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

Percentage Accurate: 99.5% → 99.8%

Time: 11.7s

Alternatives: 14

Speedup: 1.2×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

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 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 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. Add Preprocessing

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 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. Add Preprocessing

Alternative 3: 50.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.3:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-167}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-193}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-126}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 59000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+221}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* y (* z -6.0))))
   (if (<= z -5.5e+182)
     (* z (* x 6.0))
     (if (<= z -0.3)
       t_1
       (if (<= z -4.5e-167)
         t_0
         (if (<= z -1.25e-193)
           (* x -3.0)
           (if (<= z 8.2e-259)
             t_0
             (if (<= z 5.7e-126)
               (* x -3.0)
               (if (<= z 59000000000000.0)
                 t_0
                 (if (<= z 7.6e+59)
                   t_1
                   (if (<= z 3.4e+92)
                     (* 6.0 (* x z))
                     (if (<= z 3.1e+177)
                       t_1
                       (if (<= z 2.5e+221)
                         (* x (* z 6.0))
                         (* -6.0 (* y z)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -5.5e+182) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.3) {
		tmp = t_1;
	} else if (z <= -4.5e-167) {
		tmp = t_0;
	} else if (z <= -1.25e-193) {
		tmp = x * -3.0;
	} else if (z <= 8.2e-259) {
		tmp = t_0;
	} else if (z <= 5.7e-126) {
		tmp = x * -3.0;
	} else if (z <= 59000000000000.0) {
		tmp = t_0;
	} else if (z <= 7.6e+59) {
		tmp = t_1;
	} else if (z <= 3.4e+92) {
		tmp = 6.0 * (x * z);
	} else if (z <= 3.1e+177) {
		tmp = t_1;
	} else if (z <= 2.5e+221) {
		tmp = x * (z * 6.0);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = y * (z * (-6.0d0))
    if (z <= (-5.5d+182)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-0.3d0)) then
        tmp = t_1
    else if (z <= (-4.5d-167)) then
        tmp = t_0
    else if (z <= (-1.25d-193)) then
        tmp = x * (-3.0d0)
    else if (z <= 8.2d-259) then
        tmp = t_0
    else if (z <= 5.7d-126) then
        tmp = x * (-3.0d0)
    else if (z <= 59000000000000.0d0) then
        tmp = t_0
    else if (z <= 7.6d+59) then
        tmp = t_1
    else if (z <= 3.4d+92) then
        tmp = 6.0d0 * (x * z)
    else if (z <= 3.1d+177) then
        tmp = t_1
    else if (z <= 2.5d+221) then
        tmp = x * (z * 6.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -5.5e+182) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.3) {
		tmp = t_1;
	} else if (z <= -4.5e-167) {
		tmp = t_0;
	} else if (z <= -1.25e-193) {
		tmp = x * -3.0;
	} else if (z <= 8.2e-259) {
		tmp = t_0;
	} else if (z <= 5.7e-126) {
		tmp = x * -3.0;
	} else if (z <= 59000000000000.0) {
		tmp = t_0;
	} else if (z <= 7.6e+59) {
		tmp = t_1;
	} else if (z <= 3.4e+92) {
		tmp = 6.0 * (x * z);
	} else if (z <= 3.1e+177) {
		tmp = t_1;
	} else if (z <= 2.5e+221) {
		tmp = x * (z * 6.0);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = y * (z * -6.0)
	tmp = 0
	if z <= -5.5e+182:
		tmp = z * (x * 6.0)
	elif z <= -0.3:
		tmp = t_1
	elif z <= -4.5e-167:
		tmp = t_0
	elif z <= -1.25e-193:
		tmp = x * -3.0
	elif z <= 8.2e-259:
		tmp = t_0
	elif z <= 5.7e-126:
		tmp = x * -3.0
	elif z <= 59000000000000.0:
		tmp = t_0
	elif z <= 7.6e+59:
		tmp = t_1
	elif z <= 3.4e+92:
		tmp = 6.0 * (x * z)
	elif z <= 3.1e+177:
		tmp = t_1
	elif z <= 2.5e+221:
		tmp = x * (z * 6.0)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -5.5e+182)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -0.3)
		tmp = t_1;
	elseif (z <= -4.5e-167)
		tmp = t_0;
	elseif (z <= -1.25e-193)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.2e-259)
		tmp = t_0;
	elseif (z <= 5.7e-126)
		tmp = Float64(x * -3.0);
	elseif (z <= 59000000000000.0)
		tmp = t_0;
	elseif (z <= 7.6e+59)
		tmp = t_1;
	elseif (z <= 3.4e+92)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= 3.1e+177)
		tmp = t_1;
	elseif (z <= 2.5e+221)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -5.5e+182)
		tmp = z * (x * 6.0);
	elseif (z <= -0.3)
		tmp = t_1;
	elseif (z <= -4.5e-167)
		tmp = t_0;
	elseif (z <= -1.25e-193)
		tmp = x * -3.0;
	elseif (z <= 8.2e-259)
		tmp = t_0;
	elseif (z <= 5.7e-126)
		tmp = x * -3.0;
	elseif (z <= 59000000000000.0)
		tmp = t_0;
	elseif (z <= 7.6e+59)
		tmp = t_1;
	elseif (z <= 3.4e+92)
		tmp = 6.0 * (x * z);
	elseif (z <= 3.1e+177)
		tmp = t_1;
	elseif (z <= 2.5e+221)
		tmp = x * (z * 6.0);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+182], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.3], t$95$1, If[LessEqual[z, -4.5e-167], t$95$0, If[LessEqual[z, -1.25e-193], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.2e-259], t$95$0, If[LessEqual[z, 5.7e-126], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 59000000000000.0], t$95$0, If[LessEqual[z, 7.6e+59], t$95$1, If[LessEqual[z, 3.4e+92], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+177], t$95$1, If[LessEqual[z, 2.5e+221], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -5.49999999999999977e182

