision], LessEqual[z, 7.4e+245]]], t$95$0, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.69999999999999981e-5 or 0.660000000000000031 < z < 2.3499999999999999e113 or 7.00000000000000027e206 < z < 7.4000000000000002e245

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in x around 0 65.7%

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

   4. Taylor expanded in z around inf 63.2%

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

      1. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if -3.69999999999999981e-5 < z < -3.6e-119 or -1.49999999999999987e-181 < z < -3.2e-275 or 4.89999999999999999e-269 < z < 0.660000000000000031

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 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 x around 0 63.6%

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

   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 -3.6e-119 < z < -1.49999999999999987e-181 or -3.2e-275 < z < 4.89999999999999999e-269

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. distribute-lft-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. metadata-eval 76.7%

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

      6. neg-mul-1 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. distribute-rgt-in 76.7%

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

      10. distribute-lft-in 76.7%

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

      11. associate-+r+ 76.7%

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

      12. metadata-eval 76.7%

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

      13. metadata-eval 76.7%

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

      14. metadata-eval 76.7%

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

      15. distribute-lft-in 76.7%

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

      16. +-commutative 76.7%

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

      17. distribute-rgt-in 76.7%

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

      18. *-commutative 76.7%

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

      19. associate-*l* 76.7%

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

      20. metadata-eval 76.7%

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

      21. metadata-eval 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if 2.3499999999999999e113 < z < 7.00000000000000027e206 or 7.4000000000000002e245 < 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 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 83.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+113} \lor \neg \left(z \leq 7 \cdot 10^{+206}\right) \land z \leq 7.4 \cdot 10^{+245}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-268}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+112} \lor \neg \left(z \leq 7.5 \cdot 10^{+206}\right) \land z \leq 3.4 \cdot 10^{+250}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3.7e-5)
     t_0
     (if (<= z -2.5e-119)
       (* 4.0 y)
       (if (<= z -9.2e-182)
         (* x -3.0)
         (if (<= z -6.5e-275)
           (* 4.0 y)
           (if (<= z 2.4e-268)
             (* x -3.0)
             (if (<= z 0.66)
               (* 4.0 y)
               (if (or (<= z 4.2e+112)
                       (and (not (<= z 7.5e+206)) (<= z 3.4e+250)))
                 t_0
                 (* x (* z 6.0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -3.7e-5) {
		tmp = t_0;
	} else if (z <= -2.5e-119) {
		tmp = 4.0 * y;
	} else if (z <= -9.2e-182) {
		tmp = x * -3.0;
	} else if (z <= -6.5e-275) {
		tmp = 4.0 * y;
	} else if (z <= 2.4e-268) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if ((z <= 4.2e+112) || (!(z <= 7.5e+206) && (z <= 3.4e+250))) {
		tmp = t_0;
	} else {
		tmp = x * (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 * z)
    if (z <= (-3.7d-5)) then
        tmp = t_0
    else if (z <= (-2.5d-119)) then
        tmp = 4.0d0 * y
    else if (z <= (-9.2d-182)) then
        tmp = x * (-3.0d0)
    else if (z <= (-6.5d-275)) then
        tmp = 4.0d0 * y
    else if (z <= 2.4d-268) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = 4.0d0 * y
    else if ((z <= 4.2d+112) .or. (.not. (z <= 7.5d+206)) .and. (z <= 3.4d+250)) then
        tmp = t_0
    else
        tmp = x * (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 * z);
	double tmp;
	if (z <= -3.7e-5) {
		tmp = t_0;
	} else if (z <= -2.5e-119) {
		tmp = 4.0 * y;
	} else if (z <= -9.2e-182) {
		tmp = x * -3.0;
	} else if (z <= -6.5e-275) {
		tmp = 4.0 * y;
	} else if (z <= 2.4e-268) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if ((z <= 4.2e+112) || (!(z <= 7.5e+206) && (z <= 3.4e+250))) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -3.7e-5:
		tmp = t_0
	elif z <= -2.5e-119:
		tmp = 4.0 * y
	elif z <= -9.2e-182:
		tmp = x * -3.0
	elif z <= -6.5e-275:
		tmp = 4.0 * y
	elif z <= 2.4e-268:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = 4.0 * y
	elif (z <= 4.2e+112) or (not (z <= 7.5e+206) and (z <= 3.4e+250)):
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.7e-5)
		tmp = t_0;
	elseif (z <= -2.5e-119)
		tmp = Float64(4.0 * y);
	elseif (z <= -9.2e-182)
		tmp = Float64(x * -3.0);
	elseif (z <= -6.5e-275)
		tmp = Float64(4.0 * y);
	elseif (z <= 2.4e-268)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(4.0 * y);
	elseif ((z <= 4.2e+112) || (!(z <= 7.5e+206) && (z <= 3.4e+250)))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.7e-5)
		tmp = t_0;
	elseif (z <= -2.5e-119)
		tmp = 4.0 * y;
	elseif (z <= -9.2e-182)
		tmp = x * -3.0;
	elseif (z <= -6.5e-275)
		tmp = 4.0 * y;
	elseif (z <= 2.4e-268)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = 4.0 * y;
	elseif ((z <= 4.2e+112) || (~((z <= 7.5e+206)) && (z <= 3.4e+250)))
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	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, -3.7e-5], t$95$0, If[LessEqual[z, -2.5e-119], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -9.2e-182], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -6.5e-275], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 2.4e-268], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], If[Or[LessEqual[z, 4.2e+112], And[N[Not[LessEqual[z, 7.5e+206]], $MachinePrecision], LessEqual[z, 3.4e+250]]], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.69999999999999981e-5 or 0.660000000000000031 < z < 4.1999999999999998e112 or 7.49999999999999958e206 < z < 3.39999999999999973e250

