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

Percentage Accurate: 99.5% → 99.8%

Time: 14.3s

Alternatives: 18

Speedup: 1.2×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   3. fma-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 2: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-305}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+146} \lor \neg \left(z \leq 8 \cdot 10^{+221}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -2.8e+256)
     t_0
     (if (<= z -1.95e+214)
       t_1
       (if (<= z -3.2e+47)
         t_0
         (if (<= z -920.0)
           t_1
           (if (<= z -2.9e-102)
             (* x -3.0)
             (if (<= z -1.05e-129)
               (* y 4.0)
               (if (<= z -5.5e-148)
                 (* x -3.0)
                 (if (<= z -1.18e-263)
                   (* y 4.0)
                   (if (<= z -4.8e-305)
                     (* x -3.0)
                     (if (<= z 2.15e-305)
                       (* y 4.0)
                       (if (<= z 3.9e-253)
                         (* x -3.0)
                         (if (<= z 4.8e-190)
                           (* y 4.0)
                           (if (<= z 0.185)
                             (* x -3.0)
                             (if (or (<= z 1.65e+146) (not (<= z 8e+221)))
                               t_1
                               t_0))))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.8e+256) {
		tmp = t_0;
	} else if (z <= -1.95e+214) {
		tmp = t_1;
	} else if (z <= -3.2e+47) {
		tmp = t_0;
	} else if (z <= -920.0) {
		tmp = t_1;
	} else if (z <= -2.9e-102) {
		tmp = x * -3.0;
	} else if (z <= -1.05e-129) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.18e-263) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-305) {
		tmp = x * -3.0;
	} else if (z <= 2.15e-305) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-253) {
		tmp = x * -3.0;
	} else if (z <= 4.8e-190) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 1.65e+146) || !(z <= 8e+221)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-2.8d+256)) then
        tmp = t_0
    else if (z <= (-1.95d+214)) then
        tmp = t_1
    else if (z <= (-3.2d+47)) then
        tmp = t_0
    else if (z <= (-920.0d0)) then
        tmp = t_1
    else if (z <= (-2.9d-102)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.05d-129)) then
        tmp = y * 4.0d0
    else if (z <= (-5.5d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.18d-263)) then
        tmp = y * 4.0d0
    else if (z <= (-4.8d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.15d-305) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 4.8d-190) then
        tmp = y * 4.0d0
    else if (z <= 0.185d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 1.65d+146) .or. (.not. (z <= 8d+221))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.8e+256) {
		tmp = t_0;
	} else if (z <= -1.95e+214) {
		tmp = t_1;
	} else if (z <= -3.2e+47) {
		tmp = t_0;
	} else if (z <= -920.0) {
		tmp = t_1;
	} else if (z <= -2.9e-102) {
		tmp = x * -3.0;
	} else if (z <= -1.05e-129) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.18e-263) {
		tmp = y * 4.0;
	} else if (z <= -4.8e-305) {
		tmp = x * -3.0;
	} else if (z <= 2.15e-305) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-253) {
		tmp = x * -3.0;
	} else if (z <= 4.8e-190) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 1.65e+146) || !(z <= 8e+221)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.8e+256:
		tmp = t_0
	elif z <= -1.95e+214:
		tmp = t_1
	elif z <= -3.2e+47:
		tmp = t_0
	elif z <= -920.0:
		tmp = t_1
	elif z <= -2.9e-102:
		tmp = x * -3.0
	elif z <= -1.05e-129:
		tmp = y * 4.0
	elif z <= -5.5e-148:
		tmp = x * -3.0
	elif z <= -1.18e-263:
		tmp = y * 4.0
	elif z <= -4.8e-305:
		tmp = x * -3.0
	elif z <= 2.15e-305:
		tmp = y * 4.0
	elif z <= 3.9e-253:
		tmp = x * -3.0
	elif z <= 4.8e-190:
		tmp = y * 4.0
	elif z <= 0.185:
		tmp = x * -3.0
	elif (z <= 1.65e+146) or not (z <= 8e+221):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.8e+256)
		tmp = t_0;
	elseif (z <= -1.95e+214)
		tmp = t_1;
	elseif (z <= -3.2e+47)
		tmp = t_0;
	elseif (z <= -920.0)
		tmp = t_1;
	elseif (z <= -2.9e-102)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.05e-129)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.5e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.18e-263)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.8e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.15e-305)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.8e-190)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.185)
		tmp = Float64(x * -3.0);
	elseif ((z <= 1.65e+146) || !(z <= 8e+221))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.8e+256)
		tmp = t_0;
	elseif (z <= -1.95e+214)
		tmp = t_1;
	elseif (z <= -3.2e+47)
		tmp = t_0;
	elseif (z <= -920.0)
		tmp = t_1;
	elseif (z <= -2.9e-102)
		tmp = x * -3.0;
	elseif (z <= -1.05e-129)
		tmp = y * 4.0;
	elseif (z <= -5.5e-148)
		tmp = x * -3.0;
	elseif (z <= -1.18e-263)
		tmp = y * 4.0;
	elseif (z <= -4.8e-305)
		tmp = x * -3.0;
	elseif (z <= 2.15e-305)
		tmp = y * 4.0;
	elseif (z <= 3.9e-253)
		tmp = x * -3.0;
	elseif (z <= 4.8e-190)
		tmp = y * 4.0;
	elseif (z <= 0.185)
		tmp = x * -3.0;
	elseif ((z <= 1.65e+146) || ~((z <= 8e+221)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+256], t$95$0, If[LessEqual[z, -1.95e+214], t$95$1, If[LessEqual[z, -3.2e+47], t$95$0, If[LessEqual[z, -920.0], t$95$1, If[LessEqual[z, -2.9e-102], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.05e-129], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.5e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.18e-263], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.8e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.15e-305], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.8e-190], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.185], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 1.65e+146], N[Not[LessEqual[z, 8e+221]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.79999999999999988e256 or -1.95000000000000007e214 < z < -3.2e47 or 1.65000000000000008e146 < z < 8.0000000000000004e221

