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

Percentage Accurate: 99.5% → 99.8%

Time: 13.3s

Alternatives: 19

Speedup: 1.2×

• 21.3% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. sub-neg 99.8%

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

   5. +-commutative 99.8%

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

   6. distribute-lft-in 99.8%

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

   7. 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. distribute-lft-neg-in 99.8%

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

   9. *-commutative 99.8%

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

   10. fma-def 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 49.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot -6\right)\\ t_1 := y \cdot \left(z \cdot -6\right)\\ t_2 := z \cdot \left(x \cdot 6\right)\\ t_3 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+195}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+167}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-124}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-45}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y -6.0)))
        (t_1 (* y (* z -6.0)))
        (t_2 (* z (* x 6.0)))
        (t_3 (* x (* z 6.0))))
   (if (<= z -3.8e+237)
     t_1
     (if (<= z -1.3e+195)
       t_3
       (if (<= z -3.8e+167)
         t_0
         (if (<= z -4.8e+150)
           t_2
           (if (<= z -5.7e+113)
             t_1
             (if (<= z -1.05e+14)
               t_2
               (if (<= z -8.6e-55)
                 (* y 4.0)
                 (if (<= z -5.3e-214)
                   (* x -3.0)
                   (if (<= z 4.9e-298)
                     (* y 4.0)
                     (if (<= z 1.8e-168)
                       (* x -3.0)
                       (if (<= z 3.3e-124)
                         (* y 4.0)
                         (if (<= z 1.85e-45)
                           (* x -3.0)
                           (if (<= z 8.8e-9)
                             (* y 4.0)
                             (if (<= z 1.15e+184) t_0 t_3))))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * -6.0);
	double t_1 = y * (z * -6.0);
	double t_2 = z * (x * 6.0);
	double t_3 = x * (z * 6.0);
	double tmp;
	if (z <= -3.8e+237) {
		tmp = t_1;
	} else if (z <= -1.3e+195) {
		tmp = t_3;
	} else if (z <= -3.8e+167) {
		tmp = t_0;
	} else if (z <= -4.8e+150) {
		tmp = t_2;
	} else if (z <= -5.7e+113) {
		tmp = t_1;
	} else if (z <= -1.05e+14) {
		tmp = t_2;
	} else if (z <= -8.6e-55) {
		tmp = y * 4.0;
	} else if (z <= -5.3e-214) {
		tmp = x * -3.0;
	} else if (z <= 4.9e-298) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-168) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-124) {
		tmp = y * 4.0;
	} else if (z <= 1.85e-45) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 1.15e+184) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = z * (y * (-6.0d0))
    t_1 = y * (z * (-6.0d0))
    t_2 = z * (x * 6.0d0)
    t_3 = x * (z * 6.0d0)
    if (z <= (-3.8d+237)) then
        tmp = t_1
    else if (z <= (-1.3d+195)) then
        tmp = t_3
    else if (z <= (-3.8d+167)) then
        tmp = t_0
    else if (z <= (-4.8d+150)) then
        tmp = t_2
    else if (z <= (-5.7d+113)) then
        tmp = t_1
    else if (z <= (-1.05d+14)) then
        tmp = t_2
    else if (z <= (-8.6d-55)) then
        tmp = y * 4.0d0
    else if (z <= (-5.3d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.9d-298) then
        tmp = y * 4.0d0
    else if (z <= 1.8d-168) then
        tmp = x * (-3.0d0)
    else if (z <= 3.3d-124) then
        tmp = y * 4.0d0
    else if (z <= 1.85d-45) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-9) then
        tmp = y * 4.0d0
    else if (z <= 1.15d+184) then
        tmp = t_0
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * -6.0);
	double t_1 = y * (z * -6.0);
	double t_2 = z * (x * 6.0);
	double t_3 = x * (z * 6.0);
	double tmp;
	if (z <= -3.8e+237) {
		tmp = t_1;
	} else if (z <= -1.3e+195) {
		tmp = t_3;
	} else if (z <= -3.8e+167) {
		tmp = t_0;
	} else if (z <= -4.8e+150) {
		tmp = t_2;
	} else if (z <= -5.7e+113) {
		tmp = t_1;
	} else if (z <= -1.05e+14) {
		tmp = t_2;
	} else if (z <= -8.6e-55) {
		tmp = y * 4.0;
	} else if (z <= -5.3e-214) {
		tmp = x * -3.0;
	} else if (z <= 4.9e-298) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-168) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-124) {
		tmp = y * 4.0;
	} else if (z <= 1.85e-45) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 1.15e+184) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * -6.0)
	t_1 = y * (z * -6.0)
	t_2 = z * (x * 6.0)
	t_3 = x * (z * 6.0)
	tmp = 0
	if z <= -3.8e+237:
		tmp = t_1
	elif z <= -1.3e+195:
		tmp = t_3
	elif z <= -3.8e+167:
		tmp = t_0
	elif z <= -4.8e+150:
		tmp = t_2
	elif z <= -5.7e+113:
		tmp = t_1
	elif z <= -1.05e+14:
		tmp = t_2
	elif z <= -8.6e-55:
		tmp = y * 4.0
	elif z <= -5.3e-214:
		tmp = x * -3.0
	elif z <= 4.9e-298:
		tmp = y * 4.0
	elif z <= 1.8e-168:
		tmp = x * -3.0
	elif z <= 3.3e-124:
		tmp = y * 4.0
	elif z <= 1.85e-45:
		tmp = x * -3.0
	elif z <= 8.8e-9:
		tmp = y * 4.0
	elif z <= 1.15e+184:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * -6.0))
	t_1 = Float64(y * Float64(z * -6.0))
	t_2 = Float64(z * Float64(x * 6.0))
	t_3 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.8e+237)
		tmp = t_1;
	elseif (z <= -1.3e+195)
		tmp = t_3;
	elseif (z <= -3.8e+167)
		tmp = t_0;
	elseif (z <= -4.8e+150)
		tmp = t_2;
	elseif (z <= -5.7e+113)
		tmp = t_1;
	elseif (z <= -1.05e+14)
		tmp = t_2;
	elseif (z <= -8.6e-55)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.3e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.9e-298)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.8e-168)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.3e-124)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.85e-45)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-9)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.15e+184)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * -6.0);
	t_1 = y * (z * -6.0);
	t_2 = z * (x * 6.0);
	t_3 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.8e+237)
		tmp = t_1;
	elseif (z <= -1.3e+195)
		tmp = t_3;
	elseif (z <= -3.8e+167)
		tmp = t_0;
	elseif (z <= -4.8e+150)
		tmp = t_2;
	elseif (z <= -5.7e+113)
		tmp = t_1;
	elseif (z <= -1.05e+14)
		tmp = t_2;
	elseif (z <= -8.6e-55)
		tmp = y * 4.0;
	elseif (z <= -5.3e-214)
		tmp = x * -3.0;
	elseif (z <= 4.9e-298)
		tmp = y * 4.0;
	elseif (z <= 1.8e-168)
		tmp = x * -3.0;
	elseif (z <= 3.3e-124)
		tmp = y * 4.0;
	elseif (z <= 1.85e-45)
		tmp = x * -3.0;
	elseif (z <= 8.8e-9)
		tmp = y * 4.0;
	elseif (z <= 1.15e+184)
		tmp = t_0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+237], t$95$1, If[LessEqual[z, -1.3e+195], t$95$3, If[LessEqual[z, -3.8e+167], t$95$0, If[LessEqual[z, -4.8e+150], t$95$2, If[LessEqual[z, -5.7e+113], t$95$1, If[LessEqual[z, -1.05e+14], t$95$2, If[LessEqual[z, -8.6e-55], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.3e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.9e-298], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.8e-168], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.3e-124], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.85e-45], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-9], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.15e+184], t$95$0, t$95$3]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.8e237 or -4.80000000000000005e150 < z < -5.6999999999999998e113

