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

Percentage Accurate: 99.5% → 99.7%

Time: 11.2s

Alternatives: 15

Speedup: 1.2×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-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. +-commutative 99.8%

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

   6. distribute-lft-in 99.8%

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

   7. distribute-rgt-neg-out 99.8%

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

   8. *-commutative 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. fma-define 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.7% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-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 3: 50.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+233}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+165}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.00052:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+205} \lor \neg \left(z \leq 3.2 \cdot 10^{+249}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.85e+233)
     t_0
     (if (<= z -8.2e+214)
       t_1
       (if (<= z -9e+165)
         t_0
         (if (<= z -0.00052)
           t_1
           (if (<= z -2.15e-247)
             (* x -3.0)
             (if (<= z 2.1e-286)
               (* y 4.0)
               (if (<= z 8.6e-205)
                 (* x -3.0)
                 (if (<= z 490000.0)
                   (* y 4.0)
                   (if (or (<= z 3.15e+205) (not (<= z 3.2e+249)))
                     t_1
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.85e+233) {
		tmp = t_0;
	} else if (z <= -8.2e+214) {
		tmp = t_1;
	} else if (z <= -9e+165) {
		tmp = t_0;
	} else if (z <= -0.00052) {
		tmp = t_1;
	} else if (z <= -2.15e-247) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-286) {
		tmp = y * 4.0;
	} else if (z <= 8.6e-205) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else if ((z <= 3.15e+205) || !(z <= 3.2e+249)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-1.85d+233)) then
        tmp = t_0
    else if (z <= (-8.2d+214)) then
        tmp = t_1
    else if (z <= (-9d+165)) then
        tmp = t_0
    else if (z <= (-0.00052d0)) then
        tmp = t_1
    else if (z <= (-2.15d-247)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.1d-286) then
        tmp = y * 4.0d0
    else if (z <= 8.6d-205) then
        tmp = x * (-3.0d0)
    else if (z <= 490000.0d0) then
        tmp = y * 4.0d0
    else if ((z <= 3.15d+205) .or. (.not. (z <= 3.2d+249))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.85e+233) {
		tmp = t_0;
	} else if (z <= -8.2e+214) {
		tmp = t_1;
	} else if (z <= -9e+165) {
		tmp = t_0;
	} else if (z <= -0.00052) {
		tmp = t_1;
	} else if (z <= -2.15e-247) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-286) {
		tmp = y * 4.0;
	} else if (z <= 8.6e-205) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else if ((z <= 3.15e+205) || !(z <= 3.2e+249)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.85e+233:
		tmp = t_0
	elif z <= -8.2e+214:
		tmp = t_1
	elif z <= -9e+165:
		tmp = t_0
	elif z <= -0.00052:
		tmp = t_1
	elif z <= -2.15e-247:
		tmp = x * -3.0
	elif z <= 2.1e-286:
		tmp = y * 4.0
	elif z <= 8.6e-205:
		tmp = x * -3.0
	elif z <= 490000.0:
		tmp = y * 4.0
	elif (z <= 3.15e+205) or not (z <= 3.2e+249):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.85e+233)
		tmp = t_0;
	elseif (z <= -8.2e+214)
		tmp = t_1;
	elseif (z <= -9e+165)
		tmp = t_0;
	elseif (z <= -0.00052)
		tmp = t_1;
	elseif (z <= -2.15e-247)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.1e-286)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.6e-205)
		tmp = Float64(x * -3.0);
	elseif (z <= 490000.0)
		tmp = Float64(y * 4.0);
	elseif ((z <= 3.15e+205) || !(z <= 3.2e+249))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.85e+233)
		tmp = t_0;
	elseif (z <= -8.2e+214)
		tmp = t_1;
	elseif (z <= -9e+165)
		tmp = t_0;
	elseif (z <= -0.00052)
		tmp = t_1;
	elseif (z <= -2.15e-247)
		tmp = x * -3.0;
	elseif (z <= 2.1e-286)
		tmp = y * 4.0;
	elseif (z <= 8.6e-205)
		tmp = x * -3.0;
	elseif (z <= 490000.0)
		tmp = y * 4.0;
	elseif ((z <= 3.15e+205) || ~((z <= 3.2e+249)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+233], t$95$0, If[LessEqual[z, -8.2e+214], t$95$1, If[LessEqual[z, -9e+165], t$95$0, If[LessEqual[z, -0.00052], t$95$1, If[LessEqual[z, -2.15e-247], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.1e-286], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.6e-205], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 490000.0], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 3.15e+205], N[Not[LessEqual[z, 3.2e+249]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8499999999999999e233 or -8.2e214 < z < -8.9999999999999993e165 or 3.15000000000000007e205 < z < 3.20000000000000014e249