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. associate-*r* 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. distribute-lft-neg-in 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. rem-cube-cbrt 98.8%

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

      8. rem-cube-cbrt 99.8%

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

      9. *-commutative 99.8%

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

      10. distribute-rgt-neg-in 99.8%

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

      11. *-commutative 99.8%

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

      12. rem-cube-cbrt 98.8%

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

      13. mul-1-neg 98.8%

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

      14. rem-cube-cbrt 99.8%

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

      15. associate-*r* 99.8%

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

      16. metadata-eval 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around 0 66.9%

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

       1. *-commutative 66.9%

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

       2. *-commutative 66.9%

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

       3. associate-*r* 67.0%

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

   11. Simplified 67.0%

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

   if -5.49999999999999977e182 < z < -0.299999999999999989 or 5.9e13 < z < 7.6000000000000002e59 or 3.3999999999999998e92 < z < 3.0999999999999999e177

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 96.7%

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

      1. associate-*r* 96.9%

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

      2. metadata-eval 96.9%

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

      3. distribute-lft-neg-in 96.9%

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

      4. distribute-lft-neg-in 96.9%

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

      5. *-commutative 96.9%

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

      6. associate-*r* 96.8%

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

      7. rem-cube-cbrt 95.5%

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

      8. rem-cube-cbrt 96.8%

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

      9. *-commutative 96.8%

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

      10. distribute-rgt-neg-in 96.8%

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

      11. *-commutative 96.8%

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

      12. rem-cube-cbrt 95.5%

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

      13. mul-1-neg 95.5%

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

      14. rem-cube-cbrt 96.8%

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

      15. associate-*r* 96.8%

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

      16. metadata-eval 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in y around inf 63.1%

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

       1. *-commutative 63.1%

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

       2. associate-*r* 63.3%

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

       3. *-commutative 63.3%

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

   11. Simplified 63.3%

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

   if -0.299999999999999989 < z < -4.5000000000000001e-167 or -1.2500000000000001e-193 < z < 8.1999999999999996e-259 or 5.69999999999999979e-126 < z < 5.9e13

   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 y around inf 65.4%

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

   6. Taylor expanded in z around 0 64.4%

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

   if -4.5000000000000001e-167 < z < -1.2500000000000001e-193 or 8.1999999999999996e-259 < z < 5.69999999999999979e-126

   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 70.7%

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

      1. sub-neg 70.7%

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

      2. distribute-rgt-in 70.7%

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

      3. metadata-eval 70.7%

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

      4. distribute-lft-neg-in 70.7%

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

      5. associate-+r+ 70.7%

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

      6. metadata-eval 70.7%

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

      7. distribute-rgt-neg-in 70.7%

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

      8. metadata-eval 70.7%

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

   7. Simplified 70.7%

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

   8. Taylor expanded in z around 0 70.7%

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

      1. *-commutative 70.7%

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

   10. Simplified 70.7%

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

   if 7.6000000000000002e59 < z < 3.3999999999999998e92

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.4%

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

      2. metadata-eval 99.4%

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

      3. distribute-lft-neg-in 99.4%

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

      4. distribute-lft-neg-in 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. rem-cube-cbrt 98.0%

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

      8. rem-cube-cbrt 99.4%

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

      9. *-commutative 99.4%

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

      10. distribute-rgt-neg-in 99.4%

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

      11. *-commutative 99.4%

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

      12. rem-cube-cbrt 98.0%

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

      13. mul-1-neg 98.0%

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

      14. rem-cube-cbrt 99.4%

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

      15. associate-*r* 99.4%

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

      16. metadata-eval 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around 0 99.7%

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

   if 3.0999999999999999e177 < z < 2.5000000000000001e221

   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 81.0%

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

      1. sub-neg 81.0%

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

      2. distribute-rgt-in 81.0%

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

      3. metadata-eval 81.0%

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

      4. distribute-lft-neg-in 81.0%

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

      5. associate-+r+ 81.0%

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

      6. metadata-eval 81.0%

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

      7. distribute-rgt-neg-in 81.0%

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

      8. metadata-eval 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in z around inf 81.0%