   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. Step-by-step derivation

      1. flip-+ 26.0%

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

      2. div-inv 25.9%

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

      3. pow2 25.9%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 25.9%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 25.9%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 26.0%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 26.0%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in z around inf 79.1%

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

   if -3.8e237 < z < -1.30000000000000001e195 or 1.15e184 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 64.7%

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

      1. sub-neg 64.7%

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

      2. distribute-rgt-in 64.7%

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

      3. metadata-eval 64.7%

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

      4. metadata-eval 64.7%

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

      5. distribute-lft-neg-in 64.7%

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

      6. associate-+r+ 64.7%

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

      7. metadata-eval 64.7%

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

      8. metadata-eval 64.7%

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

      9. distribute-rgt-neg-in 64.7%

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

      10. metadata-eval 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in z around inf 64.7%

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

   if -1.30000000000000001e195 < z < -3.79999999999999994e167 or 8.7999999999999994e-9 < z < 1.15e184

   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* 99.6%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around -inf 99.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]

   6. Taylor expanded in z around inf 87.6%

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

   7. Taylor expanded in y around inf 56.6%

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

   if -3.79999999999999994e167 < z < -4.80000000000000005e150 or -5.6999999999999998e113 < z < -1.05e14

   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. +-commutative 99.8%

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

      2. associate-*l* 99.3%

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

      3. fma-def 99.4%

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

      4. sub-neg 99.4%

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

      5. distribute-rgt-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. metadata-eval 99.4%

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

      8. distribute-lft-neg-out 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around -inf 99.4%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]

   6. Taylor expanded in z around inf 99.7%

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

   7. Taylor expanded in y around 0 74.1%

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

   if -1.05e14 < z < -8.60000000000000021e-55 or -5.30000000000000005e-214 < z < 4.9e-298 or 1.7999999999999999e-168 < z < 3.29999999999999984e-124 or 1.85e-45 < z < 8.7999999999999994e-9

   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. Step-by-step derivation

      1. flip-+ 46.9%

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

      2. div-inv 46.8%

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

      3. pow2 46.8%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 46.8%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 46.8%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 46.9%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

   10. Simplified 74.0%

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

   11. Taylor expanded in z around 0 67.1%

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

       1. *-commutative 67.1%

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

   13. Simplified 67.1%

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

   if -8.60000000000000021e-55 < z < -5.30000000000000005e-214 or 4.9e-298 < z < 1.7999999999999999e-168 or 3.29999999999999984e-124 < z < 1.85e-45

   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 73.7%

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

      1. sub-neg 73.7%

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

      2. distribute-rgt-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. metadata-eval 73.7%

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

      5. distribute-lft-neg-in 73.7%

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

      6. associate-+r+ 73.7%

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

      7. metadata-eval 73.7%

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

      8. metadata-eval 73.7%

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

      9. distribute-rgt-neg-in 73.7%

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

      10. metadata-eval 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in z around 0 73.7%

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

      1. *-commutative 73.7%

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

   10. Simplified 73.7%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-124}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-45}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-54}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-168}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.03 \cdot 10^{-44}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+183}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -3.3e+237)
     t_0
     (if (<= z -1.02e+151)
       t_1
       (if (<= z -3e+105)
         t_0
         (if (<= z -1.05e+14)
           t_1
           (if (<= z -1.08e-54)
             (* y 4.0)
             (if (<= z -4.2e-214)
               (* x -3.0)
               (if (<= z 2.1e-298)
                 (* y 4.0)
                 (if (<= z 3.9e-168)
                   (* x -3.0)
                   (if (<= z 6.6e-116)
                     (* y 4.0)
                     (if (<= z 1.03e-44)
                       (* x -3.0)
                       (if (<= z 8.8e-9)
                         (* y 4.0)
                         (if (<= z 6e+183) t_0 t_1))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -3.3e+237) {
		tmp = t_0;
	} else if (z <= -1.02e+151) {
		tmp = t_1;
	} else if (z <= -3e+105) {
		tmp = t_0;
	} else if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -1.08e-54) {
		tmp = y * 4.0;
	} else if (z <= -4.2e-214) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-298) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-168) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-116) {
		tmp = y * 4.0;
	} else if (z <= 1.03e-44) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 6e+183) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * (z * 6.0d0)
    if (z <= (-3.3d+237)) then
        tmp = t_0
    else if (z <= (-1.02d+151)) then
        tmp = t_1
    else if (z <= (-3d+105)) then
        tmp = t_0
    else if (z <= (-1.05d+14)) then
        tmp = t_1
    else if (z <= (-1.08d-54)) then
        tmp = y * 4.0d0
    else if (z <= (-4.2d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.1d-298) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-168) then
        tmp = x * (-3.0d0)
    else if (z <= 6.6d-116) then
        tmp = y * 4.0d0
    else if (z <= 1.03d-44) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-9) then
        tmp = y * 4.0d0
    else if (z <= 6d+183) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -3.3e+237) {
		tmp = t_0;
	} else if (z <= -1.02e+151) {
		tmp = t_1;
	} else if (z <= -3e+105) {
		tmp = t_0;
	} else if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -1.08e-54) {
		tmp = y * 4.0;
	} else if (z <= -4.2e-214) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-298) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-168) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-116) {
		tmp = y * 4.0;
	} else if (z <= 1.03e-44) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 6e+183) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -3.3e+237:
		tmp = t_0
	elif z <= -1.02e+151:
		tmp = t_1
	elif z <= -3e+105:
		tmp = t_0
	elif z <= -1.05e+14:
		tmp = t_1
	elif z <= -1.08e-54:
		tmp = y * 4.0
	elif z <= -4.2e-214:
		tmp = x * -3.0
	elif z <= 2.1e-298:
		tmp = y * 4.0
	elif z <= 3.9e-168:
		tmp = x * -3.0
	elif z <= 6.6e-116:
		tmp = y * 4.0
	elif z <= 1.03e-44:
		tmp = x * -3.0
	elif z <= 8.8e-9:
		tmp = y * 4.0
	elif z <= 6e+183:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.3e+237)
		tmp = t_0;
	elseif (z <= -1.02e+151)
		tmp = t_1;
	elseif (z <= -3e+105)
		tmp = t_0;
	elseif (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -1.08e-54)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.2e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.1e-298)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-168)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.6e-116)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.03e-44)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-9)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e+183)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.3e+237)
		tmp = t_0;
	elseif (z <= -1.02e+151)
		tmp = t_1;
	elseif (z <= -3e+105)
		tmp = t_0;
	elseif (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -1.08e-54)
		tmp = y * 4.0;
	elseif (z <= -4.2e-214)
		tmp = x * -3.0;
	elseif (z <= 2.1e-298)
		tmp = y * 4.0;
	elseif (z <= 3.9e-168)
		tmp = x * -3.0;
	elseif (z <= 6.6e-116)
		tmp = y * 4.0;
	elseif (z <= 1.03e-44)
		tmp = x * -3.0;
	elseif (z <= 8.8e-9)
		tmp = y * 4.0;
	elseif (z <= 6e+183)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+237], t$95$0, If[LessEqual[z, -1.02e+151], t$95$1, If[LessEqual[z, -3e+105], t$95$0, If[LessEqual[z, -1.05e+14], t$95$1, If[LessEqual[z, -1.08e-54], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.2e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.1e-298], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-168], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.6e-116], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.03e-44], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-9], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e+183], t$95$0, t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3000000000000001e237 or -1.02000000000000002e151 < z < -3.0000000000000001e105 or 8.7999999999999994e-9 < z < 5.99999999999999992e183