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in x around 0 65.7%

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

   4. Taylor expanded in z around inf 63.2%

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

      1. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if -3.69999999999999981e-5 < z < -2.49999999999999996e-119 or -9.1999999999999996e-182 < z < -6.500000000000001e-275 or 2.3999999999999999e-268 < z < 0.660000000000000031

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 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 x around 0 63.6%

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

   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 -2.49999999999999996e-119 < z < -9.1999999999999996e-182 or -6.500000000000001e-275 < z < 2.3999999999999999e-268

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. distribute-lft-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. metadata-eval 76.7%

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

      6. neg-mul-1 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. distribute-rgt-in 76.7%

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

      10. distribute-lft-in 76.7%

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

      11. associate-+r+ 76.7%

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

      12. metadata-eval 76.7%

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

      13. metadata-eval 76.7%

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

      14. metadata-eval 76.7%

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

      15. distribute-lft-in 76.7%

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

      16. +-commutative 76.7%

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

      17. distribute-rgt-in 76.7%

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

      18. *-commutative 76.7%

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

      19. associate-*l* 76.7%

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

      20. metadata-eval 76.7%

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

      21. metadata-eval 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if 4.1999999999999998e112 < z < 7.49999999999999958e206 or 3.39999999999999973e250 < 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 x around inf 83.4%