   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* 99.8%

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

      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. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in z around inf 72.2%

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

   if -2.79999999999999988e256 < z < -1.95000000000000007e214 or -3.2e47 < z < -920 or 0.185 < z < 1.65000000000000008e146 or 8.0000000000000004e221 < z

   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 69.9%

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

      1. sub-neg 69.9%

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

      2. distribute-rgt-in 69.9%

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

      3. metadata-eval 69.9%

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

      4. metadata-eval 69.9%

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

      5. distribute-lft-neg-in 69.9%

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

      6. associate-+r+ 69.9%

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

      7. metadata-eval 69.9%

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

      8. metadata-eval 69.9%

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

      9. distribute-rgt-neg-in 69.9%

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

      10. metadata-eval 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in z around inf 68.1%

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

   if -920 < z < -2.89999999999999986e-102 or -1.05e-129 < z < -5.5000000000000003e-148 or -1.17999999999999998e-263 < z < -4.80000000000000039e-305 or 2.1500000000000001e-305 < z < 3.8999999999999999e-253 or 4.8000000000000001e-190 < z < 0.185

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. metadata-eval 70.2%

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

      5. distribute-lft-neg-in 70.2%

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

      6. associate-+r+ 70.2%

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

      7. metadata-eval 70.2%

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

      8. metadata-eval 70.2%

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

      9. distribute-rgt-neg-in 70.2%

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

      10. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around 0 68.9%

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

      1. *-commutative 68.9%

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

   10. Simplified 68.9%

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

   if -2.89999999999999986e-102 < z < -1.05e-129 or -5.5000000000000003e-148 < z < -1.17999999999999998e-263 or -4.80000000000000039e-305 < z < 2.1500000000000001e-305 or 3.8999999999999999e-253 < z < 4.8000000000000001e-190

