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

Percentage Accurate: 99.5% → 99.8%

Time: 10.8s

Alternatives: 16

Speedup: 1.2×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. +-commutative 99.3%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-23}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+64} \lor \neg \left(z \leq 7.5 \cdot 10^{+145}\right) \land z \leq 5.6 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1.3e+94)
     t_0
     (if (<= z -430000.0)
       t_1
       (if (<= z -3.1e-23)
         (* x -3.0)
         (if (<= z -7.2e-122)
           (* y 4.0)
           (if (<= z -4.6e-206)
             (* x -3.0)
             (if (<= z 0.65)
               (* y 4.0)
               (if (or (<= z 4.6e+64)
                       (and (not (<= z 7.5e+145)) (<= z 5.6e+214)))
                 t_0
                 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.3e+94) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -3.1e-23) {
		tmp = x * -3.0;
	} else if (z <= -7.2e-122) {
		tmp = y * 4.0;
	} else if (z <= -4.6e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 4.6e+64) || (!(z <= 7.5e+145) && (z <= 5.6e+214))) {
		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 * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1.3d+94)) then
        tmp = t_0
    else if (z <= (-430000.0d0)) then
        tmp = t_1
    else if (z <= (-3.1d-23)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.2d-122)) then
        tmp = y * 4.0d0
    else if (z <= (-4.6d-206)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if ((z <= 4.6d+64) .or. (.not. (z <= 7.5d+145)) .and. (z <= 5.6d+214)) 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 * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.3e+94) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -3.1e-23) {
		tmp = x * -3.0;
	} else if (z <= -7.2e-122) {
		tmp = y * 4.0;
	} else if (z <= -4.6e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 4.6e+64) || (!(z <= 7.5e+145) && (z <= 5.6e+214))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.3e+94:
		tmp = t_0
	elif z <= -430000.0:
		tmp = t_1
	elif z <= -3.1e-23:
		tmp = x * -3.0
	elif z <= -7.2e-122:
		tmp = y * 4.0
	elif z <= -4.6e-206:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif (z <= 4.6e+64) or (not (z <= 7.5e+145) and (z <= 5.6e+214)):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.3e+94)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -3.1e-23)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.2e-122)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.6e-206)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif ((z <= 4.6e+64) || (!(z <= 7.5e+145) && (z <= 5.6e+214)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.3e+94)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -3.1e-23)
		tmp = x * -3.0;
	elseif (z <= -7.2e-122)
		tmp = y * 4.0;
	elseif (z <= -4.6e-206)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif ((z <= 4.6e+64) || (~((z <= 7.5e+145)) && (z <= 5.6e+214)))
		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 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+94], t$95$0, If[LessEqual[z, -430000.0], t$95$1, If[LessEqual[z, -3.1e-23], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.2e-122], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.6e-206], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 4.6e+64], And[N[Not[LessEqual[z, 7.5e+145]], $MachinePrecision], LessEqual[z, 5.6e+214]]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e94 or 0.650000000000000022 < z < 4.6e64 or 7.50000000000000006e145 < z < 5.5999999999999996e214

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.5%

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

      1. associate-*r* 98.6%

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

      2. *-commutative 98.6%

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

      3. associate-*r* 98.4%

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

   8. Simplified 98.4%

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

   9. Taylor expanded in y around inf 68.1%

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

       1. *-commutative 68.1%

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

   11. Simplified 68.1%

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

   if -1.3e94 < z < -4.3e5 or 4.6e64 < z < 7.50000000000000006e145 or 5.5999999999999996e214 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 99.0%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*r* 99.1%

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

   8. Simplified 99.1%

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

   9. Taylor expanded in y around 0 63.9%

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

   if -4.3e5 < z < -3.0999999999999999e-23 or -7.19999999999999989e-122 < z < -4.6e-206

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. distribute-rgt-in 60.2%

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

      3. metadata-eval 60.2%

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

      4. distribute-lft-neg-in 60.2%

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

      5. associate-+r+ 60.2%

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

      6. metadata-eval 60.2%

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

      7. distribute-rgt-neg-in 60.2%

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

      8. metadata-eval 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -3.0999999999999999e-23 < z < -7.19999999999999989e-122 or -4.6e-206 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 55.2%