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

      1. *-commutative 83.4%

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

      2. sub-neg 83.4%

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

      3. distribute-lft-in 83.4%

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

      4. metadata-eval 83.4%

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

      5. metadata-eval 83.4%

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

      6. neg-mul-1 83.4%

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

      7. *-commutative 83.4%

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

      8. associate-*l* 83.4%

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

      9. distribute-rgt-in 83.4%

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

      10. distribute-lft-in 83.4%

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

      11. associate-+r+ 83.4%

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

      12. metadata-eval 83.4%

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

      13. metadata-eval 83.4%

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

      14. metadata-eval 83.4%

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

      15. distribute-lft-in 83.4%

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

      16. +-commutative 83.4%

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

      17. distribute-rgt-in 83.4%

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

      18. *-commutative 83.4%

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

      19. associate-*l* 83.4%

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

      20. metadata-eval 83.4%

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

      21. metadata-eval 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in z around inf 83.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-268}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+112} \lor \neg \left(z \leq 7.5 \cdot 10^{+206}\right) \land z \leq 3.4 \cdot 10^{+250}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 4: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-267}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+114} \lor \neg \left(z \leq 6.4 \cdot 10^{+206}\right) \land z \leq 2.2 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e-5)
   (* -6.0 (* y z))
   (if (<= z -9.5e-120)
     (* 4.0 y)
     (if (<= z -3.3e-182)
       (* x -3.0)
       (if (<= z -3e-275)
         (* 4.0 y)
         (if (<= z 1.1e-267)
           (* x -3.0)
           (if (<= z 0.66)
             (* 4.0 y)
             (if (or (<= z 1.2e+114)
                     (and (not (<= z 6.4e+206)) (<= z 2.2e+247)))
               (* z (* y -6.0))
               (* x (* z 6.0))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e-5) {
		tmp = -6.0 * (y * z);
	} else if (z <= -9.5e-120) {
		tmp = 4.0 * y;
	} else if (z <= -3.3e-182) {
		tmp = x * -3.0;
	} else if (z <= -3e-275) {
		tmp = 4.0 * y;
	} else if (z <= 1.1e-267) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if ((z <= 1.2e+114) || (!(z <= 6.4e+206) && (z <= 2.2e+247))) {
		tmp = z * (y * -6.0);
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.7d-5)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-9.5d-120)) then
        tmp = 4.0d0 * y
    else if (z <= (-3.3d-182)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3d-275)) then
        tmp = 4.0d0 * y
    else if (z <= 1.1d-267) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = 4.0d0 * y
    else if ((z <= 1.2d+114) .or. (.not. (z <= 6.4d+206)) .and. (z <= 2.2d+247)) then
        tmp = z * (y * (-6.0d0))
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e-5) {
		tmp = -6.0 * (y * z);
	} else if (z <= -9.5e-120) {
		tmp = 4.0 * y;
	} else if (z <= -3.3e-182) {
		tmp = x * -3.0;
	} else if (z <= -3e-275) {
		tmp = 4.0 * y;
	} else if (z <= 1.1e-267) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = 4.0 * y;
	} else if ((z <= 1.2e+114) || (!(z <= 6.4e+206) && (z <= 2.2e+247))) {
		tmp = z * (y * -6.0);
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e-5:
		tmp = -6.0 * (y * z)
	elif z <= -9.5e-120:
		tmp = 4.0 * y
	elif z <= -3.3e-182:
		tmp = x * -3.0
	elif z <= -3e-275:
		tmp = 4.0 * y
	elif z <= 1.1e-267:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = 4.0 * y
	elif (z <= 1.2e+114) or (not (z <= 6.4e+206) and (z <= 2.2e+247)):
		tmp = z * (y * -6.0)
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e-5)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -9.5e-120)
		tmp = Float64(4.0 * y);
	elseif (z <= -3.3e-182)
		tmp = Float64(x * -3.0);
	elseif (z <= -3e-275)
		tmp = Float64(4.0 * y);
	elseif (z <= 1.1e-267)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(4.0 * y);
	elseif ((z <= 1.2e+114) || (!(z <= 6.4e+206) && (z <= 2.2e+247)))
		tmp = Float64(z * Float64(y * -6.0));
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e-5)
		tmp = -6.0 * (y * z);
	elseif (z <= -9.5e-120)
		tmp = 4.0 * y;
	elseif (z <= -3.3e-182)
		tmp = x * -3.0;
	elseif (z <= -3e-275)
		tmp = 4.0 * y;
	elseif (z <= 1.1e-267)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = 4.0 * y;
	elseif ((z <= 1.2e+114) || (~((z <= 6.4e+206)) && (z <= 2.2e+247)))
		tmp = z * (y * -6.0);
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e-5], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-120], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -3.3e-182], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3e-275], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 1.1e-267], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], If[Or[LessEqual[z, 1.2e+114], And[N[Not[LessEqual[z, 6.4e+206]], $MachinePrecision], LessEqual[z, 2.2e+247]]], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.69999999999999981e-5

   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 x around 0 62.3%

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

   4. Taylor expanded in z around inf 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -3.69999999999999981e-5 < z < -9.49999999999999937e-120 or -3.29999999999999996e-182 < z < -3e-275 or 1.09999999999999994e-267 < z < 0.660000000000000031

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 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 x around 0 63.6%

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

   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 -9.49999999999999937e-120 < z < -3.29999999999999996e-182 or -3e-275 < z < 1.09999999999999994e-267

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. distribute-lft-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. metadata-eval 76.7%

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

      6. neg-mul-1 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. distribute-rgt-in 76.7%

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

      10. distribute-lft-in 76.7%

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

      11. associate-+r+ 76.7%

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

      12. metadata-eval 76.7%

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

      13. metadata-eval 76.7%

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

      14. metadata-eval 76.7%

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

      15. distribute-lft-in 76.7%

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

      16. +-commutative 76.7%

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

      17. distribute-rgt-in 76.7%

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

      18. *-commutative 76.7%

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

      19. associate-*l* 76.7%

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

      20. metadata-eval 76.7%

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

      21. metadata-eval 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if 0.660000000000000031 < z < 1.2e114 or 6.40000000000000011e206 < z < 2.20000000000000011e247

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 95.9%

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

   4. Taylor expanded in y around inf 71.3%

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

      1. associate-*r* 71.4%

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

   6. Simplified 71.4%

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

   if 1.2e114 < z < 6.40000000000000011e206 or 2.20000000000000011e247 < 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 x around inf 83.4%