   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. Step-by-step derivation

      1. flip-+ 21.5%

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

      2. div-inv 21.4%

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

      3. pow2 21.4%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 21.4%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 21.3%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 21.4%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 21.4%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 64.7%

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

      1. *-commutative 64.7%

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

   10. Simplified 64.7%

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

   11. Taylor expanded in z around inf 62.9%

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

   if -3.3000000000000001e237 < z < -1.02000000000000002e151 or -3.0000000000000001e105 < z < -1.05e14 or 5.99999999999999992e183 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 64.0%

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

      1. sub-neg 64.0%

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

      2. distribute-rgt-in 64.0%

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

      3. metadata-eval 64.0%

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

      4. metadata-eval 64.0%

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

      5. distribute-lft-neg-in 64.0%

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

      6. associate-+r+ 64.0%

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

      7. metadata-eval 64.0%

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

      8. metadata-eval 64.0%

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

      9. distribute-rgt-neg-in 64.0%

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

      10. metadata-eval 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around inf 64.0%

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

   if -1.05e14 < z < -1.08000000000000002e-54 or -4.19999999999999984e-214 < z < 2.10000000000000005e-298 or 3.90000000000000012e-168 < z < 6.60000000000000002e-116 or 1.03e-44 < z < 8.7999999999999994e-9

   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. Step-by-step derivation

      1. flip-+ 46.9%

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

      2. div-inv 46.8%

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

      3. pow2 46.8%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 46.8%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 46.8%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 46.9%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

   10. Simplified 74.0%

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

   11. Taylor expanded in z around 0 67.1%

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

       1. *-commutative 67.1%

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

   13. Simplified 67.1%

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

   if -1.08000000000000002e-54 < z < -4.19999999999999984e-214 or 2.10000000000000005e-298 < z < 3.90000000000000012e-168 or 6.60000000000000002e-116 < z < 1.03e-44

   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 73.7%

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

      1. sub-neg 73.7%

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

      2. distribute-rgt-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. metadata-eval 73.7%

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

      5. distribute-lft-neg-in 73.7%

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

      6. associate-+r+ 73.7%

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

      7. metadata-eval 73.7%

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

      8. metadata-eval 73.7%

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

      9. distribute-rgt-neg-in 73.7%

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

      10. metadata-eval 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in z around 0 73.7%

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

      1. *-commutative 73.7%

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

   10. Simplified 73.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+237}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+105}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-54}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-168}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.03 \cdot 10^{-44}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+183}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-167}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-48}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+185}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))) (t_1 (* x (* z 6.0))))
   (if (<= z -2.85e+237)
     t_0
     (if (<= z -7.8e+148)
       t_1
       (if (<= z -7.1e+106)
         t_0
         (if (<= z -1.05e+14)
           t_1
           (if (<= z -3.5e-54)
             (* y 4.0)
             (if (<= z -6e-214)
               (* x -3.0)
               (if (<= z 1.35e-296)
                 (* y 4.0)
                 (if (<= z 7.6e-167)
                   (* x -3.0)
                   (if (<= z 4.5e-119)
                     (* y 4.0)
                     (if (<= z 1.3e-48)
                       (* x -3.0)
                       (if (<= z 8.8e-9)
                         (* y 4.0)
                         (if (<= z 8e+185) t_0 t_1))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -2.85e+237) {
		tmp = t_0;
	} else if (z <= -7.8e+148) {
		tmp = t_1;
	} else if (z <= -7.1e+106) {
		tmp = t_0;
	} else if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -3.5e-54) {
		tmp = y * 4.0;
	} else if (z <= -6e-214) {
		tmp = x * -3.0;
	} else if (z <= 1.35e-296) {
		tmp = y * 4.0;
	} else if (z <= 7.6e-167) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-119) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-48) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 8e+185) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (z * (-6.0d0))
    t_1 = x * (z * 6.0d0)
    if (z <= (-2.85d+237)) then
        tmp = t_0
    else if (z <= (-7.8d+148)) then
        tmp = t_1
    else if (z <= (-7.1d+106)) then
        tmp = t_0
    else if (z <= (-1.05d+14)) then
        tmp = t_1
    else if (z <= (-3.5d-54)) then
        tmp = y * 4.0d0
    else if (z <= (-6d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.35d-296) then
        tmp = y * 4.0d0
    else if (z <= 7.6d-167) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-119) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-48) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-9) then
        tmp = y * 4.0d0
    else if (z <= 8d+185) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -2.85e+237) {
		tmp = t_0;
	} else if (z <= -7.8e+148) {
		tmp = t_1;
	} else if (z <= -7.1e+106) {
		tmp = t_0;
	} else if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -3.5e-54) {
		tmp = y * 4.0;
	} else if (z <= -6e-214) {
		tmp = x * -3.0;
	} else if (z <= 1.35e-296) {
		tmp = y * 4.0;
	} else if (z <= 7.6e-167) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-119) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-48) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 8e+185) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -2.85e+237:
		tmp = t_0
	elif z <= -7.8e+148:
		tmp = t_1
	elif z <= -7.1e+106:
		tmp = t_0
	elif z <= -1.05e+14:
		tmp = t_1
	elif z <= -3.5e-54:
		tmp = y * 4.0
	elif z <= -6e-214:
		tmp = x * -3.0
	elif z <= 1.35e-296:
		tmp = y * 4.0
	elif z <= 7.6e-167:
		tmp = x * -3.0
	elif z <= 4.5e-119:
		tmp = y * 4.0
	elif z <= 1.3e-48:
		tmp = x * -3.0
	elif z <= 8.8e-9:
		tmp = y * 4.0
	elif z <= 8e+185:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -2.85e+237)
		tmp = t_0;
	elseif (z <= -7.8e+148)
		tmp = t_1;
	elseif (z <= -7.1e+106)
		tmp = t_0;
	elseif (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -3.5e-54)
		tmp = Float64(y * 4.0);
	elseif (z <= -6e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.35e-296)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.6e-167)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-119)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-48)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-9)
		tmp = Float64(y * 4.0);
	elseif (z <= 8e+185)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -2.85e+237)
		tmp = t_0;
	elseif (z <= -7.8e+148)
		tmp = t_1;
	elseif (z <= -7.1e+106)
		tmp = t_0;
	elseif (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -3.5e-54)
		tmp = y * 4.0;
	elseif (z <= -6e-214)
		tmp = x * -3.0;
	elseif (z <= 1.35e-296)
		tmp = y * 4.0;
	elseif (z <= 7.6e-167)
		tmp = x * -3.0;
	elseif (z <= 4.5e-119)
		tmp = y * 4.0;
	elseif (z <= 1.3e-48)
		tmp = x * -3.0;
	elseif (z <= 8.8e-9)
		tmp = y * 4.0;
	elseif (z <= 8e+185)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e+237], t$95$0, If[LessEqual[z, -7.8e+148], t$95$1, If[LessEqual[z, -7.1e+106], t$95$0, If[LessEqual[z, -1.05e+14], t$95$1, If[LessEqual[z, -3.5e-54], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.35e-296], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.6e-167], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-119], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-48], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-9], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8e+185], t$95$0, t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.84999999999999997e237 or -7.80000000000000004e148 < z < -7.1000000000000003e106 or 8.7999999999999994e-9 < z < 7.9999999999999998e185