   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 x around inf 76.0%

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

      1. sub-neg 76.0%

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

      2. distribute-rgt-in 76.0%

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

      3. metadata-eval 76.0%

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

      4. distribute-lft-neg-in 76.0%

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

      5. associate-+r+ 76.0%

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

      6. metadata-eval 76.0%

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

      7. distribute-rgt-neg-in 76.0%

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

      8. metadata-eval 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in z around inf 76.1%

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

      1. *-commutative 76.1%

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

   10. Simplified 76.1%

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

   if -1.8499999999999999e233 < z < -8.2e214 or -8.9999999999999993e165 < z < -5.19999999999999954e-4 or 4.9e5 < z < 3.15000000000000007e205 or 3.20000000000000014e249 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 86.8%

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

   6. Taylor expanded in x around 0 69.3%

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

   7. Taylor expanded in z around inf 67.2%

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

   if -5.19999999999999954e-4 < z < -2.15000000000000003e-247 or 2.09999999999999988e-286 < z < 8.5999999999999998e-205

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. sub-neg 62.1%

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

      2. distribute-rgt-in 62.1%

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

      3. metadata-eval 62.1%

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

      4. distribute-lft-neg-in 62.1%

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

      5. associate-+r+ 62.1%

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

      6. metadata-eval 62.1%

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

      7. distribute-rgt-neg-in 62.1%

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

      8. metadata-eval 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in z around 0 62.1%

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

   if -2.15000000000000003e-247 < z < 2.09999999999999988e-286 or 8.5999999999999998e-205 < z < 4.9e5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 85.7%