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

   7. Taylor expanded in z around 0 54.7%

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

      1. *-commutative 54.7%

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

   9. Simplified 54.7%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+94}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-23}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-122}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+64} \lor \neg \left(z \leq 7.5 \cdot 10^{+145}\right) \land z \leq 5.6 \cdot 10^{+214}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-121}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-208}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+212}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1.95e+93)
     t_0
     (if (<= z -430000.0)
       t_1
       (if (<= z -3.5e-27)
         (* x -3.0)
         (if (<= z -8e-121)
           (* y 4.0)
           (if (<= z -3.6e-208)
             (* x -3.0)
             (if (<= z 0.65)
               (* y 4.0)
               (if (<= z 2.4e+64)
                 t_0
                 (if (<= z 1.82e+148)
                   (* x (* z 6.0))
                   (if (<= z 1.6e+212) t_0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.95e+93) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -3.5e-27) {
		tmp = x * -3.0;
	} else if (z <= -8e-121) {
		tmp = y * 4.0;
	} else if (z <= -3.6e-208) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 2.4e+64) {
		tmp = t_0;
	} else if (z <= 1.82e+148) {
		tmp = x * (z * 6.0);
	} else if (z <= 1.6e+212) {
		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 * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1.95d+93)) then
        tmp = t_0
    else if (z <= (-430000.0d0)) then
        tmp = t_1
    else if (z <= (-3.5d-27)) then
        tmp = x * (-3.0d0)
    else if (z <= (-8d-121)) then
        tmp = y * 4.0d0
    else if (z <= (-3.6d-208)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 2.4d+64) then
        tmp = t_0
    else if (z <= 1.82d+148) then
        tmp = x * (z * 6.0d0)
    else if (z <= 1.6d+212) 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 * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.95e+93) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -3.5e-27) {
		tmp = x * -3.0;
	} else if (z <= -8e-121) {
		tmp = y * 4.0;
	} else if (z <= -3.6e-208) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 2.4e+64) {
		tmp = t_0;
	} else if (z <= 1.82e+148) {
		tmp = x * (z * 6.0);
	} else if (z <= 1.6e+212) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.95e+93:
		tmp = t_0
	elif z <= -430000.0:
		tmp = t_1
	elif z <= -3.5e-27:
		tmp = x * -3.0
	elif z <= -8e-121:
		tmp = y * 4.0
	elif z <= -3.6e-208:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 2.4e+64:
		tmp = t_0
	elif z <= 1.82e+148:
		tmp = x * (z * 6.0)
	elif z <= 1.6e+212:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.95e+93)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -3.5e-27)
		tmp = Float64(x * -3.0);
	elseif (z <= -8e-121)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.6e-208)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.4e+64)
		tmp = t_0;
	elseif (z <= 1.82e+148)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= 1.6e+212)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.95e+93)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -3.5e-27)
		tmp = x * -3.0;
	elseif (z <= -8e-121)
		tmp = y * 4.0;
	elseif (z <= -3.6e-208)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 2.4e+64)
		tmp = t_0;
	elseif (z <= 1.82e+148)
		tmp = x * (z * 6.0);
	elseif (z <= 1.6e+212)
		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 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+93], t$95$0, If[LessEqual[z, -430000.0], t$95$1, If[LessEqual[z, -3.5e-27], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -8e-121], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.6e-208], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.4e+64], t$95$0, If[LessEqual[z, 1.82e+148], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+212], t$95$0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.9500000000000001e93 or 0.650000000000000022 < z < 2.39999999999999999e64 or 1.8200000000000001e148 < z < 1.5999999999999999e212

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.5%

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

      1. associate-*r* 98.6%

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

      2. *-commutative 98.6%

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

      3. associate-*r* 98.4%

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

   8. Simplified 98.4%

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

   9. Taylor expanded in y around inf 68.1%

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

       1. *-commutative 68.1%

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

   11. Simplified 68.1%

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

   if -1.9500000000000001e93 < z < -4.3e5 or 1.5999999999999999e212 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*r* 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 63.2%