   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. Step-by-step derivation

      1. flip-+ 21.5%

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

      2. div-inv 21.4%

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

      3. pow2 21.4%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 21.4%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 21.3%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 21.4%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 21.4%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 64.7%

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

      1. *-commutative 64.7%

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

   10. Simplified 64.7%

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

   11. Taylor expanded in z around inf 63.0%

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

   if -2.84999999999999997e237 < z < -7.80000000000000004e148 or -7.1000000000000003e106 < z < -1.05e14 or 7.9999999999999998e185 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 64.0%

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

      1. sub-neg 64.0%

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

      2. distribute-rgt-in 64.0%

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

      3. metadata-eval 64.0%

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

      4. metadata-eval 64.0%

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

      5. distribute-lft-neg-in 64.0%

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

      6. associate-+r+ 64.0%

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

      7. metadata-eval 64.0%

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

      8. metadata-eval 64.0%

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

      9. distribute-rgt-neg-in 64.0%

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

      10. metadata-eval 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around inf 64.0%

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

   if -1.05e14 < z < -3.49999999999999982e-54 or -5.99999999999999989e-214 < z < 1.34999999999999999e-296 or 7.59999999999999934e-167 < z < 4.5000000000000003e-119 or 1.29999999999999994e-48 < z < 8.7999999999999994e-9

   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. Step-by-step derivation

      1. flip-+ 46.9%

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

      2. div-inv 46.8%

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

      3. pow2 46.8%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 46.8%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 46.8%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 46.9%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

   10. Simplified 74.0%

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

   11. Taylor expanded in z around 0 67.1%

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

       1. *-commutative 67.1%

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

   13. Simplified 67.1%

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

   if -3.49999999999999982e-54 < z < -5.99999999999999989e-214 or 1.34999999999999999e-296 < z < 7.59999999999999934e-167 or 4.5000000000000003e-119 < z < 1.29999999999999994e-48

   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 73.7%

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

      1. sub-neg 73.7%

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

      2. distribute-rgt-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. metadata-eval 73.7%

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

      5. distribute-lft-neg-in 73.7%

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

      6. associate-+r+ 73.7%

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

      7. metadata-eval 73.7%

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

      8. metadata-eval 73.7%

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

      9. distribute-rgt-neg-in 73.7%

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

      10. metadata-eval 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in z around 0 73.7%