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

   if 2.5000000000000001e221 < 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 z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. associate-*r* 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. distribute-lft-neg-in 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.9%

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

      7. rem-cube-cbrt 99.3%

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

      8. rem-cube-cbrt 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-rgt-neg-in 99.9%

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

      11. *-commutative 99.9%

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

      12. rem-cube-cbrt 99.3%

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

      13. mul-1-neg 99.3%

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

      14. rem-cube-cbrt 99.9%

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

      15. associate-*r* 99.9%

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

      16. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 64.4%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.3:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-167}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-193}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-259}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-126}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 59000000000000:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+221}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+180}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+221}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))))
   (if (<= z -3.3e+180)
     (* z (* x 6.0))
     (if (<= z -8100000000.0)
       t_0
       (if (<= z 0.66)
         (* x -3.0)
         (if (<= z 7.5e+59)
           t_0
           (if (<= z 1.4e+92)
             (* 6.0 (* x z))
             (if (<= z 3.2e+177)
               t_0
               (if (<= z 1.9e+221) (* x (* z 6.0)) (* -6.0 (* y z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -3.3e+180) {
		tmp = z * (x * 6.0);
	} else if (z <= -8100000000.0) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = x * -3.0;
	} else if (z <= 7.5e+59) {
		tmp = t_0;
	} else if (z <= 1.4e+92) {
		tmp = 6.0 * (x * z);
	} else if (z <= 3.2e+177) {
		tmp = t_0;
	} else if (z <= 1.9e+221) {
		tmp = x * (z * 6.0);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * (-6.0d0))
    if (z <= (-3.3d+180)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-8100000000.0d0)) then
        tmp = t_0
    else if (z <= 0.66d0) then
        tmp = x * (-3.0d0)
    else if (z <= 7.5d+59) then
        tmp = t_0
    else if (z <= 1.4d+92) then
        tmp = 6.0d0 * (x * z)
    else if (z <= 3.2d+177) then
        tmp = t_0
    else if (z <= 1.9d+221) then
        tmp = x * (z * 6.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -3.3e+180) {
		tmp = z * (x * 6.0);
	} else if (z <= -8100000000.0) {
		tmp = t_0;
	} else if (z <= 0.66) {
		tmp = x * -3.0;
	} else if (z <= 7.5e+59) {
		tmp = t_0;
	} else if (z <= 1.4e+92) {
		tmp = 6.0 * (x * z);
	} else if (z <= 3.2e+177) {
		tmp = t_0;
	} else if (z <= 1.9e+221) {
		tmp = x * (z * 6.0);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	tmp = 0
	if z <= -3.3e+180:
		tmp = z * (x * 6.0)
	elif z <= -8100000000.0:
		tmp = t_0
	elif z <= 0.66:
		tmp = x * -3.0
	elif z <= 7.5e+59:
		tmp = t_0
	elif z <= 1.4e+92:
		tmp = 6.0 * (x * z)
	elif z <= 3.2e+177:
		tmp = t_0
	elif z <= 1.9e+221:
		tmp = x * (z * 6.0)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -3.3e+180)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -8100000000.0)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.5e+59)
		tmp = t_0;
	elseif (z <= 1.4e+92)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= 3.2e+177)
		tmp = t_0;
	elseif (z <= 1.9e+221)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -3.3e+180)
		tmp = z * (x * 6.0);
	elseif (z <= -8100000000.0)
		tmp = t_0;
	elseif (z <= 0.66)
		tmp = x * -3.0;
	elseif (z <= 7.5e+59)
		tmp = t_0;
	elseif (z <= 1.4e+92)
		tmp = 6.0 * (x * z);
	elseif (z <= 3.2e+177)
		tmp = t_0;
	elseif (z <= 1.9e+221)
		tmp = x * (z * 6.0);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+180], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8100000000.0], t$95$0, If[LessEqual[z, 0.66], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.5e+59], t$95$0, If[LessEqual[z, 1.4e+92], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+177], t$95$0, If[LessEqual[z, 1.9e+221], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.29999999999999989e180

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. associate-*r* 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. distribute-lft-neg-in 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.8%

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

      7. rem-cube-cbrt 98.8%

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

      8. rem-cube-cbrt 99.8%

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

      9. *-commutative 99.8%

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

      10. distribute-rgt-neg-in 99.8%

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

      11. *-commutative 99.8%

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

      12. rem-cube-cbrt 98.8%

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

      13. mul-1-neg 98.8%

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

      14. rem-cube-cbrt 99.8%

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

      15. associate-*r* 99.8%

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

      16. metadata-eval 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around 0 66.9%

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

       1. *-commutative 66.9%

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

       2. *-commutative 66.9%

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

       3. associate-*r* 67.0%

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

   11. Simplified 67.0%

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

   if -3.29999999999999989e180 < z < -8.1e9 or 0.660000000000000031 < z < 7.4999999999999996e59 or 1.4e92 < z < 3.2e177