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

      1. *-commutative 83.4%

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

      2. sub-neg 83.4%

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

      3. distribute-lft-in 83.4%

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

      4. metadata-eval 83.4%

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

      5. metadata-eval 83.4%

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

      6. neg-mul-1 83.4%

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

      7. *-commutative 83.4%

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

      8. associate-*l* 83.4%

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

      9. distribute-rgt-in 83.4%

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

      10. distribute-lft-in 83.4%

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

      11. associate-+r+ 83.4%

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

      12. metadata-eval 83.4%

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

      13. metadata-eval 83.4%

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

      14. metadata-eval 83.4%

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

      15. distribute-lft-in 83.4%

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

      16. +-commutative 83.4%

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

      17. distribute-rgt-in 83.4%

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

      18. *-commutative 83.4%

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

      19. associate-*l* 83.4%

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

      20. metadata-eval 83.4%

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

      21. metadata-eval 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in z around inf 83.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-267}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+114} \lor \neg \left(z \leq 6.4 \cdot 10^{+206}\right) \land z \leq 2.2 \cdot 10^{+247}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 5: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -3.6e-5)
     t_0
     (if (<= z -4e-119)
       (* 4.0 y)
       (if (<= z -4.4e-182)
         (* x -3.0)
         (if (<= z -3.8e-275)
           (* 4.0 y)
           (if (<= z 5e-269) (* x -3.0) (if (<= z 0.5) (* 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 <= -3.6e-5) {
		tmp = t_0;
	} else if (z <= -4e-119) {
		tmp = 4.0 * y;
	} else if (z <= -4.4e-182) {
		tmp = x * -3.0;
	} else if (z <= -3.8e-275) {
		tmp = 4.0 * y;
	} else if (z <= 5e-269) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		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 <= (-3.6d-5)) then
        tmp = t_0
    else if (z <= (-4d-119)) then
        tmp = 4.0d0 * y
    else if (z <= (-4.4d-182)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.8d-275)) then
        tmp = 4.0d0 * y
    else if (z <= 5d-269) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) 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 <= -3.6e-5) {
		tmp = t_0;
	} else if (z <= -4e-119) {
		tmp = 4.0 * y;
	} else if (z <= -4.4e-182) {
		tmp = x * -3.0;
	} else if (z <= -3.8e-275) {
		tmp = 4.0 * y;
	} else if (z <= 5e-269) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		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 <= -3.6e-5:
		tmp = t_0
	elif z <= -4e-119:
		tmp = 4.0 * y
	elif z <= -4.4e-182:
		tmp = x * -3.0
	elif z <= -3.8e-275:
		tmp = 4.0 * y
	elif z <= 5e-269:
		tmp = x * -3.0
	elif z <= 0.5:
		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 <= -3.6e-5)
		tmp = t_0;
	elseif (z <= -4e-119)
		tmp = Float64(4.0 * y);
	elseif (z <= -4.4e-182)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.8e-275)
		tmp = Float64(4.0 * y);
	elseif (z <= 5e-269)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		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 <= -3.6e-5)
		tmp = t_0;
	elseif (z <= -4e-119)
		tmp = 4.0 * y;
	elseif (z <= -4.4e-182)
		tmp = x * -3.0;
	elseif (z <= -3.8e-275)
		tmp = 4.0 * y;
	elseif (z <= 5e-269)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		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, -3.6e-5], t$95$0, If[LessEqual[z, -4e-119], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -4.4e-182], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.8e-275], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 5e-269], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(4.0 * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000009e-5 or 0.5 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 96.3%

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

   if -3.60000000000000009e-5 < z < -4.00000000000000005e-119 or -4.3999999999999999e-182 < z < -3.79999999999999972e-275 or 4.99999999999999979e-269 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 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 x around 0 63.6%

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

   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 -4.00000000000000005e-119 < z < -4.3999999999999999e-182 or -3.79999999999999972e-275 < z < 4.99999999999999979e-269

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. distribute-lft-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. metadata-eval 76.7%

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

      6. neg-mul-1 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. distribute-rgt-in 76.7%