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

   6. Taylor expanded in x around 0 60.0%

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

   7. Taylor expanded in z around 0 60.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+233}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+214}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+165}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.00052:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+205} \lor \neg \left(z \leq 3.2 \cdot 10^{+249}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := z \cdot \left(y \cdot -6\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+232}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.00052:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-248}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+204} \lor \neg \left(z \leq 3.4 \cdot 10^{+250}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* z (* y -6.0))))
   (if (<= z -3.2e+232)
     t_0
     (if (<= z -2.7e+215)
       t_1
       (if (<= z -4.1e+162)
         t_0
         (if (<= z -0.00052)
           t_1
           (if (<= z -3.4e-248)
             (* x -3.0)
             (if (<= z 2.3e-286)
               (* y 4.0)
               (if (<= z 4.4e-206)
                 (* x -3.0)
                 (if (<= z 490000.0)
                   (* y 4.0)
                   (if (or (<= z 8.5e+204) (not (<= z 3.4e+250)))
                     t_1
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = z * (y * -6.0);
	double tmp;
	if (z <= -3.2e+232) {
		tmp = t_0;
	} else if (z <= -2.7e+215) {
		tmp = t_1;
	} else if (z <= -4.1e+162) {
		tmp = t_0;
	} else if (z <= -0.00052) {
		tmp = t_1;
	} else if (z <= -3.4e-248) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-286) {
		tmp = y * 4.0;
	} else if (z <= 4.4e-206) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else if ((z <= 8.5e+204) || !(z <= 3.4e+250)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = z * (y * (-6.0d0))
    if (z <= (-3.2d+232)) then
        tmp = t_0
    else if (z <= (-2.7d+215)) then
        tmp = t_1
    else if (z <= (-4.1d+162)) then
        tmp = t_0
    else if (z <= (-0.00052d0)) then
        tmp = t_1
    else if (z <= (-3.4d-248)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.3d-286) then
        tmp = y * 4.0d0
    else if (z <= 4.4d-206) then
        tmp = x * (-3.0d0)
    else if (z <= 490000.0d0) then
        tmp = y * 4.0d0
    else if ((z <= 8.5d+204) .or. (.not. (z <= 3.4d+250))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = z * (y * -6.0);
	double tmp;
	if (z <= -3.2e+232) {
		tmp = t_0;
	} else if (z <= -2.7e+215) {
		tmp = t_1;
	} else if (z <= -4.1e+162) {
		tmp = t_0;
	} else if (z <= -0.00052) {
		tmp = t_1;
	} else if (z <= -3.4e-248) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-286) {
		tmp = y * 4.0;
	} else if (z <= 4.4e-206) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else if ((z <= 8.5e+204) || !(z <= 3.4e+250)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = z * (y * -6.0)
	tmp = 0
	if z <= -3.2e+232:
		tmp = t_0
	elif z <= -2.7e+215:
		tmp = t_1
	elif z <= -4.1e+162:
		tmp = t_0
	elif z <= -0.00052:
		tmp = t_1
	elif z <= -3.4e-248:
		tmp = x * -3.0
	elif z <= 2.3e-286:
		tmp = y * 4.0
	elif z <= 4.4e-206:
		tmp = x * -3.0
	elif z <= 490000.0:
		tmp = y * 4.0
	elif (z <= 8.5e+204) or not (z <= 3.4e+250):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(z * Float64(y * -6.0))
	tmp = 0.0
	if (z <= -3.2e+232)
		tmp = t_0;
	elseif (z <= -2.7e+215)
		tmp = t_1;
	elseif (z <= -4.1e+162)
		tmp = t_0;
	elseif (z <= -0.00052)
		tmp = t_1;
	elseif (z <= -3.4e-248)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.3e-286)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.4e-206)
		tmp = Float64(x * -3.0);
	elseif (z <= 490000.0)
		tmp = Float64(y * 4.0);
	elseif ((z <= 8.5e+204) || !(z <= 3.4e+250))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = z * (y * -6.0);
	tmp = 0.0;
	if (z <= -3.2e+232)
		tmp = t_0;
	elseif (z <= -2.7e+215)
		tmp = t_1;
	elseif (z <= -4.1e+162)
		tmp = t_0;
	elseif (z <= -0.00052)
		tmp = t_1;
	elseif (z <= -3.4e-248)
		tmp = x * -3.0;
	elseif (z <= 2.3e-286)
		tmp = y * 4.0;
	elseif (z <= 4.4e-206)
		tmp = x * -3.0;
	elseif (z <= 490000.0)
		tmp = y * 4.0;
	elseif ((z <= 8.5e+204) || ~((z <= 3.4e+250)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+232], t$95$0, If[LessEqual[z, -2.7e+215], t$95$1, If[LessEqual[z, -4.1e+162], t$95$0, If[LessEqual[z, -0.00052], t$95$1, If[LessEqual[z, -3.4e-248], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.3e-286], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.4e-206], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 490000.0], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 8.5e+204], N[Not[LessEqual[z, 3.4e+250]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2000000000000002e232 or -2.7e215 < z < -4.0999999999999999e162 or 8.5e204 < z < 3.39999999999999973e250

   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 x around inf 76.0%

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

      1. sub-neg 76.0%

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

      2. distribute-rgt-in 76.0%

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

      3. metadata-eval 76.0%

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

      4. distribute-lft-neg-in 76.0%

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

      5. associate-+r+ 76.0%

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

      6. metadata-eval 76.0%

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

      7. distribute-rgt-neg-in 76.0%

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

      8. metadata-eval 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in z around inf 76.1%

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

      1. *-commutative 76.1%

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

   10. Simplified 76.1%

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

   if -3.2000000000000002e232 < z < -2.7e215 or -4.0999999999999999e162 < z < -5.19999999999999954e-4 or 4.9e5 < z < 8.5e204 or 3.39999999999999973e250 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 95.5%