   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 y around inf 76.8%

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

   6. Taylor expanded in z around 0 76.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+214}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+47}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-129}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-305}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-190}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+146} \lor \neg \left(z \leq 8 \cdot 10^{+221}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-304}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-191}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+146} \lor \neg \left(z \leq 1.55 \cdot 10^{+219}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -2.2e+256)
     t_0
     (if (<= z -9.5e+212)
       t_1
       (if (<= z -1.5e+47)
         t_0
         (if (<= z -920.0)
           t_1
           (if (<= z -4.2e-102)
             (* x -3.0)
             (if (<= z -3.9e-130)
               (* y 4.0)
               (if (<= z -8.5e-147)
                 (* x -3.0)
                 (if (<= z -7.8e-263)
                   (* y 4.0)
                   (if (<= z -1.66e-304)
                     (* x -3.0)
                     (if (<= z 7.2e-306)
                       (* y 4.0)
                       (if (<= z 4e-253)
                         (* x -3.0)
                         (if (<= z 1.9e-191)
                           (* y 4.0)
                           (if (<= z 0.185)
                             (* x -3.0)
                             (if (or (<= z 1.7e+146) (not (<= z 1.55e+219)))
                               t_1
                               t_0))))))))))))))))

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 <= -2.2e+256) {
		tmp = t_0;
	} else if (z <= -9.5e+212) {
		tmp = t_1;
	} else if (z <= -1.5e+47) {
		tmp = t_0;
	} else if (z <= -920.0) {
		tmp = t_1;
	} else if (z <= -4.2e-102) {
		tmp = x * -3.0;
	} else if (z <= -3.9e-130) {
		tmp = y * 4.0;
	} else if (z <= -8.5e-147) {
		tmp = x * -3.0;
	} else if (z <= -7.8e-263) {
		tmp = y * 4.0;
	} else if (z <= -1.66e-304) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-306) {
		tmp = y * 4.0;
	} else if (z <= 4e-253) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-191) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 1.7e+146) || !(z <= 1.55e+219)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * (z * 6.0d0)
    if (z <= (-2.2d+256)) then
        tmp = t_0
    else if (z <= (-9.5d+212)) then
        tmp = t_1
    else if (z <= (-1.5d+47)) then
        tmp = t_0
    else if (z <= (-920.0d0)) then
        tmp = t_1
    else if (z <= (-4.2d-102)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.9d-130)) then
        tmp = y * 4.0d0
    else if (z <= (-8.5d-147)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.8d-263)) then
        tmp = y * 4.0d0
    else if (z <= (-1.66d-304)) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d-306) then
        tmp = y * 4.0d0
    else if (z <= 4d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 1.9d-191) then
        tmp = y * 4.0d0
    else if (z <= 0.185d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 1.7d+146) .or. (.not. (z <= 1.55d+219))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -2.2e+256) {
		tmp = t_0;
	} else if (z <= -9.5e+212) {
		tmp = t_1;
	} else if (z <= -1.5e+47) {
		tmp = t_0;
	} else if (z <= -920.0) {
		tmp = t_1;
	} else if (z <= -4.2e-102) {
		tmp = x * -3.0;
	} else if (z <= -3.9e-130) {
		tmp = y * 4.0;
	} else if (z <= -8.5e-147) {
		tmp = x * -3.0;
	} else if (z <= -7.8e-263) {
		tmp = y * 4.0;
	} else if (z <= -1.66e-304) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-306) {
		tmp = y * 4.0;
	} else if (z <= 4e-253) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-191) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 1.7e+146) || !(z <= 1.55e+219)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -2.2e+256:
		tmp = t_0
	elif z <= -9.5e+212:
		tmp = t_1
	elif z <= -1.5e+47:
		tmp = t_0
	elif z <= -920.0:
		tmp = t_1
	elif z <= -4.2e-102:
		tmp = x * -3.0
	elif z <= -3.9e-130:
		tmp = y * 4.0
	elif z <= -8.5e-147:
		tmp = x * -3.0
	elif z <= -7.8e-263:
		tmp = y * 4.0
	elif z <= -1.66e-304:
		tmp = x * -3.0
	elif z <= 7.2e-306:
		tmp = y * 4.0
	elif z <= 4e-253:
		tmp = x * -3.0
	elif z <= 1.9e-191:
		tmp = y * 4.0
	elif z <= 0.185:
		tmp = x * -3.0
	elif (z <= 1.7e+146) or not (z <= 1.55e+219):
		tmp = t_1
	else:
		tmp = t_0
	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 <= -2.2e+256)
		tmp = t_0;
	elseif (z <= -9.5e+212)
		tmp = t_1;
	elseif (z <= -1.5e+47)
		tmp = t_0;
	elseif (z <= -920.0)
		tmp = t_1;
	elseif (z <= -4.2e-102)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.9e-130)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.5e-147)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.8e-263)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.66e-304)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e-306)
		tmp = Float64(y * 4.0);
	elseif (z <= 4e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.9e-191)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.185)
		tmp = Float64(x * -3.0);
	elseif ((z <= 1.7e+146) || !(z <= 1.55e+219))
		tmp = t_1;
	else
		tmp = t_0;
	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 <= -2.2e+256)
		tmp = t_0;
	elseif (z <= -9.5e+212)
		tmp = t_1;
	elseif (z <= -1.5e+47)
		tmp = t_0;
	elseif (z <= -920.0)
		tmp = t_1;
	elseif (z <= -4.2e-102)
		tmp = x * -3.0;
	elseif (z <= -3.9e-130)
		tmp = y * 4.0;
	elseif (z <= -8.5e-147)
		tmp = x * -3.0;
	elseif (z <= -7.8e-263)
		tmp = y * 4.0;
	elseif (z <= -1.66e-304)
		tmp = x * -3.0;
	elseif (z <= 7.2e-306)
		tmp = y * 4.0;
	elseif (z <= 4e-253)
		tmp = x * -3.0;
	elseif (z <= 1.9e-191)
		tmp = y * 4.0;
	elseif (z <= 0.185)
		tmp = x * -3.0;
	elseif ((z <= 1.7e+146) || ~((z <= 1.55e+219)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+256], t$95$0, If[LessEqual[z, -9.5e+212], t$95$1, If[LessEqual[z, -1.5e+47], t$95$0, If[LessEqual[z, -920.0], t$95$1, If[LessEqual[z, -4.2e-102], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.9e-130], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.5e-147], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.8e-263], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.66e-304], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e-306], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.9e-191], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.185], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 1.7e+146], N[Not[LessEqual[z, 1.55e+219]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999999e256 or -9.4999999999999993e212 < z < -1.5000000000000001e47 or 1.69999999999999995e146 < z < 1.54999999999999984e219