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 96.3%

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

      1. associate-*r* 96.6%

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

      2. metadata-eval 96.6%

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

      3. distribute-lft-neg-in 96.6%

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

      4. distribute-lft-neg-in 96.6%

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

      5. *-commutative 96.6%

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

      6. associate-*r* 96.4%

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

      7. rem-cube-cbrt 95.1%

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

      8. rem-cube-cbrt 96.4%

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

      9. *-commutative 96.4%

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

      10. distribute-rgt-neg-in 96.4%

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

      11. *-commutative 96.4%

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

      12. rem-cube-cbrt 95.1%

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

      13. mul-1-neg 95.1%

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

      14. rem-cube-cbrt 96.4%

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

      15. associate-*r* 96.4%

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

      16. metadata-eval 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in y around inf 62.4%

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

       1. *-commutative 62.4%

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

       2. associate-*r* 62.6%

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

       3. *-commutative 62.6%

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

   11. Simplified 62.6%

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

   if -8.1e9 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 43.7%

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

      1. sub-neg 43.7%

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

      2. distribute-rgt-in 43.7%

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

      3. metadata-eval 43.7%

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

      4. distribute-lft-neg-in 43.7%

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

      5. associate-+r+ 43.7%

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

      6. metadata-eval 43.7%

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

      7. distribute-rgt-neg-in 43.7%

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

      8. metadata-eval 43.7%

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

   7. Simplified 43.7%

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

   8. Taylor expanded in z around 0 41.6%

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

      1. *-commutative 41.6%

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

   10. Simplified 41.6%

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

   if 7.4999999999999996e59 < z < 1.4e92

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.4%

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

      2. metadata-eval 99.4%

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

      3. distribute-lft-neg-in 99.4%

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

      4. distribute-lft-neg-in 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. rem-cube-cbrt 98.0%

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

      8. rem-cube-cbrt 99.4%

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

      9. *-commutative 99.4%

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

      10. distribute-rgt-neg-in 99.4%

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

      11. *-commutative 99.4%

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

      12. rem-cube-cbrt 98.0%

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

      13. mul-1-neg 98.0%

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

      14. rem-cube-cbrt 99.4%

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

      15. associate-*r* 99.4%

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

      16. metadata-eval 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around 0 99.7%

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

   if 3.2e177 < z < 1.90000000000000017e221

   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 81.0%

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

      1. sub-neg 81.0%

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

      2. distribute-rgt-in 81.0%

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

      3. metadata-eval 81.0%

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

      4. distribute-lft-neg-in 81.0%

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

      5. associate-+r+ 81.0%

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

      6. metadata-eval 81.0%

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

      7. distribute-rgt-neg-in 81.0%

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

      8. metadata-eval 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in z around inf 81.0%

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

   if 1.90000000000000017e221 < 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 z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. associate-*r* 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. distribute-lft-neg-in 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.9%

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

      7. rem-cube-cbrt 99.3%

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

      8. rem-cube-cbrt 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-rgt-neg-in 99.9%

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

      11. *-commutative 99.9%

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

      12. rem-cube-cbrt 99.3%

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

      13. mul-1-neg 99.3%

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

      14. rem-cube-cbrt 99.9%

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

      15. associate-*r* 99.9%

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

      16. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 64.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+180}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+221}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ t_1 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+183}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))) (t_1 (* y (* z -6.0))))
   (if (<= z -2e+183)
     t_0
     (if (<= z -8100000000.0)
       t_1
       (if (<= z 0.65)
         (* x -3.0)
         (if (<= z 1e+60)
           t_1
           (if (<= z 1.75e+92)
             (* 6.0 (* x z))
             (if (<= z 2e+178)
               t_1
               (if (<= z 1.15e+224) t_0 (* -6.0 (* y z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -2e+183) {
		tmp = t_0;
	} else if (z <= -8100000000.0) {
		tmp = t_1;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else if (z <= 1e+60) {
		tmp = t_1;
	} else if (z <= 1.75e+92) {
		tmp = 6.0 * (x * z);
	} else if (z <= 2e+178) {
		tmp = t_1;
	} else if (z <= 1.15e+224) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    t_1 = y * (z * (-6.0d0))
    if (z <= (-2d+183)) then
        tmp = t_0
    else if (z <= (-8100000000.0d0)) then
        tmp = t_1
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1d+60) then
        tmp = t_1
    else if (z <= 1.75d+92) then
        tmp = 6.0d0 * (x * z)
    else if (z <= 2d+178) then
        tmp = t_1
    else if (z <= 1.15d+224) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -2e+183) {
		tmp = t_0;
	} else if (z <= -8100000000.0) {
		tmp = t_1;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else if (z <= 1e+60) {
		tmp = t_1;
	} else if (z <= 1.75e+92) {
		tmp = 6.0 * (x * z);
	} else if (z <= 2e+178) {
		tmp = t_1;
	} else if (z <= 1.15e+224) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	t_1 = y * (z * -6.0)
	tmp = 0
	if z <= -2e+183:
		tmp = t_0
	elif z <= -8100000000.0:
		tmp = t_1
	elif z <= 0.65:
		tmp = x * -3.0
	elif z <= 1e+60:
		tmp = t_1
	elif z <= 1.75e+92:
		tmp = 6.0 * (x * z)
	elif z <= 2e+178:
		tmp = t_1
	elif z <= 1.15e+224:
		tmp = t_0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	t_1 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -2e+183)
		tmp = t_0;
	elseif (z <= -8100000000.0)
		tmp = t_1;
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	elseif (z <= 1e+60)
		tmp = t_1;
	elseif (z <= 1.75e+92)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= 2e+178)
		tmp = t_1;
	elseif (z <= 1.15e+224)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	t_1 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -2e+183)
		tmp = t_0;
	elseif (z <= -8100000000.0)
		tmp = t_1;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	elseif (z <= 1e+60)
		tmp = t_1;
	elseif (z <= 1.75e+92)
		tmp = 6.0 * (x * z);
	elseif (z <= 2e+178)
		tmp = t_1;
	elseif (z <= 1.15e+224)
		tmp = t_0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+183], t$95$0, If[LessEqual[z, -8100000000.0], t$95$1, If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1e+60], t$95$1, If[LessEqual[z, 1.75e+92], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+178], t$95$1, If[LessEqual[z, 1.15e+224], t$95$0, N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999989e183 or 2.0000000000000001e178 < z < 1.1500000000000001e224