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

   if -4.3e5 < z < -3.5000000000000001e-27 or -7.9999999999999998e-121 < z < -3.5999999999999998e-208

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. distribute-rgt-in 60.2%

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

      3. metadata-eval 60.2%

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

      4. distribute-lft-neg-in 60.2%

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

      5. associate-+r+ 60.2%

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

      6. metadata-eval 60.2%

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

      7. distribute-rgt-neg-in 60.2%

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

      8. metadata-eval 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -3.5000000000000001e-27 < z < -7.9999999999999998e-121 or -3.5999999999999998e-208 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 55.2%

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

   7. Taylor expanded in z around 0 54.7%

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

      1. *-commutative 54.7%

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

   9. Simplified 54.7%

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

   if 2.39999999999999999e64 < z < 1.8200000000000001e148

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. distribute-rgt-in 65.1%

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

      3. metadata-eval 65.1%

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

      4. distribute-lft-neg-in 65.1%

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

      5. associate-+r+ 65.1%

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

      6. metadata-eval 65.1%

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

      7. distribute-rgt-neg-in 65.1%

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

      8. metadata-eval 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in z around inf 65.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+93}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-121}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-208}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+212}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+215}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -2.1e+93)
     t_0
     (if (<= z -430000.0)
       t_1
       (if (<= z -5.6e-27)
         (* x -3.0)
         (if (<= z -2.6e-120)
           (* y 4.0)
           (if (<= z -4.8e-206)
             (* x -3.0)
             (if (<= z 0.65)
               (* y 4.0)
               (if (<= z 9.5e+64)
                 (* y (* z -6.0))
                 (if (<= z 6.5e+147)
                   (* x (* z 6.0))
                   (if (<= z 1.2e+215) t_0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.1e+93) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -5.6e-27) {
		tmp = x * -3.0;
	} else if (z <= -2.6e-120) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 9.5e+64) {
		tmp = y * (z * -6.0);
	} else if (z <= 6.5e+147) {
		tmp = x * (z * 6.0);
	} else if (z <= 1.2e+215) {
		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 * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-2.1d+93)) then
        tmp = t_0
    else if (z <= (-430000.0d0)) then
        tmp = t_1
    else if (z <= (-5.6d-27)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.6d-120)) then
        tmp = y * 4.0d0
    else if (z <= (-4.8d-206)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 9.5d+64) then
        tmp = y * (z * (-6.0d0))
    else if (z <= 6.5d+147) then
        tmp = x * (z * 6.0d0)
    else if (z <= 1.2d+215) 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 * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.1e+93) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -5.6e-27) {
		tmp = x * -3.0;
	} else if (z <= -2.6e-120) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-206) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 9.5e+64) {
		tmp = y * (z * -6.0);
	} else if (z <= 6.5e+147) {
		tmp = x * (z * 6.0);
	} else if (z <= 1.2e+215) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.1e+93:
		tmp = t_0
	elif z <= -430000.0:
		tmp = t_1
	elif z <= -5.6e-27:
		tmp = x * -3.0
	elif z <= -2.6e-120:
		tmp = y * 4.0
	elif z <= -4.8e-206:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 9.5e+64:
		tmp = y * (z * -6.0)
	elif z <= 6.5e+147:
		tmp = x * (z * 6.0)
	elif z <= 1.2e+215:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.1e+93)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -5.6e-27)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.6e-120)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.8e-206)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.5e+64)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= 6.5e+147)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= 1.2e+215)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.1e+93)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -5.6e-27)
		tmp = x * -3.0;
	elseif (z <= -2.6e-120)
		tmp = y * 4.0;
	elseif (z <= -4.8e-206)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 9.5e+64)
		tmp = y * (z * -6.0);
	elseif (z <= 6.5e+147)
		tmp = x * (z * 6.0);
	elseif (z <= 1.2e+215)
		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 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+93], t$95$0, If[LessEqual[z, -430000.0], t$95$1, If[LessEqual[z, -5.6e-27], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.6e-120], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.8e-206], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.5e+64], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+147], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+215], t$95$0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.0999999999999998e93 or 6.5e147 < z < 1.2e215