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

      1. *-commutative 73.7%

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

   10. Simplified 73.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-296}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-167}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-48}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-297}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-166}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-123}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))) (t_1 (* x (* z 6.0))))
   (if (<= z -1.5e+237)
     t_0
     (if (<= z -4.9e+150)
       t_1
       (if (<= z -4.5e+93)
         t_0
         (if (<= z -1.05e+14)
           t_1
           (if (<= z -4e-55)
             (* y 4.0)
             (if (<= z -3.1e-214)
               (* x -3.0)
               (if (<= z 2.1e-297)
                 (* y 4.0)
                 (if (<= z 1.45e-166)
                   (* x -3.0)
                   (if (<= z 3.2e-123)
                     (* y 4.0)
                     (if (<= z 1.45e-47)
                       (* x -3.0)
                       (if (<= z 8.8e-9)
                         (* y 4.0)
                         (if (<= z 3.1e+184) (* z (* y -6.0)) t_1))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.5e+237) {
		tmp = t_0;
	} else if (z <= -4.9e+150) {
		tmp = t_1;
	} else if (z <= -4.5e+93) {
		tmp = t_0;
	} else if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -4e-55) {
		tmp = y * 4.0;
	} else if (z <= -3.1e-214) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-297) {
		tmp = y * 4.0;
	} else if (z <= 1.45e-166) {
		tmp = x * -3.0;
	} else if (z <= 3.2e-123) {
		tmp = y * 4.0;
	} else if (z <= 1.45e-47) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 3.1e+184) {
		tmp = z * (y * -6.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (z * (-6.0d0))
    t_1 = x * (z * 6.0d0)
    if (z <= (-1.5d+237)) then
        tmp = t_0
    else if (z <= (-4.9d+150)) then
        tmp = t_1
    else if (z <= (-4.5d+93)) then
        tmp = t_0
    else if (z <= (-1.05d+14)) then
        tmp = t_1
    else if (z <= (-4d-55)) then
        tmp = y * 4.0d0
    else if (z <= (-3.1d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.1d-297) then
        tmp = y * 4.0d0
    else if (z <= 1.45d-166) then
        tmp = x * (-3.0d0)
    else if (z <= 3.2d-123) then
        tmp = y * 4.0d0
    else if (z <= 1.45d-47) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-9) then
        tmp = y * 4.0d0
    else if (z <= 3.1d+184) then
        tmp = z * (y * (-6.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.5e+237) {
		tmp = t_0;
	} else if (z <= -4.9e+150) {
		tmp = t_1;
	} else if (z <= -4.5e+93) {
		tmp = t_0;
	} else if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -4e-55) {
		tmp = y * 4.0;
	} else if (z <= -3.1e-214) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-297) {
		tmp = y * 4.0;
	} else if (z <= 1.45e-166) {
		tmp = x * -3.0;
	} else if (z <= 3.2e-123) {
		tmp = y * 4.0;
	} else if (z <= 1.45e-47) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else if (z <= 3.1e+184) {
		tmp = z * (y * -6.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -1.5e+237:
		tmp = t_0
	elif z <= -4.9e+150:
		tmp = t_1
	elif z <= -4.5e+93:
		tmp = t_0
	elif z <= -1.05e+14:
		tmp = t_1
	elif z <= -4e-55:
		tmp = y * 4.0
	elif z <= -3.1e-214:
		tmp = x * -3.0
	elif z <= 2.1e-297:
		tmp = y * 4.0
	elif z <= 1.45e-166:
		tmp = x * -3.0
	elif z <= 3.2e-123:
		tmp = y * 4.0
	elif z <= 1.45e-47:
		tmp = x * -3.0
	elif z <= 8.8e-9:
		tmp = y * 4.0
	elif z <= 3.1e+184:
		tmp = z * (y * -6.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -1.5e+237)
		tmp = t_0;
	elseif (z <= -4.9e+150)
		tmp = t_1;
	elseif (z <= -4.5e+93)
		tmp = t_0;
	elseif (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -4e-55)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.1e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.1e-297)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.45e-166)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.2e-123)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.45e-47)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-9)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.1e+184)
		tmp = Float64(z * Float64(y * -6.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -1.5e+237)
		tmp = t_0;
	elseif (z <= -4.9e+150)
		tmp = t_1;
	elseif (z <= -4.5e+93)
		tmp = t_0;
	elseif (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -4e-55)
		tmp = y * 4.0;
	elseif (z <= -3.1e-214)
		tmp = x * -3.0;
	elseif (z <= 2.1e-297)
		tmp = y * 4.0;
	elseif (z <= 1.45e-166)
		tmp = x * -3.0;
	elseif (z <= 3.2e-123)
		tmp = y * 4.0;
	elseif (z <= 1.45e-47)
		tmp = x * -3.0;
	elseif (z <= 8.8e-9)
		tmp = y * 4.0;
	elseif (z <= 3.1e+184)
		tmp = z * (y * -6.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+237], t$95$0, If[LessEqual[z, -4.9e+150], t$95$1, If[LessEqual[z, -4.5e+93], t$95$0, If[LessEqual[z, -1.05e+14], t$95$1, If[LessEqual[z, -4e-55], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.1e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.1e-297], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.45e-166], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.2e-123], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.45e-47], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-9], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.1e+184], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5e237 or -4.90000000000000007e150 < z < -4.49999999999999991e93

   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. Step-by-step derivation

      1. flip-+ 26.0%

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

      2. div-inv 25.9%

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

      3. pow2 25.9%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 25.9%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 25.9%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 26.0%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 26.0%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in z around inf 79.1%

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

   if -1.5e237 < z < -4.90000000000000007e150 or -4.49999999999999991e93 < z < -1.05e14 or 3.0999999999999998e184 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 64.0%

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

      1. sub-neg 64.0%

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

      2. distribute-rgt-in 64.0%

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

      3. metadata-eval 64.0%

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

      4. metadata-eval 64.0%

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

      5. distribute-lft-neg-in 64.0%

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

      6. associate-+r+ 64.0%

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

      7. metadata-eval 64.0%

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

      8. metadata-eval 64.0%

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

      9. distribute-rgt-neg-in 64.0%

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

      10. metadata-eval 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in z around inf 64.0%

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

   if -1.05e14 < z < -3.99999999999999998e-55 or -3.10000000000000004e-214 < z < 2.10000000000000013e-297 or 1.45e-166 < z < 3.19999999999999979e-123 or 1.45e-47 < z < 8.7999999999999994e-9

   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. Step-by-step derivation

      1. flip-+ 46.9%

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

      2. div-inv 46.8%

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

      3. pow2 46.8%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 46.8%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 46.8%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 46.9%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 46.9%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

   10. Simplified 74.0%

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

   11. Taylor expanded in z around 0 67.1%

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

       1. *-commutative 67.1%

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

   13. Simplified 67.1%

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

   if -3.99999999999999998e-55 < z < -3.10000000000000004e-214 or 2.10000000000000013e-297 < z < 1.45e-166 or 3.19999999999999979e-123 < z < 1.45e-47

   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 73.7%

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

      1. sub-neg 73.7%

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

      2. distribute-rgt-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. metadata-eval 73.7%

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

      5. distribute-lft-neg-in 73.7%

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

      6. associate-+r+ 73.7%

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

      7. metadata-eval 73.7%

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

      8. metadata-eval 73.7%

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

      9. distribute-rgt-neg-in 73.7%

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

      10. metadata-eval 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in z around 0 73.7%

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

      1. *-commutative 73.7%

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

   10. Simplified 73.7%

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

   if 8.7999999999999994e-9 < z < 3.0999999999999998e184

   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* 99.6%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around -inf 99.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]

   6. Taylor expanded in z around inf 85.6%

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

   7. Taylor expanded in y around inf 52.0%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+237}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-297}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-166}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-123}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-297}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-168}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-50}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 12500000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -1.05e+14)
     t_1
     (if (<= z -1.8e-83)
       t_0
       (if (<= z -5.3e-214)
         (* x -3.0)
         (if (<= z 6e-297)
           (* y 4.0)
           (if (<= z 6.3e-168)
             (* x -3.0)
             (if (<= z 1.8e-126)
               (* y 4.0)
               (if (<= z 6.3e-50)
                 (* x -3.0)
                 (if (<= z 12500000.0) t_0 t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -1.8e-83) {
		tmp = t_0;
	} else if (z <= -5.3e-214) {
		tmp = x * -3.0;
	} else if (z <= 6e-297) {
		tmp = y * 4.0;
	} else if (z <= 6.3e-168) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-126) {
		tmp = y * 4.0;
	} else if (z <= 6.3e-50) {
		tmp = x * -3.0;
	} else if (z <= 12500000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-1.05d+14)) then
        tmp = t_1
    else if (z <= (-1.8d-83)) then
        tmp = t_0
    else if (z <= (-5.3d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 6d-297) then
        tmp = y * 4.0d0
    else if (z <= 6.3d-168) then
        tmp = x * (-3.0d0)
    else if (z <= 1.8d-126) then
        tmp = y * 4.0d0
    else if (z <= 6.3d-50) then
        tmp = x * (-3.0d0)
    else if (z <= 12500000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.05e+14) {
		tmp = t_1;
	} else if (z <= -1.8e-83) {
		tmp = t_0;
	} else if (z <= -5.3e-214) {
		tmp = x * -3.0;
	} else if (z <= 6e-297) {
		tmp = y * 4.0;
	} else if (z <= 6.3e-168) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-126) {
		tmp = y * 4.0;
	} else if (z <= 6.3e-50) {
		tmp = x * -3.0;
	} else if (z <= 12500000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -1.05e+14:
		tmp = t_1
	elif z <= -1.8e-83:
		tmp = t_0
	elif z <= -5.3e-214:
		tmp = x * -3.0
	elif z <= 6e-297:
		tmp = y * 4.0
	elif z <= 6.3e-168:
		tmp = x * -3.0
	elif z <= 1.8e-126:
		tmp = y * 4.0
	elif z <= 6.3e-50:
		tmp = x * -3.0
	elif z <= 12500000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -1.8e-83)
		tmp = t_0;
	elseif (z <= -5.3e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 6e-297)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.3e-168)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.8e-126)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.3e-50)
		tmp = Float64(x * -3.0);
	elseif (z <= 12500000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -1.05e+14)
		tmp = t_1;
	elseif (z <= -1.8e-83)
		tmp = t_0;
	elseif (z <= -5.3e-214)
		tmp = x * -3.0;
	elseif (z <= 6e-297)
		tmp = y * 4.0;
	elseif (z <= 6.3e-168)
		tmp = x * -3.0;
	elseif (z <= 1.8e-126)
		tmp = y * 4.0;
	elseif (z <= 6.3e-50)
		tmp = x * -3.0;
	elseif (z <= 12500000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+14], t$95$1, If[LessEqual[z, -1.8e-83], t$95$0, If[LessEqual[z, -5.3e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6e-297], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.3e-168], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.8e-126], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.3e-50], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 12500000.0], t$95$0, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e14 or 1.25e7 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. flip-+ 19.3%