   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* 99.8%

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

      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. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in z around inf 72.2%

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

   if -2.1999999999999999e256 < z < -9.4999999999999993e212 or -1.5000000000000001e47 < z < -920 or 0.185 < z < 1.69999999999999995e146 or 1.54999999999999984e219 < z

   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 69.9%

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

      1. sub-neg 69.9%

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

      2. distribute-rgt-in 69.9%

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

      3. metadata-eval 69.9%

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

      4. metadata-eval 69.9%

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

      5. distribute-lft-neg-in 69.9%

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

      6. associate-+r+ 69.9%

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

      7. metadata-eval 69.9%

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

      8. metadata-eval 69.9%

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

      9. distribute-rgt-neg-in 69.9%

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

      10. metadata-eval 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in z around inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r* 68.3%

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

      4. *-commutative 68.3%

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

   10. Simplified 68.3%

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

   if -920 < z < -4.2e-102 or -3.9000000000000001e-130 < z < -8.5000000000000002e-147 or -7.79999999999999939e-263 < z < -1.66e-304 or 7.19999999999999982e-306 < z < 4.0000000000000003e-253 or 1.8999999999999999e-191 < z < 0.185

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. metadata-eval 70.2%

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

      5. distribute-lft-neg-in 70.2%

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

      6. associate-+r+ 70.2%

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

      7. metadata-eval 70.2%

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

      8. metadata-eval 70.2%

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

      9. distribute-rgt-neg-in 70.2%

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

      10. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around 0 68.9%

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

      1. *-commutative 68.9%

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

   10. Simplified 68.9%

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

   if -4.2e-102 < z < -3.9000000000000001e-130 or -8.5000000000000002e-147 < z < -7.79999999999999939e-263 or -1.66e-304 < z < 7.19999999999999982e-306 or 4.0000000000000003e-253 < z < 1.8999999999999999e-191