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 68.1%

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

       1. *-commutative 68.1%

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

   11. Simplified 68.1%

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

   if -2.0999999999999998e93 < z < -4.3e5 or 1.2e215 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*r* 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in y around 0 63.2%

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

   if -4.3e5 < z < -5.5999999999999999e-27 or -2.6000000000000001e-120 < z < -4.7999999999999999e-206

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. distribute-rgt-in 60.2%

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

      3. metadata-eval 60.2%

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

      4. distribute-lft-neg-in 60.2%

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

      5. associate-+r+ 60.2%

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

      6. metadata-eval 60.2%

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

      7. distribute-rgt-neg-in 60.2%

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

      8. metadata-eval 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -5.5999999999999999e-27 < z < -2.6000000000000001e-120 or -4.7999999999999999e-206 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 55.2%

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

   7. Taylor expanded in z around 0 54.7%

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

      1. *-commutative 54.7%

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

   9. Simplified 54.7%

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

   if 0.650000000000000022 < z < 9.50000000000000028e64

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.2%

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

   6. Taylor expanded in z around inf 92.6%

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

      1. associate-*r* 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*r* 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around inf 68.3%

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

       1. associate-*r* 68.3%

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

       2. *-commutative 68.3%

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

       3. associate-*r* 68.4%

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

   11. Simplified 68.4%

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

   if 9.50000000000000028e64 < z < 6.5e147

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. distribute-rgt-in 65.1%

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

      3. metadata-eval 65.1%

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

      4. distribute-lft-neg-in 65.1%

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

      5. associate-+r+ 65.1%

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

      6. metadata-eval 65.1%

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

      7. distribute-rgt-neg-in 65.1%

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

      8. metadata-eval 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in z around inf 65.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+93}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-120}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+215}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-207}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+210}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* z (* x 6.0))))
   (if (<= z -2.2e+54)
     t_0
     (if (<= z -430000.0)
       t_1
       (if (<= z -6.5e-29)
         (* x -3.0)
         (if (<= z -3.8e-116)
           (* y 4.0)
           (if (<= z -5.4e-207)
             (* x -3.0)
             (if (<= z 0.65)
               (* y 4.0)
               (if (<= z 8.2e+64)
                 (* y (* z -6.0))
                 (if (<= z 6.2e+146)
                   (* x (* z 6.0))
                   (if (<= z 7.5e+210) t_0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -2.2e+54) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -6.5e-29) {
		tmp = x * -3.0;
	} else if (z <= -3.8e-116) {
		tmp = y * 4.0;
	} else if (z <= -5.4e-207) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 8.2e+64) {
		tmp = y * (z * -6.0);
	} else if (z <= 6.2e+146) {
		tmp = x * (z * 6.0);
	} else if (z <= 7.5e+210) {
		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 * z)
    t_1 = z * (x * 6.0d0)
    if (z <= (-2.2d+54)) then
        tmp = t_0
    else if (z <= (-430000.0d0)) then
        tmp = t_1
    else if (z <= (-6.5d-29)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.8d-116)) then
        tmp = y * 4.0d0
    else if (z <= (-5.4d-207)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 8.2d+64) then
        tmp = y * (z * (-6.0d0))
    else if (z <= 6.2d+146) then
        tmp = x * (z * 6.0d0)
    else if (z <= 7.5d+210) 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 * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -2.2e+54) {
		tmp = t_0;
	} else if (z <= -430000.0) {
		tmp = t_1;
	} else if (z <= -6.5e-29) {
		tmp = x * -3.0;
	} else if (z <= -3.8e-116) {
		tmp = y * 4.0;
	} else if (z <= -5.4e-207) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 8.2e+64) {
		tmp = y * (z * -6.0);
	} else if (z <= 6.2e+146) {
		tmp = x * (z * 6.0);
	} else if (z <= 7.5e+210) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = z * (x * 6.0)
	tmp = 0
	if z <= -2.2e+54:
		tmp = t_0
	elif z <= -430000.0:
		tmp = t_1
	elif z <= -6.5e-29:
		tmp = x * -3.0
	elif z <= -3.8e-116:
		tmp = y * 4.0
	elif z <= -5.4e-207:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 8.2e+64:
		tmp = y * (z * -6.0)
	elif z <= 6.2e+146:
		tmp = x * (z * 6.0)
	elif z <= 7.5e+210:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -2.2e+54)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -6.5e-29)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.8e-116)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.4e-207)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.2e+64)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= 6.2e+146)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= 7.5e+210)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -2.2e+54)
		tmp = t_0;
	elseif (z <= -430000.0)
		tmp = t_1;
	elseif (z <= -6.5e-29)
		tmp = x * -3.0;
	elseif (z <= -3.8e-116)
		tmp = y * 4.0;
	elseif (z <= -5.4e-207)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 8.2e+64)
		tmp = y * (z * -6.0);
	elseif (z <= 6.2e+146)
		tmp = x * (z * 6.0);
	elseif (z <= 7.5e+210)
		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 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+54], t$95$0, If[LessEqual[z, -430000.0], t$95$1, If[LessEqual[z, -6.5e-29], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.8e-116], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.4e-207], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.2e+64], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+146], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+210], t$95$0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.1999999999999999e54 or 6.2000000000000004e146 < z < 7.5e210