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

      2. div-inv 19.2%

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

      3. pow2 19.2%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 19.2%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 19.1%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 19.2%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 19.2%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in z around inf 99.3%

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

   if -1.05e14 < z < -1.80000000000000006e-83 or 6.30000000000000023e-50 < z < 1.25e7

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 66.0%

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

   6. Taylor expanded in x around 0 66.1%

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

   if -1.80000000000000006e-83 < z < -5.30000000000000005e-214 or 5.9999999999999999e-297 < z < 6.29999999999999958e-168 or 1.8e-126 < z < 6.30000000000000023e-50

   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 76.0%

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

      1. sub-neg 76.0%

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

      2. distribute-rgt-in 76.0%

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

      3. metadata-eval 76.0%

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

      4. metadata-eval 76.0%

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

      5. distribute-lft-neg-in 76.0%

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

      6. associate-+r+ 76.0%

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

      7. metadata-eval 76.0%

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

      8. metadata-eval 76.0%

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

      9. distribute-rgt-neg-in 76.0%

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

      10. metadata-eval 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in z around 0 76.0%

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

      1. *-commutative 76.0%

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

   10. Simplified 76.0%

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

   if -5.30000000000000005e-214 < z < 5.9999999999999999e-297 or 6.29999999999999958e-168 < z < 1.8e-126

   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. Step-by-step derivation

      1. flip-+ 48.1%

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

      2. div-inv 48.0%

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

      3. pow2 48.0%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 48.0%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 48.0%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 48.1%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 48.1%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 72.3%

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

      1. *-commutative 72.3%

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

   10. Simplified 72.3%

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

   11. Taylor expanded in z around 0 72.3%

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

       1. *-commutative 72.3%

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

   13. Simplified 72.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-297}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-168}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-50}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 12500000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-124}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -6.6e-9)
     t_0
     (if (<= z -2.7e-214)
       (* x -3.0)
       (if (<= z 1.05e-298)
         (* y 4.0)
         (if (<= z 2.9e-166)
           (* x -3.0)
           (if (<= z 4.5e-124)
             (* y 4.0)
             (if (<= z 4.1e-57)
               (* x -3.0)
               (if (<= z 0.62) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -6.6e-9) {
		tmp = t_0;
	} else if (z <= -2.7e-214) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-298) {
		tmp = y * 4.0;
	} else if (z <= 2.9e-166) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-124) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-57) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-6.6d-9)) then
        tmp = t_0
    else if (z <= (-2.7d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d-298) then
        tmp = y * 4.0d0
    else if (z <= 2.9d-166) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-124) then
        tmp = y * 4.0d0
    else if (z <= 4.1d-57) then
        tmp = x * (-3.0d0)
    else if (z <= 0.62d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -6.6e-9) {
		tmp = t_0;
	} else if (z <= -2.7e-214) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-298) {
		tmp = y * 4.0;
	} else if (z <= 2.9e-166) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-124) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-57) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -6.6e-9:
		tmp = t_0
	elif z <= -2.7e-214:
		tmp = x * -3.0
	elif z <= 1.05e-298:
		tmp = y * 4.0
	elif z <= 2.9e-166:
		tmp = x * -3.0
	elif z <= 4.5e-124:
		tmp = y * 4.0
	elif z <= 4.1e-57:
		tmp = x * -3.0
	elif z <= 0.62:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -6.6e-9)
		tmp = t_0;
	elseif (z <= -2.7e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05e-298)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.9e-166)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-124)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.1e-57)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.62)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -6.6e-9)
		tmp = t_0;
	elseif (z <= -2.7e-214)
		tmp = x * -3.0;
	elseif (z <= 1.05e-298)
		tmp = y * 4.0;
	elseif (z <= 2.9e-166)
		tmp = x * -3.0;
	elseif (z <= 4.5e-124)
		tmp = y * 4.0;
	elseif (z <= 4.1e-57)
		tmp = x * -3.0;
	elseif (z <= 0.62)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-9], t$95$0, If[LessEqual[z, -2.7e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05e-298], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.9e-166], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-124], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.1e-57], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.60000000000000037e-9 or 0.619999999999999996 < 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. Step-by-step derivation

      1. flip-+ 21.4%

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

      2. div-inv 21.3%

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

      3. pow2 21.3%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 21.3%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 21.2%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 21.3%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 21.3%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in z around inf 95.8%

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

   if -6.60000000000000037e-9 < z < -2.7000000000000001e-214 or 1.05000000000000002e-298 < z < 2.9e-166 or 4.4999999999999996e-124 < z < 4.1000000000000001e-57

   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 71.5%

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

      1. sub-neg 71.5%

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

      2. distribute-rgt-in 71.5%

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

      3. metadata-eval 71.5%

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

      4. metadata-eval 71.5%

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

      5. distribute-lft-neg-in 71.5%

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

      6. associate-+r+ 71.5%

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

      7. metadata-eval 71.5%

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

      8. metadata-eval 71.5%

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

      9. distribute-rgt-neg-in 71.5%

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

      10. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in z around 0 71.5%

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

      1. *-commutative 71.5%

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

   10. Simplified 71.5%

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

   if -2.7000000000000001e-214 < z < 1.05000000000000002e-298 or 2.9e-166 < z < 4.4999999999999996e-124 or 4.1000000000000001e-57 < z < 0.619999999999999996