   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 72.4%

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

      1. sub-neg 72.4%

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

      2. distribute-rgt-in 72.4%

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

      3. metadata-eval 72.4%

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

      4. distribute-lft-neg-in 72.4%

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

      5. associate-+r+ 72.4%

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

      6. metadata-eval 72.4%

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

      7. distribute-rgt-neg-in 72.4%

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

      8. metadata-eval 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in z around inf 72.4%

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

   if -1.99999999999999989e183 < z < -8.1e9 or 0.650000000000000022 < z < 9.9999999999999995e59 or 1.74999999999999993e92 < z < 2.0000000000000001e178

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 96.3%

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

      1. associate-*r* 96.6%

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

      2. metadata-eval 96.6%

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

      3. distribute-lft-neg-in 96.6%

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

      4. distribute-lft-neg-in 96.6%

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

      5. *-commutative 96.6%

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

      6. associate-*r* 96.4%

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

      7. rem-cube-cbrt 95.1%

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

      8. rem-cube-cbrt 96.4%

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

      9. *-commutative 96.4%

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

      10. distribute-rgt-neg-in 96.4%

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

      11. *-commutative 96.4%

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

      12. rem-cube-cbrt 95.1%

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

      13. mul-1-neg 95.1%

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

      14. rem-cube-cbrt 96.4%

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

      15. associate-*r* 96.4%

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

      16. metadata-eval 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in y around inf 62.4%

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

       1. *-commutative 62.4%

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

       2. associate-*r* 62.6%

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

       3. *-commutative 62.6%

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

   11. Simplified 62.6%

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

   if -8.1e9 < z < 0.650000000000000022

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 43.7%

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

      1. sub-neg 43.7%

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

      2. distribute-rgt-in 43.7%

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

      3. metadata-eval 43.7%

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

      4. distribute-lft-neg-in 43.7%

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

      5. associate-+r+ 43.7%

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

      6. metadata-eval 43.7%

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

      7. distribute-rgt-neg-in 43.7%

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

      8. metadata-eval 43.7%

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

   7. Simplified 43.7%

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

   8. Taylor expanded in z around 0 41.6%

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

      1. *-commutative 41.6%

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

   10. Simplified 41.6%

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

   if 9.9999999999999995e59 < z < 1.74999999999999993e92

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.4%

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

      2. metadata-eval 99.4%

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

      3. distribute-lft-neg-in 99.4%

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

      4. distribute-lft-neg-in 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. rem-cube-cbrt 98.0%

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

      8. rem-cube-cbrt 99.4%

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

      9. *-commutative 99.4%

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

      10. distribute-rgt-neg-in 99.4%

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

      11. *-commutative 99.4%

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

      12. rem-cube-cbrt 98.0%

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

      13. mul-1-neg 98.0%

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

      14. rem-cube-cbrt 99.4%

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

      15. associate-*r* 99.4%

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

      16. metadata-eval 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around 0 99.7%

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

   if 1.1500000000000001e224 < 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 z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. associate-*r* 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-neg-in 99.8%