   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 y around inf 76.8%

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

   6. Taylor expanded in z around 0 76.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.66 \cdot 10^{-304}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-191}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+146} \lor \neg \left(z \leq 1.55 \cdot 10^{+219}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-304}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-191}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+146} \lor \neg \left(z \leq 2.7 \cdot 10^{+221}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -2.7e+256)
     t_0
     (if (<= z -2.3e+214)
       t_1
       (if (<= z -1.5e+47)
         (* y (* z -6.0))
         (if (<= z -920.0)
           t_1
           (if (<= z -5.2e-102)
             (* x -3.0)
             (if (<= z -1.8e-131)
               (* y 4.0)
               (if (<= z -4.4e-148)
                 (* x -3.0)
                 (if (<= z -4.4e-266)
                   (* y 4.0)
                   (if (<= z -1.12e-305)
                     (* x -3.0)
                     (if (<= z 1.55e-304)
                       (* y 4.0)
                       (if (<= z 2.55e-253)
                         (* x -3.0)
                         (if (<= z 2.7e-191)
                           (* y 4.0)
                           (if (<= z 0.185)
                             (* x -3.0)
                             (if (or (<= z 2.2e+146) (not (<= z 2.7e+221)))
                               t_1
                               t_0))))))))))))))))

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 <= -2.7e+256) {
		tmp = t_0;
	} else if (z <= -2.3e+214) {
		tmp = t_1;
	} else if (z <= -1.5e+47) {
		tmp = y * (z * -6.0);
	} else if (z <= -920.0) {
		tmp = t_1;
	} else if (z <= -5.2e-102) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-131) {
		tmp = y * 4.0;
	} else if (z <= -4.4e-148) {
		tmp = x * -3.0;
	} else if (z <= -4.4e-266) {
		tmp = y * 4.0;
	} else if (z <= -1.12e-305) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-304) {
		tmp = y * 4.0;
	} else if (z <= 2.55e-253) {
		tmp = x * -3.0;
	} else if (z <= 2.7e-191) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 2.2e+146) || !(z <= 2.7e+221)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * (z * 6.0d0)
    if (z <= (-2.7d+256)) then
        tmp = t_0
    else if (z <= (-2.3d+214)) then
        tmp = t_1
    else if (z <= (-1.5d+47)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-920.0d0)) then
        tmp = t_1
    else if (z <= (-5.2d-102)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.8d-131)) then
        tmp = y * 4.0d0
    else if (z <= (-4.4d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.4d-266)) then
        tmp = y * 4.0d0
    else if (z <= (-1.12d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.55d-304) then
        tmp = y * 4.0d0
    else if (z <= 2.55d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 2.7d-191) then
        tmp = y * 4.0d0
    else if (z <= 0.185d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 2.2d+146) .or. (.not. (z <= 2.7d+221))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -2.7e+256) {
		tmp = t_0;
	} else if (z <= -2.3e+214) {
		tmp = t_1;
	} else if (z <= -1.5e+47) {
		tmp = y * (z * -6.0);
	} else if (z <= -920.0) {
		tmp = t_1;
	} else if (z <= -5.2e-102) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-131) {
		tmp = y * 4.0;
	} else if (z <= -4.4e-148) {
		tmp = x * -3.0;
	} else if (z <= -4.4e-266) {
		tmp = y * 4.0;
	} else if (z <= -1.12e-305) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-304) {
		tmp = y * 4.0;
	} else if (z <= 2.55e-253) {
		tmp = x * -3.0;
	} else if (z <= 2.7e-191) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 2.2e+146) || !(z <= 2.7e+221)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -2.7e+256:
		tmp = t_0
	elif z <= -2.3e+214:
		tmp = t_1
	elif z <= -1.5e+47:
		tmp = y * (z * -6.0)
	elif z <= -920.0:
		tmp = t_1
	elif z <= -5.2e-102:
		tmp = x * -3.0
	elif z <= -1.8e-131:
		tmp = y * 4.0
	elif z <= -4.4e-148:
		tmp = x * -3.0
	elif z <= -4.4e-266:
		tmp = y * 4.0
	elif z <= -1.12e-305:
		tmp = x * -3.0
	elif z <= 1.55e-304:
		tmp = y * 4.0
	elif z <= 2.55e-253:
		tmp = x * -3.0
	elif z <= 2.7e-191:
		tmp = y * 4.0
	elif z <= 0.185:
		tmp = x * -3.0
	elif (z <= 2.2e+146) or not (z <= 2.7e+221):
		tmp = t_1
	else:
		tmp = t_0
	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 <= -2.7e+256)
		tmp = t_0;
	elseif (z <= -2.3e+214)
		tmp = t_1;