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

      10. distribute-lft-in 76.7%

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

      11. associate-+r+ 76.7%

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

      12. metadata-eval 76.7%

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

      13. metadata-eval 76.7%

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

      14. metadata-eval 76.7%

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

      15. distribute-lft-in 76.7%

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

      16. +-commutative 76.7%

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

      17. distribute-rgt-in 76.7%

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

      18. *-commutative 76.7%

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

      19. associate-*l* 76.7%

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

      20. metadata-eval 76.7%

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

      21. metadata-eval 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-182}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-181}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 145000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -4.1e+14)
     t_1
     (if (<= z -4e-119)
       t_0
       (if (<= z -1.75e-181)
         (* x -3.0)
         (if (<= z -8.5e-275)
           (* 4.0 y)
           (if (<= z 4.2e-269)
             (* x -3.0)
             (if (<= z 145000000.0) 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 <= -4.1e+14) {
		tmp = t_1;
	} else if (z <= -4e-119) {
		tmp = t_0;
	} else if (z <= -1.75e-181) {
		tmp = x * -3.0;
	} else if (z <= -8.5e-275) {
		tmp = 4.0 * y;
	} else if (z <= 4.2e-269) {
		tmp = x * -3.0;
	} else if (z <= 145000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-4.1d+14)) then
        tmp = t_1
    else if (z <= (-4d-119)) then
        tmp = t_0
    else if (z <= (-1.75d-181)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8.5d-275)) then
        tmp = 4.0d0 * y
    else if (z <= 4.2d-269) then
        tmp = x * (-3.0d0)
    else if (z <= 145000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -4.1e+14) {
		tmp = t_1;
	} else if (z <= -4e-119) {
		tmp = t_0;
	} else if (z <= -1.75e-181) {
		tmp = x * -3.0;
	} else if (z <= -8.5e-275) {
		tmp = 4.0 * y;
	} else if (z <= 4.2e-269) {
		tmp = x * -3.0;
	} else if (z <= 145000000.0) {
		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 <= -4.1e+14:
		tmp = t_1
	elif z <= -4e-119:
		tmp = t_0
	elif z <= -1.75e-181:
		tmp = x * -3.0
	elif z <= -8.5e-275:
		tmp = 4.0 * y
	elif z <= 4.2e-269:
		tmp = x * -3.0
	elif z <= 145000000.0:
		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 <= -4.1e+14)
		tmp = t_1;
	elseif (z <= -4e-119)
		tmp = t_0;
	elseif (z <= -1.75e-181)
		tmp = Float64(x * -3.0);
	elseif (z <= -8.5e-275)
		tmp = Float64(4.0 * y);
	elseif (z <= 4.2e-269)
		tmp = Float64(x * -3.0);
	elseif (z <= 145000000.0)
		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 <= -4.1e+14)
		tmp = t_1;
	elseif (z <= -4e-119)
		tmp = t_0;
	elseif (z <= -1.75e-181)
		tmp = x * -3.0;
	elseif (z <= -8.5e-275)
		tmp = 4.0 * y;
	elseif (z <= 4.2e-269)
		tmp = x * -3.0;
	elseif (z <= 145000000.0)
		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, -4.1e+14], t$95$1, If[LessEqual[z, -4e-119], t$95$0, If[LessEqual[z, -1.75e-181], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8.5e-275], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 4.2e-269], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 145000000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1e14 or 1.45e8 < 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 99.7%

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

   3. Taylor expanded in z around inf 99.6%

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

   if -4.1e14 < z < -4.00000000000000005e-119 or 4.20000000000000009e-269 < z < 1.45e8

   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 63.2%

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

   3. Taylor expanded in x around 0 63.9%

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

   if -4.00000000000000005e-119 < z < -1.74999999999999998e-181 or -8.49999999999999952e-275 < z < 4.20000000000000009e-269

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. distribute-lft-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. metadata-eval 76.7%

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

      6. neg-mul-1 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. distribute-rgt-in 76.7%

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

      10. distribute-lft-in 76.7%

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

      11. associate-+r+ 76.7%

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

      12. metadata-eval 76.7%

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

      13. metadata-eval 76.7%

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

      14. metadata-eval 76.7%

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

      15. distribute-lft-in 76.7%

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

      16. +-commutative 76.7%

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

      17. distribute-rgt-in 76.7%

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

      18. *-commutative 76.7%

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

      19. associate-*l* 76.7%

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

      20. metadata-eval 76.7%

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

      21. metadata-eval 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -1.74999999999999998e-181 < z < -8.49999999999999952e-275