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

      4. distribute-lft-neg-in 99.8%

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

      5. *-commutative 99.8%

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

      6. associate-*r* 99.9%

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

      7. rem-cube-cbrt 99.3%

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

      8. rem-cube-cbrt 99.9%

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

      9. *-commutative 99.9%

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

      10. distribute-rgt-neg-in 99.9%

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

      11. *-commutative 99.9%

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

      12. rem-cube-cbrt 99.3%

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

      13. mul-1-neg 99.3%

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

      14. rem-cube-cbrt 99.9%

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

      15. associate-*r* 99.9%

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

      16. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 64.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 10^{+60}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -1.65e-5)
     t_1
     (if (<= z 1.2e-256)
       t_0
       (if (<= z 1.7e-128) (* x -3.0) (if (<= z 5.8e-16) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.65e-5) {
		tmp = t_1;
	} else if (z <= 1.2e-256) {
		tmp = t_0;
	} else if (z <= 1.7e-128) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-16) {
		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 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-1.65d-5)) then
        tmp = t_1
    else if (z <= 1.2d-256) then
        tmp = t_0
    else if (z <= 1.7d-128) then
        tmp = x * (-3.0d0)
    else if (z <= 5.8d-16) 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 = x + (y * 4.0);
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.65e-5) {
		tmp = t_1;
	} else if (z <= 1.2e-256) {
		tmp = t_0;
	} else if (z <= 1.7e-128) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-16) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -1.65e-5:
		tmp = t_1
	elif z <= 1.2e-256:
		tmp = t_0
	elif z <= 1.7e-128:
		tmp = x * -3.0
	elif z <= 5.8e-16:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -1.65e-5)
		tmp = t_1;
	elseif (z <= 1.2e-256)
		tmp = t_0;
	elseif (z <= 1.7e-128)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.8e-16)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -1.65e-5)
		tmp = t_1;
	elseif (z <= 1.2e-256)
		tmp = t_0;
	elseif (z <= 1.7e-128)
		tmp = x * -3.0;
	elseif (z <= 5.8e-16)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-5], t$95$1, If[LessEqual[z, 1.2e-256], t$95$0, If[LessEqual[z, 1.7e-128], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.8e-16], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6500000000000001e-5 or 5.7999999999999996e-16 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 96.4%

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

   if -1.6500000000000001e-5 < z < 1.2e-256 or 1.69999999999999987e-128 < z < 5.7999999999999996e-16

   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 y around inf 64.0%

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

   6. Taylor expanded in z around 0 64.0%

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

   if 1.2e-256 < z < 1.69999999999999987e-128

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 67.9%

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

      1. sub-neg 67.9%

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

      2. distribute-rgt-in 67.9%

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

      3. metadata-eval 67.9%

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

      4. distribute-lft-neg-in 67.9%

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

      5. associate-+r+ 67.9%

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

      6. metadata-eval 67.9%

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

      7. distribute-rgt-neg-in 67.9%

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

      8. metadata-eval 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in z around 0 67.9%

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

      1. *-commutative 67.9%

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

   10. Simplified 67.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-256}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+173}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+222}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.18e+173)
     t_0
     (if (<= z -8100000000.0)
       t_1
       (if (<= z 12.0) (* x -3.0) (if (<= z 2.3e+222) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.18e+173) {
		tmp = t_0;
	} else if (z <= -8100000000.0) {
		tmp = t_1;
	} else if (z <= 12.0) {
		tmp = x * -3.0;
	} else if (z <= 2.3e+222) {
		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 = x * (z * 6.0d0)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-1.18d+173)) then
        tmp = t_0
    else if (z <= (-8100000000.0d0)) then
        tmp = t_1
    else if (z <= 12.0d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.3d+222) 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 = x * (z * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.18e+173) {
		tmp = t_0;
	} else if (z <= -8100000000.0) {
		tmp = t_1;
	} else if (z <= 12.0) {
		tmp = x * -3.0;
	} else if (z <= 2.3e+222) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.18e+173:
		tmp = t_0
	elif z <= -8100000000.0:
		tmp = t_1
	elif z <= 12.0:
		tmp = x * -3.0
	elif z <= 2.3e+222:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.18e+173)
		tmp = t_0;
	elseif (z <= -8100000000.0)
		tmp = t_1;
	elseif (z <= 12.0)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.3e+222)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.18e+173)
		tmp = t_0;
	elseif (z <= -8100000000.0)
		tmp = t_1;
	elseif (z <= 12.0)
		tmp = x * -3.0;
	elseif (z <= 2.3e+222)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.18e+173], t$95$0, If[LessEqual[z, -8100000000.0], t$95$1, If[LessEqual[z, 12.0], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.3e+222], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18e173 or 12 < z < 2.30000000000000011e222

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.1%

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

      1. sub-neg 61.1%

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

      2. distribute-rgt-in 61.1%

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

      3. metadata-eval 61.1%

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

      4. distribute-lft-neg-in 61.1%

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

      5. associate-+r+ 61.1%

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

      6. metadata-eval 61.1%

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

      7. distribute-rgt-neg-in 61.1%

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

      8. metadata-eval 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in z around inf 59.8%

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

   if -1.18e173 < z < -8.1e9 or 2.30000000000000011e222 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.4%

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

      1. associate-*r* 99.4%

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

      2. metadata-eval 99.4%

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

      3. distribute-lft-neg-in 99.4%

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

      4. distribute-lft-neg-in 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. rem-cube-cbrt 98.5%