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

      1. fma-define 95.5%

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

      2. *-commutative 95.5%

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

      3. +-commutative 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in z around inf 97.3%

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

   9. Taylor expanded in y around inf 67.4%

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

       1. *-commutative 67.4%

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

   11. Simplified 67.4%

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

   if -5.19999999999999954e-4 < z < -3.3999999999999998e-248 or 2.3000000000000002e-286 < z < 4.3999999999999997e-206

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. sub-neg 62.1%

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

      2. distribute-rgt-in 62.1%

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

      3. metadata-eval 62.1%

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

      4. distribute-lft-neg-in 62.1%

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

      5. associate-+r+ 62.1%

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

      6. metadata-eval 62.1%

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

      7. distribute-rgt-neg-in 62.1%

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

      8. metadata-eval 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in z around 0 62.1%

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

   if -3.3999999999999998e-248 < z < 2.3000000000000002e-286 or 4.3999999999999997e-206 < z < 4.9e5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 85.7%

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

   6. Taylor expanded in x around 0 60.0%

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

   7. Taylor expanded in z around 0 60.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+232}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+162}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.00052:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-248}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+204} \lor \neg \left(z \leq 3.4 \cdot 10^{+250}\right):\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+233}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.00052:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-204}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+201}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+249}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -3.1e+233)
     t_0
     (if (<= z -2.75e+215)
       t_1
       (if (<= z -2.2e+162)
         t_0
         (if (<= z -0.00052)
           t_1
           (if (<= z -2.75e-247)
             (* x -3.0)
             (if (<= z 1.55e-286)
               (* y 4.0)
               (if (<= z 1.95e-204)
                 (* x -3.0)
                 (if (<= z 490000.0)
                   (* y 4.0)
                   (if (<= z 3.6e+201)
                     (* y (* z -6.0))
                     (if (<= z 2.4e+249) t_0 t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -3.1e+233) {
		tmp = t_0;
	} else if (z <= -2.75e+215) {
		tmp = t_1;
	} else if (z <= -2.2e+162) {
		tmp = t_0;
	} else if (z <= -0.00052) {
		tmp = t_1;
	} else if (z <= -2.75e-247) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-286) {
		tmp = y * 4.0;
	} else if (z <= 1.95e-204) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else if (z <= 3.6e+201) {
		tmp = y * (z * -6.0);
	} else if (z <= 2.4e+249) {
		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 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-3.1d+233)) then
        tmp = t_0
    else if (z <= (-2.75d+215)) then
        tmp = t_1
    else if (z <= (-2.2d+162)) then
        tmp = t_0
    else if (z <= (-0.00052d0)) then
        tmp = t_1
    else if (z <= (-2.75d-247)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.55d-286) then
        tmp = y * 4.0d0
    else if (z <= 1.95d-204) then
        tmp = x * (-3.0d0)
    else if (z <= 490000.0d0) then
        tmp = y * 4.0d0
    else if (z <= 3.6d+201) then
        tmp = y * (z * (-6.0d0))
    else if (z <= 2.4d+249) 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 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -3.1e+233) {
		tmp = t_0;
	} else if (z <= -2.75e+215) {
		tmp = t_1;
	} else if (z <= -2.2e+162) {
		tmp = t_0;
	} else if (z <= -0.00052) {
		tmp = t_1;
	} else if (z <= -2.75e-247) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-286) {
		tmp = y * 4.0;
	} else if (z <= 1.95e-204) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else if (z <= 3.6e+201) {
		tmp = y * (z * -6.0);
	} else if (z <= 2.4e+249) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -3.1e+233:
		tmp = t_0
	elif z <= -2.75e+215:
		tmp = t_1
	elif z <= -2.2e+162:
		tmp = t_0
	elif z <= -0.00052:
		tmp = t_1
	elif z <= -2.75e-247:
		tmp = x * -3.0
	elif z <= 1.55e-286:
		tmp = y * 4.0
	elif z <= 1.95e-204:
		tmp = x * -3.0
	elif z <= 490000.0:
		tmp = y * 4.0
	elif z <= 3.6e+201:
		tmp = y * (z * -6.0)
	elif z <= 2.4e+249:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.1e+233)
		tmp = t_0;
	elseif (z <= -2.75e+215)
		tmp = t_1;
	elseif (z <= -2.2e+162)
		tmp = t_0;
	elseif (z <= -0.00052)
		tmp = t_1;
	elseif (z <= -2.75e-247)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.55e-286)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.95e-204)
		tmp = Float64(x * -3.0);
	elseif (z <= 490000.0)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.6e+201)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= 2.4e+249)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.1e+233)
		tmp = t_0;
	elseif (z <= -2.75e+215)
		tmp = t_1;
	elseif (z <= -2.2e+162)
		tmp = t_0;
	elseif (z <= -0.00052)
		tmp = t_1;
	elseif (z <= -2.75e-247)
		tmp = x * -3.0;
	elseif (z <= 1.55e-286)
		tmp = y * 4.0;
	elseif (z <= 1.95e-204)
		tmp = x * -3.0;
	elseif (z <= 490000.0)
		tmp = y * 4.0;
	elseif (z <= 3.6e+201)
		tmp = y * (z * -6.0);
	elseif (z <= 2.4e+249)
		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[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+233], t$95$0, If[LessEqual[z, -2.75e+215], t$95$1, If[LessEqual[z, -2.2e+162], t$95$0, If[LessEqual[z, -0.00052], t$95$1, If[LessEqual[z, -2.75e-247], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.55e-286], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.95e-204], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 490000.0], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.6e+201], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+249], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.10000000000000016e233 or -2.75e215 < z < -2.2000000000000002e162 or 3.59999999999999976e201 < z < 2.4e249