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 65.4%

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

       1. *-commutative 65.4%

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

   11. Simplified 65.4%

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

   if -2.1999999999999999e54 < z < -4.3e5 or 7.5e210 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.6%

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

      2. *-commutative 98.6%

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

      3. associate-*r* 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in y around 0 66.5%

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

       1. *-commutative 66.5%

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

   11. Simplified 66.5%

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

   if -4.3e5 < z < -6.5e-29 or -3.8000000000000001e-116 < z < -5.4e-207

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. distribute-rgt-in 60.2%

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

      3. metadata-eval 60.2%

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

      4. distribute-lft-neg-in 60.2%

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

      5. associate-+r+ 60.2%

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

      6. metadata-eval 60.2%

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

      7. distribute-rgt-neg-in 60.2%

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

      8. metadata-eval 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -6.5e-29 < z < -3.8000000000000001e-116 or -5.4e-207 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 55.2%

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

   7. Taylor expanded in z around 0 54.7%

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

      1. *-commutative 54.7%

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

   9. Simplified 54.7%

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

   if 0.650000000000000022 < z < 8.19999999999999956e64

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.2%

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

   6. Taylor expanded in z around inf 92.6%

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

      1. associate-*r* 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*r* 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around inf 68.3%

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

       1. associate-*r* 68.3%

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

       2. *-commutative 68.3%

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

       3. associate-*r* 68.4%

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

   11. Simplified 68.4%

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

   if 8.19999999999999956e64 < z < 6.2000000000000004e146

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 65.1%

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

      1. sub-neg 65.1%

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

      2. distribute-rgt-in 65.1%

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

      3. metadata-eval 65.1%

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

      4. distribute-lft-neg-in 65.1%

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

      5. associate-+r+ 65.1%

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

      6. metadata-eval 65.1%

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

      7. distribute-rgt-neg-in 65.1%

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

      8. metadata-eval 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in z around inf 65.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -430000:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-207}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+210}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-208}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -3600000.0)
     t_1
     (if (<= z -6.2e-119)
       t_0
       (if (<= z -3.7e-208) (* x -3.0) (if (<= z 4e+14) 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 <= -3600000.0) {
		tmp = t_1;
	} else if (z <= -6.2e-119) {
		tmp = t_0;
	} else if (z <= -3.7e-208) {
		tmp = x * -3.0;
	} else if (z <= 4e+14) {
		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 <= (-3600000.0d0)) then
        tmp = t_1
    else if (z <= (-6.2d-119)) then
        tmp = t_0
    else if (z <= (-3.7d-208)) then
        tmp = x * (-3.0d0)
    else if (z <= 4d+14) 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 <= -3600000.0) {
		tmp = t_1;
	} else if (z <= -6.2e-119) {
		tmp = t_0;
	} else if (z <= -3.7e-208) {
		tmp = x * -3.0;
	} else if (z <= 4e+14) {
		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 <= -3600000.0:
		tmp = t_1
	elif z <= -6.2e-119:
		tmp = t_0
	elif z <= -3.7e-208:
		tmp = x * -3.0
	elif z <= 4e+14:
		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 <= -3600000.0)
		tmp = t_1;
	elseif (z <= -6.2e-119)
		tmp = t_0;
	elseif (z <= -3.7e-208)
		tmp = Float64(x * -3.0);
	elseif (z <= 4e+14)
		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 <= -3600000.0)
		tmp = t_1;
	elseif (z <= -6.2e-119)
		tmp = t_0;
	elseif (z <= -3.7e-208)
		tmp = x * -3.0;
	elseif (z <= 4e+14)
		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, -3600000.0], t$95$1, If[LessEqual[z, -6.2e-119], t$95$0, If[LessEqual[z, -3.7e-208], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4e+14], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e6 or 4e14 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 99.4%