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

      8. rem-cube-cbrt 99.4%

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

      9. *-commutative 99.4%

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

      10. distribute-rgt-neg-in 99.4%

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

      11. *-commutative 99.4%

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

      12. rem-cube-cbrt 98.5%

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

      13. mul-1-neg 98.5%

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

      14. rem-cube-cbrt 99.4%

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

      15. associate-*r* 99.4%

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

      16. metadata-eval 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around inf 64.9%

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

   if -8.1e9 < z < 12

   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 43.4%

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

      1. sub-neg 43.4%

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

      2. distribute-rgt-in 43.4%

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

      3. metadata-eval 43.4%

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

      4. distribute-lft-neg-in 43.4%

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

      5. associate-+r+ 43.4%

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

      6. metadata-eval 43.4%

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

      7. distribute-rgt-neg-in 43.4%

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

      8. metadata-eval 43.4%

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

   7. Simplified 43.4%

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

   8. Taylor expanded in z around 0 41.3%

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

      1. *-commutative 41.3%

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

   10. Simplified 41.3%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+172}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8100000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+224}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -1.08e+172)
     t_0
     (if (<= z -8100000000.0)
       t_1
       (if (<= z 12.0) (* x -3.0) (if (<= z 1.6e+224) 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 <= -1.08e+172) {
		tmp = t_0;
	} else if (z <= -8100000000.0) {
		tmp = t_1;
	} else if (z <= 12.0) {
		tmp = x * -3.0;
	} else if (z <= 1.6e+224) {
		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 <= (-1.08d+172)) then
        tmp = t_0
    else if (z <= (-8100000000.0d0)) then
        tmp = t_1
    else if (z <= 12.0d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d+224) 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 <= -1.08e+172) {
		tmp = t_0;
	} else if (z <= -8100000000.0) {
		tmp = t_1;
	} else if (z <= 12.0) {
		tmp = x * -3.0;
	} else if (z <= 1.6e+224) {
		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 <= -1.08e+172:
		tmp = t_0
	elif z <= -8100000000.0:
		tmp = t_1
	elif z <= 12.0:
		tmp = x * -3.0
	elif z <= 1.6e+224:
		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 <= -1.08e+172)
		tmp = t_0;
	elseif (z <= -8100000000.0)
		tmp = t_1;
	elseif (z <= 12.0)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e+224)
		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 <= -1.08e+172)
		tmp = t_0;
	elseif (z <= -8100000000.0)
		tmp = t_1;
	elseif (z <= 12.0)
		tmp = x * -3.0;
	elseif (z <= 1.6e+224)
		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, -1.08e+172], t$95$0, If[LessEqual[z, -8100000000.0], t$95$1, If[LessEqual[z, 12.0], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e+224], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0799999999999999e172 or 12 < z < 1.60000000000000007e224

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in z around inf 98.3%

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

      1. associate-*r* 98.6%

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

      2. metadata-eval 98.6%

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

      3. distribute-lft-neg-in 98.6%

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

      4. distribute-lft-neg-in 98.6%

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

      5. *-commutative 98.6%

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

      6. associate-*r* 98.5%

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

      7. rem-cube-cbrt 97.3%

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

      8. rem-cube-cbrt 98.5%

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

      9. *-commutative 98.5%

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

      10. distribute-rgt-neg-in 98.5%

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

      11. *-commutative 98.5%

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

      12. rem-cube-cbrt 97.3%

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

      13. mul-1-neg 97.3%

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

      14. rem-cube-cbrt 98.5%

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

      15. associate-*r* 98.5%

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

      16. metadata-eval 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in y around 0 59.7%

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

   if -1.0799999999999999e172 < z < -8.1e9 or 1.60000000000000007e224 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.4%

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

      1. associate-*r* 99.4%

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

      2. metadata-eval 99.4%

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

      3. distribute-lft-neg-in 99.4%

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

      4. distribute-lft-neg-in 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. rem-cube-cbrt 98.5%

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

      8. rem-cube-cbrt 99.4%

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

      9. *-commutative 99.4%

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

      10. distribute-rgt-neg-in 99.4%

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

      11. *-commutative 99.4%

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

      12. rem-cube-cbrt 98.5%

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

      13. mul-1-neg 98.5%

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

      14. rem-cube-cbrt 99.4%

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

      15. associate-*r* 99.4%

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

      16. metadata-eval 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around inf 64.9%

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

   if -8.1e9 < z < 12

   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 43.4%

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

      1. sub-neg 43.4%

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

      2. distribute-rgt-in 43.4%

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

      3. metadata-eval 43.4%

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

      4. distribute-lft-neg-in 43.4%

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

      5. associate-+r+ 43.4%

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

      6. metadata-eval 43.4%

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

      7. distribute-rgt-neg-in 43.4%

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

      8. metadata-eval 43.4%

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

   7. Simplified 43.4%

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

   8. Taylor expanded in z around 0 41.3%

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

      1. *-commutative 41.3%

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

   10. Simplified 41.3%

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

Alternative 9: 97.8% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.5)))
   (* (- 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 <= 0.5)) {
		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 <= 0.5d0))) 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 <= 0.5)) {
		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 <= 0.5):
		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 <= 0.5))
		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 <= 0.5)))
		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, 0.5]], $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 0.5 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. flip-+ 75.5%