   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 x around inf 76.0%

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

      1. sub-neg 76.0%

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

      2. distribute-rgt-in 76.0%

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

      3. metadata-eval 76.0%

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

      4. distribute-lft-neg-in 76.0%

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

      5. associate-+r+ 76.0%

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

      6. metadata-eval 76.0%

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

      7. distribute-rgt-neg-in 76.0%

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

      8. metadata-eval 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in z around inf 76.1%

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

      1. *-commutative 76.1%

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

   10. Simplified 76.1%

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

   if -3.10000000000000016e233 < z < -2.75e215 or -2.2000000000000002e162 < z < -5.19999999999999954e-4 or 2.4e249 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 87.7%

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

   6. Taylor expanded in x around 0 74.8%

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

   7. Taylor expanded in z around inf 72.3%

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

   if -5.19999999999999954e-4 < z < -2.74999999999999997e-247 or 1.54999999999999991e-286 < z < 1.95e-204

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. sub-neg 62.1%

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

      2. distribute-rgt-in 62.1%

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

      3. metadata-eval 62.1%

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

      4. distribute-lft-neg-in 62.1%

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

      5. associate-+r+ 62.1%

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

      6. metadata-eval 62.1%

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

      7. distribute-rgt-neg-in 62.1%

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

      8. metadata-eval 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in z around 0 62.1%

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

   if -2.74999999999999997e-247 < z < 1.54999999999999991e-286 or 1.95e-204 < z < 4.9e5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 85.7%