   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. Step-by-step derivation

      1. flip-+ 43.0%

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

      2. div-inv 43.0%

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

      3. pow2 43.0%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 43.0%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 43.0%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 43.1%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 43.1%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 68.2%

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

      1. *-commutative 68.2%

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

   10. Simplified 68.2%

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

   11. Taylor expanded in z around 0 67.7%

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

       1. *-commutative 67.7%

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

   13. Simplified 67.7%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-9}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-166}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-124}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-57}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-169}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -6.6e-9)
     t_0
     (if (<= z -3.6e-214)
       (* x -3.0)
       (if (<= z 9.2e-298)
         (* y 4.0)
         (if (<= z 7e-169)
           (* x -3.0)
           (if (<= z 2.3e-117)
             (* y 4.0)
             (if (<= z 2.8e-48)
               (* x -3.0)
               (if (<= z 8.8e-9) (* y 4.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.6e-9) {
		tmp = t_0;
	} else if (z <= -3.6e-214) {
		tmp = x * -3.0;
	} else if (z <= 9.2e-298) {
		tmp = y * 4.0;
	} else if (z <= 7e-169) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-117) {
		tmp = y * 4.0;
	} else if (z <= 2.8e-48) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-6.6d-9)) then
        tmp = t_0
    else if (z <= (-3.6d-214)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.2d-298) then
        tmp = y * 4.0d0
    else if (z <= 7d-169) then
        tmp = x * (-3.0d0)
    else if (z <= 2.3d-117) then
        tmp = y * 4.0d0
    else if (z <= 2.8d-48) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-9) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.6e-9) {
		tmp = t_0;
	} else if (z <= -3.6e-214) {
		tmp = x * -3.0;
	} else if (z <= 9.2e-298) {
		tmp = y * 4.0;
	} else if (z <= 7e-169) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-117) {
		tmp = y * 4.0;
	} else if (z <= 2.8e-48) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-9) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -6.6e-9:
		tmp = t_0
	elif z <= -3.6e-214:
		tmp = x * -3.0
	elif z <= 9.2e-298:
		tmp = y * 4.0
	elif z <= 7e-169:
		tmp = x * -3.0
	elif z <= 2.3e-117:
		tmp = y * 4.0
	elif z <= 2.8e-48:
		tmp = x * -3.0
	elif z <= 8.8e-9:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -6.6e-9)
		tmp = t_0;
	elseif (z <= -3.6e-214)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.2e-298)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-169)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.3e-117)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.8e-48)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-9)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -6.6e-9)
		tmp = t_0;
	elseif (z <= -3.6e-214)
		tmp = x * -3.0;
	elseif (z <= 9.2e-298)
		tmp = y * 4.0;
	elseif (z <= 7e-169)
		tmp = x * -3.0;
	elseif (z <= 2.3e-117)
		tmp = y * 4.0;
	elseif (z <= 2.8e-48)
		tmp = x * -3.0;
	elseif (z <= 8.8e-9)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-9], t$95$0, If[LessEqual[z, -3.6e-214], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.2e-298], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-169], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.3e-117], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.8e-48], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-9], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.60000000000000037e-9 or 8.7999999999999994e-9 < 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. Step-by-step derivation

      1. flip-+ 20.9%

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

      2. div-inv 20.9%

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

      3. pow2 20.9%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 20.9%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 20.8%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 20.9%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 20.9%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 52.0%

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

      1. *-commutative 52.0%

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

   10. Simplified 52.0%

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

   11. Taylor expanded in z around inf 49.0%

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

   if -6.60000000000000037e-9 < z < -3.6e-214 or 9.2000000000000003e-298 < z < 7.0000000000000006e-169 or 2.29999999999999994e-117 < z < 2.80000000000000005e-48

   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 71.5%

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

      1. sub-neg 71.5%

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

      2. distribute-rgt-in 71.5%

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

      3. metadata-eval 71.5%

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

      4. metadata-eval 71.5%

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

      5. distribute-lft-neg-in 71.5%

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

      6. associate-+r+ 71.5%

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

      7. metadata-eval 71.5%

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

      8. metadata-eval 71.5%

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

      9. distribute-rgt-neg-in 71.5%

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

      10. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in z around 0 71.5%

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

      1. *-commutative 71.5%

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

   10. Simplified 71.5%

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

   if -3.6e-214 < z < 9.2000000000000003e-298 or 7.0000000000000006e-169 < z < 2.29999999999999994e-117 or 2.80000000000000005e-48 < z < 8.7999999999999994e-9

   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. Step-by-step derivation

      1. flip-+ 45.8%

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

      2. div-inv 45.8%

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

      3. pow2 45.8%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 45.8%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 45.8%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 45.9%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 45.9%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

   10. Simplified 72.6%

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

   11. Taylor expanded in z around 0 72.1%

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

       1. *-commutative 72.1%

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

   13. Simplified 72.1%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-9}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-214}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-298}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-169}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-117}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \left(-6 \cdot \left(\left(y - x\right) \cdot z\right) + \left(y - x\right) \cdot 8\right) + \left(x + 4 \cdot \left(x - y\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (+ (* -6.0 (* (- y x) z)) (* (- y x) 8.0)) (+ x (* 4.0 (- x y)))))

C

double code(double x, double y, double z) {
	return ((-6.0 * ((y - x) * z)) + ((y - x) * 8.0)) + (x + (4.0 * (x - y)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((-6.0d0) * ((y - x) * z)) + ((y - x) * 8.0d0)) + (x + (4.0d0 * (x - y)))
end function

Java

public static double code(double x, double y, double z) {
	return ((-6.0 * ((y - x) * z)) + ((y - x) * 8.0)) + (x + (4.0 * (x - y)));
}

Python

def code(x, y, z):
	return ((-6.0 * ((y - x) * z)) + ((y - x) * 8.0)) + (x + (4.0 * (x - y)))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(-6.0 * Float64(Float64(y - x) * z)) + Float64(Float64(y - x) * 8.0)) + Float64(x + Float64(4.0 * Float64(x - y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((-6.0 * ((y - x) * z)) + ((y - x) * 8.0)) + (x + (4.0 * (x - y)));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision] + N[(x + N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. 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. Step-by-step derivation

   1. flip-+ 35.4%

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

   2. div-inv 35.3%

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

   3. pow2 35.3%

      \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. pow2 35.3%

      \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   5. associate-*l* 35.2%

      \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   6. associate-*l* 35.3%

      \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

6. Applied egg-rr 35.3%

   \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

7. Taylor expanded in z around inf 99.7%

   \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

8. Final simplification 99.7%

   \[\leadsto \left(-6 \cdot \left(\left(y - x\right) \cdot z\right) + \left(y - x\right) \cdot 8\right) + \left(x + 4 \cdot \left(x - y\right)\right) \]
9. Add Preprocessing