   1. Initial program 99.1%

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

   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 x around 0 67.8%

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

   4. Taylor expanded in z around 0 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-119}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-181}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 145000000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 51.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-181}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3.7e-5)
     t_0
     (if (<= z -1e-119)
       (* 4.0 y)
       (if (<= z -4.7e-181)
         (* x -3.0)
         (if (<= z -3.2e-275)
           (* 4.0 y)
           (if (<= z 7.6e-269) (* x -3.0) (if (<= z 0.66) (* 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 <= -3.7e-5) {
		tmp = t_0;
	} else if (z <= -1e-119) {
		tmp = 4.0 * y;
	} else if (z <= -4.7e-181) {
		tmp = x * -3.0;
	} else if (z <= -3.2e-275) {
		tmp = 4.0 * y;
	} else if (z <= 7.6e-269) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		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 <= (-3.7d-5)) then
        tmp = t_0
    else if (z <= (-1d-119)) then
        tmp = 4.0d0 * y
    else if (z <= (-4.7d-181)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.2d-275)) then
        tmp = 4.0d0 * y
    else if (z <= 7.6d-269) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) 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 <= -3.7e-5) {
		tmp = t_0;
	} else if (z <= -1e-119) {
		tmp = 4.0 * y;
	} else if (z <= -4.7e-181) {
		tmp = x * -3.0;
	} else if (z <= -3.2e-275) {
		tmp = 4.0 * y;
	} else if (z <= 7.6e-269) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		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 <= -3.7e-5:
		tmp = t_0
	elif z <= -1e-119:
		tmp = 4.0 * y
	elif z <= -4.7e-181:
		tmp = x * -3.0
	elif z <= -3.2e-275:
		tmp = 4.0 * y
	elif z <= 7.6e-269:
		tmp = x * -3.0
	elif z <= 0.66:
		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 <= -3.7e-5)
		tmp = t_0;
	elseif (z <= -1e-119)
		tmp = Float64(4.0 * y);
	elseif (z <= -4.7e-181)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.2e-275)
		tmp = Float64(4.0 * y);
	elseif (z <= 7.6e-269)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		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 <= -3.7e-5)
		tmp = t_0;
	elseif (z <= -1e-119)
		tmp = 4.0 * y;
	elseif (z <= -4.7e-181)
		tmp = x * -3.0;
	elseif (z <= -3.2e-275)
		tmp = 4.0 * y;
	elseif (z <= 7.6e-269)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		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, -3.7e-5], t$95$0, If[LessEqual[z, -1e-119], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, -4.7e-181], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.2e-275], N[(4.0 * y), $MachinePrecision], If[LessEqual[z, 7.6e-269], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(4.0 * y), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.69999999999999981e-5 or 0.660000000000000031 < z

   1. Initial program 99.8%

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

   2. 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 x around 0 56.8%

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

   4. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   if -3.69999999999999981e-5 < z < -1.00000000000000001e-119 or -4.6999999999999998e-181 < z < -3.2e-275 or 7.6000000000000005e-269 < z < 0.660000000000000031

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 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 x around 0 63.6%

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

   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 -1.00000000000000001e-119 < z < -4.6999999999999998e-181 or -3.2e-275 < z < 7.6000000000000005e-269

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. sub-neg 76.7%

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

      3. distribute-lft-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. metadata-eval 76.7%

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

      6. neg-mul-1 76.7%

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

      7. *-commutative 76.7%

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

      8. associate-*l* 76.7%

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

      9. distribute-rgt-in 76.7%

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

      10. distribute-lft-in 76.7%

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

      11. associate-+r+ 76.7%

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

      12. metadata-eval 76.7%

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

      13. metadata-eval 76.7%

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

      14. metadata-eval 76.7%

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

      15. distribute-lft-in 76.7%

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

      16. +-commutative 76.7%

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

      17. distribute-rgt-in 76.7%

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

      18. *-commutative 76.7%

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

      19. associate-*l* 76.7%

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

      20. metadata-eval 76.7%

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

      21. metadata-eval 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-119}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-181}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-269}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -20000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 51000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -3.6e+40)
     t_1
     (if (<= x -20000.0)
       t_0
       (if (<= x -3.8e-54)
         (* -6.0 (* (- y x) z))
         (if (<= x 51000000000.0) 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 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -3.6e+40) {
		tmp = t_1;
	} else if (x <= -20000.0) {
		tmp = t_0;
	} else if (x <= -3.8e-54) {
		tmp = -6.0 * ((y - x) * z);
	} else if (x <= 51000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-3.6d+40)) then
        tmp = t_1
    else if (x <= (-20000.0d0)) then
        tmp = t_0
    else if (x <= (-3.8d-54)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (x <= 51000000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -3.6e+40) {
		tmp = t_1;
	} else if (x <= -20000.0) {
		tmp = t_0;
	} else if (x <= -3.8e-54) {
		tmp = -6.0 * ((y - x) * z);
	} else if (x <= 51000000000.0) {
		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 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -3.6e+40:
		tmp = t_1
	elif x <= -20000.0:
		tmp = t_0
	elif x <= -3.8e-54:
		tmp = -6.0 * ((y - x) * z)
	elif x <= 51000000000.0:
		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(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -3.6e+40)
		tmp = t_1;
	elseif (x <= -20000.0)
		tmp = t_0;
	elseif (x <= -3.8e-54)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (x <= 51000000000.0)
		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 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -3.6e+40)
		tmp = t_1;
	elseif (x <= -20000.0)
		tmp = t_0;
	elseif (x <= -3.8e-54)
		tmp = -6.0 * ((y - x) * z);
	elseif (x <= 51000000000.0)
		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[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+40], t$95$1, If[LessEqual[x, -20000.0], t$95$0, If[LessEqual[x, -3.8e-54], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 51000000000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.59999999999999996e40 or 5.1e10 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 83.6%