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

   6. Taylor expanded in x around 0 60.0%

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

   7. Taylor expanded in z around 0 60.1%

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

   if 4.9e5 < z < 3.59999999999999976e201

   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 y around inf 85.3%

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

   6. Taylor expanded in x around 0 60.7%

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

   7. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*r* 59.4%

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

   9. Simplified 59.4%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+233}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+215}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+162}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.00052:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-286}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-204}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+201}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+249}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-248}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-287}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.08e-5)
     t_0
     (if (<= z -9e-248)
       (* x -3.0)
       (if (<= z 7.6e-287)
         (* y 4.0)
         (if (<= z 1.95e-206)
           (* x -3.0)
           (if (<= z 490000.0) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.08e-5) {
		tmp = t_0;
	} else if (z <= -9e-248) {
		tmp = x * -3.0;
	} else if (z <= 7.6e-287) {
		tmp = y * 4.0;
	} else if (z <= 1.95e-206) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.08d-5)) then
        tmp = t_0
    else if (z <= (-9d-248)) then
        tmp = x * (-3.0d0)
    else if (z <= 7.6d-287) then
        tmp = y * 4.0d0
    else if (z <= 1.95d-206) then
        tmp = x * (-3.0d0)
    else if (z <= 490000.0d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.08e-5) {
		tmp = t_0;
	} else if (z <= -9e-248) {
		tmp = x * -3.0;
	} else if (z <= 7.6e-287) {
		tmp = y * 4.0;
	} else if (z <= 1.95e-206) {
		tmp = x * -3.0;
	} else if (z <= 490000.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.08e-5:
		tmp = t_0
	elif z <= -9e-248:
		tmp = x * -3.0
	elif z <= 7.6e-287:
		tmp = y * 4.0
	elif z <= 1.95e-206:
		tmp = x * -3.0
	elif z <= 490000.0:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.08e-5)
		tmp = t_0;
	elseif (z <= -9e-248)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.6e-287)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.95e-206)
		tmp = Float64(x * -3.0);
	elseif (z <= 490000.0)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.08e-5)
		tmp = t_0;
	elseif (z <= -9e-248)
		tmp = x * -3.0;
	elseif (z <= 7.6e-287)
		tmp = y * 4.0;
	elseif (z <= 1.95e-206)
		tmp = x * -3.0;
	elseif (z <= 490000.0)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-5], t$95$0, If[LessEqual[z, -9e-248], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.6e-287], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.95e-206], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 490000.0], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.07999999999999999e-5 or 4.9e5 < 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 y around inf 83.0%

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

   6. Taylor expanded in x around 0 58.9%

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

   7. Taylor expanded in z around inf 57.5%

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

   if -1.07999999999999999e-5 < z < -8.9999999999999992e-248 or 7.59999999999999964e-287 < z < 1.95000000000000004e-206

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. sub-neg 62.1%

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

      2. distribute-rgt-in 62.1%

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

      3. metadata-eval 62.1%

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

      4. distribute-lft-neg-in 62.1%

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

      5. associate-+r+ 62.1%

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

      6. metadata-eval 62.1%

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

      7. distribute-rgt-neg-in 62.1%

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

      8. metadata-eval 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in z around 0 62.1%

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

   if -8.9999999999999992e-248 < z < 7.59999999999999964e-287 or 1.95000000000000004e-206 < z < 4.9e5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 85.7%

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

   6. Taylor expanded in x around 0 60.0%

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

   7. Taylor expanded in z around 0 60.1%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-248}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-287}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-206}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 490000:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+128} \lor \neg \left(x \leq -5.8 \cdot 10^{+40} \lor \neg \left(x \leq -3.5 \cdot 10^{-56}\right) \land x \leq 2.8 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e+128)
         (not (or (<= x -5.8e+40) (and (not (<= x -3.5e-56)) (<= x 2.8e+19)))))
   (* x (+ -3.0 (* z 6.0)))
   (* y (* 6.0 (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e+128) || !((x <= -5.8e+40) || (!(x <= -3.5e-56) && (x <= 2.8e+19)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (6.0 * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.6d+128)) .or. (.not. (x <= (-5.8d+40)) .or. (.not. (x <= (-3.5d-56))) .and. (x <= 2.8d+19))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (6.0d0 * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e+128) || !((x <= -5.8e+40) || (!(x <= -3.5e-56) && (x <= 2.8e+19)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (6.0 * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e+128) or not ((x <= -5.8e+40) or (not (x <= -3.5e-56) and (x <= 2.8e+19))):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (6.0 * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.6e+128) || !((x <= -5.8e+40) || (!(x <= -3.5e-56) && (x <= 2.8e+19))))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(6.0 * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.6e+128) || ~(((x <= -5.8e+40) || (~((x <= -3.5e-56)) && (x <= 2.8e+19)))))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (6.0 * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e+128], N[Not[Or[LessEqual[x, -5.8e+40], And[N[Not[LessEqual[x, -3.5e-56]], $MachinePrecision], LessEqual[x, 2.8e+19]]]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999993e128 or -5.80000000000000035e40 < x < -3.4999999999999998e-56 or 2.8e19 < x