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

   if -3.6e6 < z < -6.19999999999999956e-119 or -3.7000000000000002e-208 < z < 4e14

   1. Initial program 98.7%

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

      1. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 56.3%

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

   if -6.19999999999999956e-119 < z < -3.7000000000000002e-208

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 62.7%

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

      1. sub-neg 62.7%

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

      2. distribute-rgt-in 62.7%

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

      3. metadata-eval 62.7%

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

      4. distribute-lft-neg-in 62.7%

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

      5. associate-+r+ 62.7%

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

      6. metadata-eval 62.7%

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

      7. distribute-rgt-neg-in 62.7%

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

      8. metadata-eval 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. *-commutative 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3600000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-208}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+14}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0028 \lor \neg \left(z \leq 0.64\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0028) (not (<= z 0.64))) (* -6.0 (* (- y x) z)) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0028) || !(z <= 0.64)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.0028d0)) .or. (.not. (z <= 0.64d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0028) || !(z <= 0.64)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0028) or not (z <= 0.64):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0028) || !(z <= 0.64))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0028) || ~((z <= 0.64)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0028], N[Not[LessEqual[z, 0.64]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00279999999999999997 or 0.640000000000000013 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 98.4%

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

   if -0.00279999999999999997 < z < 0.640000000000000013

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 51.1%

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

   7. Taylor expanded in z around 0 50.4%

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

      1. *-commutative 50.4%

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

   9. Simplified 50.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0028 \lor \neg \left(z \leq 0.64\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-28} \lor \neg \left(y \leq 1.6 \cdot 10^{-22}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e-28) (not (<= y 1.6e-22)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-28) || !(y <= 1.6e-22)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.9d-28)) .or. (.not. (y <= 1.6d-22))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-28) || !(y <= 1.6e-22)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e-28) or not (y <= 1.6e-22):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e-28) || !(y <= 1.6e-22))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e-28) || ~((y <= 1.6e-22)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e-28], N[Not[LessEqual[y, 1.6e-22]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000005e-28 or 1.59999999999999994e-22 < y

   1. Initial program 99.1%

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

      1. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 94.1%

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

   6. Taylor expanded in y around inf 79.4%

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

   if -1.90000000000000005e-28 < y < 1.59999999999999994e-22

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. sub-neg 85.4%

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

      2. distribute-rgt-in 85.4%

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

      3. metadata-eval 85.4%

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

      4. distribute-lft-neg-in 85.4%

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

      5. associate-+r+ 85.4%

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

      6. metadata-eval 85.4%

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

      7. distribute-rgt-neg-in 85.4%

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

      8. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-28} \lor \neg \left(y \leq 1.6 \cdot 10^{-22}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-24} \lor \neg \left(y \leq 4 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e-24) (not (<= y 4e-30)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e-24) || !(y <= 4e-30)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.8d-24)) .or. (.not. (y <= 4d-30))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e-24) || !(y <= 4e-30)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e-24) or not (y <= 4e-30):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e-24) || !(y <= 4e-30))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e-24) || ~((y <= 4e-30)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e-24], N[Not[LessEqual[y, 4e-30]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999996e-24 or 4e-30 < y