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

      1. *-commutative 83.6%

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

      2. sub-neg 83.6%

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

      3. distribute-lft-in 83.6%

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

      4. metadata-eval 83.6%

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

      5. metadata-eval 83.6%

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

      6. neg-mul-1 83.6%

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

      7. *-commutative 83.6%

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

      8. associate-*l* 83.6%

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

      9. distribute-rgt-in 83.6%

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

      10. distribute-lft-in 83.6%

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

      11. associate-+r+ 83.6%

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

      12. metadata-eval 83.6%

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

      13. metadata-eval 83.6%

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

      14. metadata-eval 83.6%

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

      15. distribute-lft-in 83.6%

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

      16. +-commutative 83.6%

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

      17. distribute-rgt-in 83.6%

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

      18. *-commutative 83.6%

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

      19. associate-*l* 83.6%

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

      20. metadata-eval 83.6%

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

      21. metadata-eval 83.6%

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

   4. Simplified 83.6%

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

   if -3.59999999999999996e40 < x < -2e4 or -3.8000000000000002e-54 < x < 5.1e10

   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 83.5%

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

   3. Taylor expanded in x around 0 83.8%

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

   if -2e4 < x < -3.8000000000000002e-54

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.5%

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

   3. Taylor expanded in z around inf 90.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -20000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 51000000000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 9: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + -6 \cdot z\right)\\ t_1 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1100:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 31500000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* -6.0 z)))) (t_1 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -1.55e+41)
     t_1
     (if (<= x -1100.0)
       t_0
       (if (<= x -1.4e-54)
         (* -6.0 (* (- y x) z))
         (if (<= x 31500000000.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (-6.0 * z));
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.55e+41) {
		tmp = t_1;
	} else if (x <= -1100.0) {
		tmp = t_0;
	} else if (x <= -1.4e-54) {
		tmp = -6.0 * ((y - x) * z);
	} else if (x <= 31500000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (4.0d0 + ((-6.0d0) * z))
    t_1 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-1.55d+41)) then
        tmp = t_1
    else if (x <= (-1100.0d0)) then
        tmp = t_0
    else if (x <= (-1.4d-54)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (x <= 31500000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (-6.0 * z));
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -1.55e+41) {
		tmp = t_1;
	} else if (x <= -1100.0) {
		tmp = t_0;
	} else if (x <= -1.4e-54) {
		tmp = -6.0 * ((y - x) * z);
	} else if (x <= 31500000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (-6.0 * z))
	t_1 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -1.55e+41:
		tmp = t_1
	elif x <= -1100.0:
		tmp = t_0
	elif x <= -1.4e-54:
		tmp = -6.0 * ((y - x) * z)
	elif x <= 31500000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(-6.0 * z)))
	t_1 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -1.55e+41)
		tmp = t_1;
	elseif (x <= -1100.0)
		tmp = t_0;
	elseif (x <= -1.4e-54)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (x <= 31500000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (-6.0 * z));
	t_1 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -1.55e+41)
		tmp = t_1;
	elseif (x <= -1100.0)
		tmp = t_0;
	elseif (x <= -1.4e-54)
		tmp = -6.0 * ((y - x) * z);
	elseif (x <= 31500000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+41], t$95$1, If[LessEqual[x, -1100.0], t$95$0, If[LessEqual[x, -1.4e-54], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 31500000000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e41 or 3.15e10 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 83.6%