   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 85.5%

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

      1. sub-neg 85.5%

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

      2. distribute-rgt-in 85.5%

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

      3. metadata-eval 85.5%

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

      4. distribute-lft-neg-in 85.5%

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

      5. associate-+r+ 85.5%

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

      6. metadata-eval 85.5%

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

      7. distribute-rgt-neg-in 85.5%

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

      8. metadata-eval 85.5%

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

   7. Simplified 85.5%

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

   if -1.59999999999999993e128 < x < -5.80000000000000035e40 or -3.4999999999999998e-56 < x < 2.8e19

   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 y around inf 96.2%

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

   6. Taylor expanded in x around 0 85.2%

      \[\leadsto y \cdot \color{blue}{\left(6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+128} \lor \neg \left(x \leq -5.8 \cdot 10^{+40} \lor \neg \left(x \leq -3.5 \cdot 10^{-56}\right) \land x \leq 2.8 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -9.2e-62)
     t_0
     (if (<= x -2.4e-178)
       (* y 4.0)
       (if (<= x 8.6e-44) (* z (* y -6.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -9.2e-62) {
		tmp = t_0;
	} else if (x <= -2.4e-178) {
		tmp = y * 4.0;
	} else if (x <= 8.6e-44) {
		tmp = z * (y * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-9.2d-62)) then
        tmp = t_0
    else if (x <= (-2.4d-178)) then
        tmp = y * 4.0d0
    else if (x <= 8.6d-44) then
        tmp = z * (y * (-6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -9.2e-62) {
		tmp = t_0;
	} else if (x <= -2.4e-178) {
		tmp = y * 4.0;
	} else if (x <= 8.6e-44) {
		tmp = z * (y * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -9.2e-62:
		tmp = t_0
	elif x <= -2.4e-178:
		tmp = y * 4.0
	elif x <= 8.6e-44:
		tmp = z * (y * -6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -9.2e-62)
		tmp = t_0;
	elseif (x <= -2.4e-178)
		tmp = Float64(y * 4.0);
	elseif (x <= 8.6e-44)
		tmp = Float64(z * Float64(y * -6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -9.2e-62)
		tmp = t_0;
	elseif (x <= -2.4e-178)
		tmp = y * 4.0;
	elseif (x <= 8.6e-44)
		tmp = z * (y * -6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.2e-62], t$95$0, If[LessEqual[x, -2.4e-178], N[(y * 4.0), $MachinePrecision], If[LessEqual[x, 8.6e-44], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.20000000000000002e-62 or 8.60000000000000027e-44 < x

   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 77.8%

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

      1. sub-neg 77.8%

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

      2. distribute-rgt-in 77.8%

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

      3. metadata-eval 77.8%

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

      4. distribute-lft-neg-in 77.8%

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

      5. associate-+r+ 77.8%

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

      6. metadata-eval 77.8%

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

      7. distribute-rgt-neg-in 77.8%

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

      8. metadata-eval 77.8%

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

   7. Simplified 77.8%

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

   if -9.20000000000000002e-62 < x < -2.40000000000000005e-178

   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 y around inf 99.9%

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

   6. Taylor expanded in x around 0 90.2%

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

   7. Taylor expanded in z around 0 55.6%

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

   if -2.40000000000000005e-178 < x < 8.60000000000000027e-44

   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 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. Step-by-step derivation

      1. fma-define 99.5%

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

      2. *-commutative 99.5%

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

      3. +-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around inf 60.0%

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

   9. Taylor expanded in y around inf 55.4%

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

       1. *-commutative 55.4%

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

   11. Simplified 55.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.65)))
   (* z (+ (* y -6.0) (* x 6.0)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.65)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.65)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.65):
		tmp = z * ((y * -6.0) + (x * 6.0))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.65))
		tmp = Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.65)))
		tmp = z * ((y * -6.0) + (x * 6.0));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.650000000000000022 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.1%

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

      1. fma-define 93.1%

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

      2. *-commutative 93.1%

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

      3. +-commutative 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in z around inf 98.3%