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

      2. metadata-eval 75.5%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{\color{blue}{16} - \left(z \cdot -6\right) \cdot \left(z \cdot -6\right)}{4 - z \cdot -6}, x\right) \]

      3. swap-sqr 75.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{16 - \color{blue}{\left(z \cdot z\right) \cdot \left(-6 \cdot -6\right)}}{4 - z \cdot -6}, x\right) \]

      4. pow2 75.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{16 - \color{blue}{{z}^{2}} \cdot \left(-6 \cdot -6\right)}{4 - z \cdot -6}, x\right) \]

      5. metadata-eval 75.4%

         \[\leadsto \mathsf{fma}\left(y - x, \frac{16 - {z}^{2} \cdot \color{blue}{36}}{4 - z \cdot -6}, x\right) \]

   6. Applied egg-rr 75.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{16 - {z}^{2} \cdot 36}{4 - z \cdot -6}}, x\right) \]

   7. Taylor expanded in z around inf 97.1%

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

      1. associate-*r* 97.2%

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

   9. Simplified 97.2%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 99.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-40} \lor \neg \left(x \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.12e-40) (not (<= x 6.5e+31)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.12e-40) || !(x <= 6.5e+31)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.12d-40)) .or. (.not. (x <= 6.5d+31))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.12e-40) || !(x <= 6.5e+31)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.12e-40) or not (x <= 6.5e+31):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.12e-40) || !(x <= 6.5e+31))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.12e-40) || ~((x <= 6.5e+31)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.12e-40], N[Not[LessEqual[x, 6.5e+31]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1200000000000001e-40 or 6.5000000000000004e31 < 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 79.8%

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

      1. sub-neg 79.8%

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

      2. distribute-rgt-in 79.8%

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

      3. metadata-eval 79.8%

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

      4. distribute-lft-neg-in 79.8%

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

      5. associate-+r+ 79.8%

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

      6. metadata-eval 79.8%

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

      7. distribute-rgt-neg-in 79.8%

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

      8. metadata-eval 79.8%

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

   7. Simplified 79.8%

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

   if -1.1200000000000001e-40 < x < 6.5000000000000004e31

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 84.5%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-40} \lor \neg \left(x \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8100000000 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8100000000.0) (not (<= z 0.65))) (* -6.0 (* y z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8100000000.0) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8100000000.0d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8100000000.0) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8100000000.0) or not (z <= 0.65):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8100000000.0) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8100000000.0) || ~((z <= 0.65)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8100000000.0], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1e9 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 98.2%

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

      1. associate-*r* 98.3%

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

      2. metadata-eval 98.3%

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

      3. distribute-lft-neg-in 98.3%

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

      4. distribute-lft-neg-in 98.3%

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

      5. *-commutative 98.3%

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

      6. associate-*r* 98.2%

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

      7. rem-cube-cbrt 97.2%

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

      8. rem-cube-cbrt 98.2%

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

      9. *-commutative 98.2%

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

      10. distribute-rgt-neg-in 98.2%

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

      11. *-commutative 98.2%

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

      12. rem-cube-cbrt 97.2%

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

      13. mul-1-neg 97.2%

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

      14. rem-cube-cbrt 98.2%

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

      15. associate-*r* 98.2%

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

      16. metadata-eval 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in y around inf 50.5%

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

   if -8.1e9 < z < 0.650000000000000022

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 43.7%

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

      1. sub-neg 43.7%

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

      2. distribute-rgt-in 43.7%

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

      3. metadata-eval 43.7%

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

      4. distribute-lft-neg-in 43.7%

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

      5. associate-+r+ 43.7%

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

      6. metadata-eval 43.7%

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

      7. distribute-rgt-neg-in 43.7%

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

      8. metadata-eval 43.7%

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

   7. Simplified 43.7%

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

   8. Taylor expanded in z around 0 41.6%

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

      1. *-commutative 41.6%

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

   10. Simplified 41.6%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8100000000 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

   \[\leadsto x + \left(-6 \cdot \left(\left(y - x\right) \cdot z\right) + \left(y - x\right) \cdot 4\right) \]
7. 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 99.5%

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

Alternative 14: 26.8% 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 48.6%

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

   1. sub-neg 48.6%

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

   2. distribute-rgt-in 48.6%

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

   3. metadata-eval 48.6%

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

   4. distribute-lft-neg-in 48.6%

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

   5. associate-+r+ 48.6%

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

   6. metadata-eval 48.6%

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

   7. distribute-rgt-neg-in 48.6%

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

   8. metadata-eval 48.6%

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

7. Simplified 48.6%

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

8. Taylor expanded in z around 0 21.5%

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

   1. *-commutative 21.5%

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

10. Simplified 21.5%

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

Reproduce

herbie shell --seed 2024086 
(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))))