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

      1. *-commutative 83.6%

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

      2. sub-neg 83.6%

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

      3. distribute-lft-in 83.6%

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

      4. metadata-eval 83.6%

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

      5. metadata-eval 83.6%

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

      6. neg-mul-1 83.6%

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

      7. *-commutative 83.6%

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

      8. associate-*l* 83.6%

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

      9. distribute-rgt-in 83.6%

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

      10. distribute-lft-in 83.6%

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

      11. associate-+r+ 83.6%

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

      12. metadata-eval 83.6%

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

      13. metadata-eval 83.6%

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

      14. metadata-eval 83.6%

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

      15. distribute-lft-in 83.6%

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

      16. +-commutative 83.6%

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

      17. distribute-rgt-in 83.6%

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

      18. *-commutative 83.6%

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

      19. associate-*l* 83.6%

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

      20. metadata-eval 83.6%

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

      21. metadata-eval 83.6%

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

   4. Simplified 83.6%

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

   if -1.55e41 < x < -1100 or -1.4000000000000001e-54 < x < 3.15e10

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 84.0%

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

   if -1100 < x < -1.4000000000000001e-54

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.5%

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

   3. Taylor expanded in z around inf 90.5%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -1100:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-54}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 31500000000:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 10: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3 + 4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.5) (+ (* x -3.0) (* 4.0 y)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = (x * -3.0) + (4.0 * y);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.5d0) then
        tmp = (x * (-3.0d0)) + (4.0d0 * y)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = (x * -3.0) + (4.0 * y);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.5:
		tmp = (x * -3.0) + (4.0 * y)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.5)
		tmp = Float64(Float64(x * -3.0) + Float64(4.0 * y));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.5)
		tmp = (x * -3.0) + (4.0 * y);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(N[(x * -3.0), $MachinePrecision] + N[(4.0 * y), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

   2. 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 96.4%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 99.6%

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

   3. Taylor expanded in z around 0 98.0%

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

   if 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 97.6%

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

      1. associate-*r* 97.7%

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

      2. *-commutative 97.7%

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

      3. associate-*l* 97.7%

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

   5. Simplified 97.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3 + 4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

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: 38.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 3000000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e+19)
   (* x -3.0)
   (if (<= x 3000000000000.0) (* 4.0 y) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+19) {
		tmp = x * -3.0;
	} else if (x <= 3000000000000.0) {
		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 <= (-3.5d+19)) then
        tmp = x * (-3.0d0)
    else if (x <= 3000000000000.0d0) 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 <= -3.5e+19) {
		tmp = x * -3.0;
	} else if (x <= 3000000000000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e+19:
		tmp = x * -3.0
	elif x <= 3000000000000.0:
		tmp = 4.0 * y
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e+19)
		tmp = Float64(x * -3.0);
	elseif (x <= 3000000000000.0)
		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 <= -3.5e+19)
		tmp = x * -3.0;
	elseif (x <= 3000000000000.0)
		tmp = 4.0 * y;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e+19], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 3000000000000.0], N[(4.0 * y), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e19 or 3e12 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

      2. sub-neg 81.2%

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

      3. distribute-lft-in 81.2%

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

      4. metadata-eval 81.2%

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

      5. metadata-eval 81.2%

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

      6. neg-mul-1 81.2%

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

      7. *-commutative 81.2%

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

      8. associate-*l* 81.2%

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

      9. distribute-rgt-in 81.2%

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

      10. distribute-lft-in 81.2%

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

      11. associate-+r+ 81.2%

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

      12. metadata-eval 81.2%

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

      13. metadata-eval 81.2%

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

      14. metadata-eval 81.2%

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

      15. distribute-lft-in 81.2%

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

      16. +-commutative 81.2%

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

      17. distribute-rgt-in 81.2%

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

      18. *-commutative 81.2%

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

      19. associate-*l* 81.2%

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

      20. metadata-eval 81.2%

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

      21. metadata-eval 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in z around 0 38.2%

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

      1. *-commutative 38.2%

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

   7. Simplified 38.2%

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

   if -3.5e19 < x < 3e12

   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. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in z around 0 40.9%

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

      1. *-commutative 40.9%

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

   6. Simplified 40.9%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 3000000000000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 14: 26.0% 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 47.6%

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

   1. *-commutative 47.6%

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

   2. sub-neg 47.6%

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

   3. distribute-lft-in 47.6%

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

   4. metadata-eval 47.6%

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

   5. metadata-eval 47.6%

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

   6. neg-mul-1 47.6%

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

   7. *-commutative 47.6%

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

   8. associate-*l* 47.6%

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

   9. distribute-rgt-in 47.6%

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

   10. distribute-lft-in 47.6%

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

   11. associate-+r+ 47.6%

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

   12. metadata-eval 47.6%

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

   13. metadata-eval 47.6%

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

   14. metadata-eval 47.6%

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

   15. distribute-lft-in 47.6%

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

   16. +-commutative 47.6%

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

   17. distribute-rgt-in 47.6%

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

   18. *-commutative 47.6%

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

   19. associate-*l* 47.6%

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

   20. metadata-eval 47.6%

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

   21. metadata-eval 47.6%

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

4. Simplified 47.6%

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

5. Taylor expanded in z around 0 23.4%

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

   1. *-commutative 23.4%

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

7. Simplified 23.4%

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

8. Final simplification 23.4%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023229 
(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))))