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 79.6%

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

   if -4.7999999999999996e-24 < y < 4e-30

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. sub-neg 85.4%

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

      2. distribute-rgt-in 85.4%

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

      3. metadata-eval 85.4%

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

      4. distribute-lft-neg-in 85.4%

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

      5. associate-+r+ 85.4%

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

      6. metadata-eval 85.4%

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

      7. distribute-rgt-neg-in 85.4%

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

      8. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-24} \lor \neg \left(y \leq 4 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.52) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} 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 <= (-0.6d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.52d0) then
        tmp = x + ((y - x) * 4.0d0)
    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 <= -0.6) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.52:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.52)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	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 <= -0.6)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.52)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.3%

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

   if -0.599999999999999978 < z < 0.52000000000000002

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 98.5%

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

   if 0.52000000000000002 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.7%

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

      2. *-commutative 98.7%

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

      3. associate-*r* 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.65) (+ (* x -3.0) (* y 4.0)) (* 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 <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} 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 <= 0.65d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    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 <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} 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 <= 0.65:
		tmp = (x * -3.0) + (y * 4.0)
	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 <= 0.65)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	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 <= 0.65)
		tmp = (x * -3.0) + (y * 4.0);
	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, 0.65], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $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 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.3%

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

   if -0.57999999999999996 < z < 0.650000000000000022

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in z around 0 98.5%

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

   if 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.7%

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

      2. *-commutative 98.7%

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

      3. associate-*r* 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.68) (not (<= z 0.65))) (* -6.0 (* y z)) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.68) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.68d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.68) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.68) or not (z <= 0.65):
		tmp = -6.0 * (y * z)
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.68) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.68) || ~((z <= 0.65)))
		tmp = -6.0 * (y * z);
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.68], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.680000000000000049 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 98.4%

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

      1. associate-*r* 98.5%

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

      2. *-commutative 98.5%

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

      3. associate-*r* 98.4%

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

   8. Simplified 98.4%

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

   9. Taylor expanded in y around inf 52.4%

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

       1. *-commutative 52.4%

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

   11. Simplified 52.4%

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

   if -0.680000000000000049 < z < 0.650000000000000022

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 51.1%

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

   7. Taylor expanded in z around 0 50.4%

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

      1. *-commutative 50.4%

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

   9. Simplified 50.4%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in z around 0 99.7%

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

6. Final simplification 99.7%

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

Alternative 14: 38.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-15} \lor \neg \left(x \leq 2.8 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e-15) (not (<= x 2.8e-78))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-15) || !(x <= 2.8e-78)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.5d-15)) .or. (.not. (x <= 2.8d-78))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e-15) || !(x <= 2.8e-78)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e-15) or not (x <= 2.8e-78):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e-15) || !(x <= 2.8e-78))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e-15) || ~((x <= 2.8e-78)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e-15], N[Not[LessEqual[x, 2.8e-78]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999991e-15 or 2.80000000000000024e-78 < x

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 72.6%

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

      1. sub-neg 72.6%

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

      2. distribute-rgt-in 72.6%

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

      3. metadata-eval 72.6%

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

      4. distribute-lft-neg-in 72.6%

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

      5. associate-+r+ 72.6%

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

      6. metadata-eval 72.6%

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

      7. distribute-rgt-neg-in 72.6%

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

      8. metadata-eval 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in z around 0 35.8%

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

      1. *-commutative 35.8%

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

   10. Simplified 35.8%

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

   if -6.49999999999999991e-15 < x < 2.80000000000000024e-78

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 79.6%

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

   7. Taylor expanded in z around 0 39.4%

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

      1. *-commutative 39.4%

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

   9. Simplified 39.4%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-15} \lor \neg \left(x \leq 2.8 \cdot 10^{-78}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

5. Final simplification 99.3%

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

Alternative 16: 26.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. metadata-eval 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in x around inf 50.2%

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

   1. sub-neg 50.2%

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

   2. distribute-rgt-in 50.2%

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

   3. metadata-eval 50.2%

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

   4. distribute-lft-neg-in 50.2%

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

   5. associate-+r+ 50.2%

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

   6. metadata-eval 50.2%

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

   7. distribute-rgt-neg-in 50.2%

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

   8. metadata-eval 50.2%

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

7. Simplified 50.2%

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

8. Taylor expanded in z around 0 23.3%

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

   1. *-commutative 23.3%

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

10. Simplified 23.3%

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

11. Final simplification 23.3%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024075 
(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))))