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

   if -0.599999999999999978 < z < 0.650000000000000022

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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 0 99.6%

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

      1. fma-define 99.6%

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

      2. *-commutative 99.6%

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

      3. +-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 99.3%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.55)))
   (* (- y x) (* z -6.0))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.55)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.58d0)) .or. (.not. (z <= 0.55d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.55)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.55):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.55))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.55)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.55]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.55000000000000004 < 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 x around 0 93.1%

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

      1. fma-define 93.1%

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

      2. *-commutative 93.1%

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

      3. +-commutative 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in z around inf 98.3%

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

      1. metadata-eval 98.3%

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

      2. associate-*r* 98.3%

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

      3. neg-mul-1 98.3%

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

      4. distribute-lft-in 98.3%

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

      5. sub-neg 98.3%

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

      6. associate-*r* 98.2%

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

      7. *-commutative 98.2%

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

   10. Simplified 98.2%

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

   if -0.57999999999999996 < z < 0.55000000000000004

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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 99.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.62 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.62) (not (<= z 0.65)))
   (* (- y x) (* z -6.0))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.62) || !(z <= 0.65)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.62d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.62) || !(z <= 0.65)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.62) or not (z <= 0.65):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.62) || !(z <= 0.65))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.62) || ~((z <= 0.65)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.62], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.619999999999999996 or 0.650000000000000022 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.1%

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

      1. fma-define 93.1%

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

      2. *-commutative 93.1%

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

      3. +-commutative 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in z around inf 98.3%

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

      1. metadata-eval 98.3%

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

      2. associate-*r* 98.3%

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

      3. neg-mul-1 98.3%

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

      4. distribute-lft-in 98.3%

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

      5. sub-neg 98.3%

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

      6. associate-*r* 98.2%

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

      7. *-commutative 98.2%

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

   10. Simplified 98.2%

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

   if -0.619999999999999996 < z < 0.650000000000000022

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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 0 99.6%

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

      1. fma-define 99.6%

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

      2. *-commutative 99.6%

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

      3. +-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 99.3%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.62 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{-53} \lor \neg \left(x \leq 330000\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.46e-53) (not (<= x 330000.0))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.46e-53) || !(x <= 330000.0)) {
		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 <= (-1.46d-53)) .or. (.not. (x <= 330000.0d0))) 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 <= -1.46e-53) || !(x <= 330000.0)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.46e-53) or not (x <= 330000.0):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.46e-53) || !(x <= 330000.0))
		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 <= -1.46e-53) || ~((x <= 330000.0)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.46e-53], N[Not[LessEqual[x, 330000.0]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45999999999999989e-53 or 3.3e5 < x

   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 79.4%

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

      1. sub-neg 79.4%

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

      2. distribute-rgt-in 79.4%

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

      3. metadata-eval 79.4%

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

      4. distribute-lft-neg-in 79.4%

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

      5. associate-+r+ 79.4%

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

      6. metadata-eval 79.4%

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

      7. distribute-rgt-neg-in 79.4%

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

      8. metadata-eval 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in z around 0 40.8%

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

   if -1.45999999999999989e-53 < x < 3.3e5

   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 y around inf 97.4%

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

   6. Taylor expanded in x around 0 85.8%

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

   7. Taylor expanded in z around 0 38.3%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{-53} \lor \neg \left(x \leq 330000\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 14: 25.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. 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 48.3%

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

   1. sub-neg 48.3%

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

   2. distribute-rgt-in 48.3%

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

   3. metadata-eval 48.3%

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

   4. distribute-lft-neg-in 48.3%

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

   5. associate-+r+ 48.3%

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

   6. metadata-eval 48.3%

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

   7. distribute-rgt-neg-in 48.3%

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

   8. metadata-eval 48.3%

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

7. Simplified 48.3%

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

8. Taylor expanded in z around 0 25.3%

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

9. Final simplification 25.3%

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

Alternative 15: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around inf 53.3%

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

6. Taylor expanded in z around 0 2.3%

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

7. Final simplification 2.3%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(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))))