Alternative 11: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-56} \lor \neg \left(x \leq 10^{-26}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.6e-56) (not (<= x 1e-26)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-56) || !(x <= 1e-26)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.6d-56)) .or. (.not. (x <= 1d-26))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-56) || !(x <= 1e-26)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.6e-56) or not (x <= 1e-26):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.6e-56) || !(x <= 1e-26))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.6e-56) || ~((x <= 1e-26)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.6e-56], N[Not[LessEqual[x, 1e-26]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999978e-56 or 1e-26 < x

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. sub-neg 77.7%

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

      2. distribute-rgt-in 77.7%

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

      3. metadata-eval 77.7%

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

      4. metadata-eval 77.7%

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

      5. distribute-lft-neg-in 77.7%

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

      6. associate-+r+ 77.7%

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

      7. metadata-eval 77.7%

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

      8. metadata-eval 77.7%

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

      9. distribute-rgt-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   if -3.59999999999999978e-56 < x < 1e-26

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 82.4%

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

   6. Taylor expanded in x around 0 82.7%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-56} \lor \neg \left(x \leq 10^{-26}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-56} \lor \neg \left(x \leq 9.6 \cdot 10^{-27}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7e-56) (not (<= x 9.6e-27)))
   (* 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 <= -7e-56) || !(x <= 9.6e-27)) {
		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 <= (-7d-56)) .or. (.not. (x <= 9.6d-27))) 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 <= -7e-56) || !(x <= 9.6e-27)) {
		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 <= -7e-56) or not (x <= 9.6e-27):
		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 <= -7e-56) || !(x <= 9.6e-27))
		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 <= -7e-56) || ~((x <= 9.6e-27)))
		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, -7e-56], N[Not[LessEqual[x, 9.6e-27]], $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 < -6.9999999999999996e-56 or 9.60000000000000008e-27 < x

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 77.7%

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

      1. sub-neg 77.7%

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

      2. distribute-rgt-in 77.7%

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

      3. metadata-eval 77.7%

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

      4. metadata-eval 77.7%

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

      5. distribute-lft-neg-in 77.7%

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

      6. associate-+r+ 77.7%

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

      7. metadata-eval 77.7%

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

      8. metadata-eval 77.7%

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

      9. distribute-rgt-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   if -6.9999999999999996e-56 < x < 9.60000000000000008e-27

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. 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 82.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-56} \lor \neg \left(x \leq 9.6 \cdot 10^{-27}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.6) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.6) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.6d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.6) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.6:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.6)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.6)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   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. Step-by-step derivation

      1. flip-+ 25.6%

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

      2. div-inv 25.5%

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

      3. pow2 25.5%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 25.5%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 25.5%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 25.6%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 25.6%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in z around inf 97.9%

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

   if -0.55000000000000004 < z < 0.599999999999999978

   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 97.6%

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

   if 0.599999999999999978 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.2%

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

      1. neg-mul-1 96.2%

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

   7. Simplified 96.2%

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

   8. Taylor expanded in z around inf 96.2%

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

      1. associate-*r* 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*l* 96.2%

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

   10. Simplified 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.5) (+ (* x -3.0) (* y 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.6d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.5d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.5:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.5)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.5)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. flip-+ 25.6%

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

      2. div-inv 25.5%

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

      3. pow2 25.5%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 25.5%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 25.5%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 25.6%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 25.6%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in z around inf 97.9%

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

   if -0.599999999999999978 < z < 0.5

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(3 + -6 \cdot z\right)\right) + y \cdot \left(4 + -6 \cdot z\right)} \]

   6. Taylor expanded in z around 0 97.6%

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

   if 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. 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 inf 96.2%

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

      1. neg-mul-1 96.2%

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

   7. Simplified 96.2%

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

   8. Taylor expanded in z around inf 96.2%

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

      1. associate-*r* 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*l* 96.2%

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

   10. Simplified 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 * (6.0d0 * (x - y))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. 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. Step-by-step derivation

   1. sub-neg 99.6%

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

   2. distribute-lft-in 99.6%

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

6. Applied egg-rr 99.6%

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

7. Final simplification 99.6%

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

Alternative 16: 37.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-63} \lor \neg \left(y \leq 1.8 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e-63) (not (<= y 1.8e+101))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e-63) || !(y <= 1.8e+101)) {
		tmp = y * 4.0;
	} 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 ((y <= (-1.05d-63)) .or. (.not. (y <= 1.8d+101))) then
        tmp = y * 4.0d0
    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 ((y <= -1.05e-63) || !(y <= 1.8e+101)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e-63) or not (y <= 1.8e+101):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e-63) || !(y <= 1.8e+101))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.05e-63) || ~((y <= 1.8e+101)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e-63], N[Not[LessEqual[y, 1.8e+101]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-63 or 1.80000000000000015e101 < y

   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. Step-by-step derivation

      1. flip-+ 20.0%

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

      2. div-inv 20.0%

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

      3. pow2 20.0%

         \[\leadsto \left(\color{blue}{{x}^{2}} - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. pow2 20.0%

         \[\leadsto \left({x}^{2} - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 20.0%

         \[\leadsto \left({x}^{2} - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      6. associate-*l* 20.1%

         \[\leadsto \left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Applied egg-rr 20.1%

      \[\leadsto \color{blue}{\left({x}^{2} - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   7. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{\left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + 8 \cdot \left(y - x\right)\right) - -1 \cdot \left(x - 4 \cdot \left(y - x\right)\right)} \]

   8. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   10. Simplified 80.4%

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

   11. Taylor expanded in z around 0 37.3%

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

       1. *-commutative 37.3%

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

   13. Simplified 37.3%

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

   if -1.05e-63 < y < 1.80000000000000015e101

   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 75.6%

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

      1. sub-neg 75.6%

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

      2. distribute-rgt-in 75.6%

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

      3. metadata-eval 75.6%

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

      4. metadata-eval 75.6%

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

      5. distribute-lft-neg-in 75.6%

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

      6. associate-+r+ 75.6%

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

      7. metadata-eval 75.6%

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

      8. metadata-eval 75.6%

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

      9. distribute-rgt-neg-in 75.6%

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

      10. metadata-eval 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in z around 0 40.6%

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

      1. *-commutative 40.6%

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

   10. Simplified 40.6%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-63} \lor \neg \left(y \leq 1.8 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 18: 26.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 53.0%

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

   1. sub-neg 53.0%

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

   2. distribute-rgt-in 53.0%

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

   3. metadata-eval 53.0%

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

   4. metadata-eval 53.0%

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

   5. distribute-lft-neg-in 53.0%

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

   6. associate-+r+ 53.0%

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

   7. metadata-eval 53.0%

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

   8. metadata-eval 53.0%

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

   9. distribute-rgt-neg-in 53.0%

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

   10. metadata-eval 53.0%

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

7. Simplified 53.0%

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

8. Taylor expanded in z around 0 28.1%

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

   1. *-commutative 28.1%

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

10. Simplified 28.1%

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

11. Final simplification 28.1%

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

Alternative 19: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around inf 48.7%

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

6. Taylor expanded in x around inf 2.5%

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

7. Final simplification 2.5%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))))