	elseif (z <= -1.5e+47)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -920.0)
		tmp = t_1;
	elseif (z <= -5.2e-102)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.8e-131)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.4e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.4e-266)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.12e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.55e-304)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.55e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.7e-191)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.185)
		tmp = Float64(x * -3.0);
	elseif ((z <= 2.2e+146) || !(z <= 2.7e+221))
		tmp = t_1;
	else
		tmp = t_0;
	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 <= -2.7e+256)
		tmp = t_0;
	elseif (z <= -2.3e+214)
		tmp = t_1;
	elseif (z <= -1.5e+47)
		tmp = y * (z * -6.0);
	elseif (z <= -920.0)
		tmp = t_1;
	elseif (z <= -5.2e-102)
		tmp = x * -3.0;
	elseif (z <= -1.8e-131)
		tmp = y * 4.0;
	elseif (z <= -4.4e-148)
		tmp = x * -3.0;
	elseif (z <= -4.4e-266)
		tmp = y * 4.0;
	elseif (z <= -1.12e-305)
		tmp = x * -3.0;
	elseif (z <= 1.55e-304)
		tmp = y * 4.0;
	elseif (z <= 2.55e-253)
		tmp = x * -3.0;
	elseif (z <= 2.7e-191)
		tmp = y * 4.0;
	elseif (z <= 0.185)
		tmp = x * -3.0;
	elseif ((z <= 2.2e+146) || ~((z <= 2.7e+221)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+256], t$95$0, If[LessEqual[z, -2.3e+214], t$95$1, If[LessEqual[z, -1.5e+47], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -920.0], t$95$1, If[LessEqual[z, -5.2e-102], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.8e-131], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.4e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.4e-266], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.12e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.55e-304], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.55e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.7e-191], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.185], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 2.2e+146], N[Not[LessEqual[z, 2.7e+221]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.69999999999999995e256 or 2.1999999999999998e146 < z < 2.7e221

   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* 99.7%

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

      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 99.7%

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

      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 y around inf 76.6%

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

   6. Taylor expanded in z around inf 76.6%

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

   if -2.69999999999999995e256 < z < -2.2999999999999999e214 or -1.5000000000000001e47 < z < -920 or 0.185 < z < 2.1999999999999998e146 or 2.7e221 < z

   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 69.9%

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

      1. sub-neg 69.9%

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

      2. distribute-rgt-in 69.9%

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

      3. metadata-eval 69.9%

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

      4. metadata-eval 69.9%

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

      5. distribute-lft-neg-in 69.9%

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

      6. associate-+r+ 69.9%

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

      7. metadata-eval 69.9%

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

      8. metadata-eval 69.9%

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

      9. distribute-rgt-neg-in 69.9%

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

      10. metadata-eval 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in z around inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r* 68.3%

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

      4. *-commutative 68.3%

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

   10. Simplified 68.3%

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

   if -2.2999999999999999e214 < z < -1.5000000000000001e47

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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 y around inf 67.5%

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

   6. Taylor expanded in z around inf 67.5%

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

   if -920 < z < -5.19999999999999973e-102 or -1.8e-131 < z < -4.40000000000000034e-148 or -4.3999999999999999e-266 < z < -1.1200000000000001e-305 or 1.54999999999999992e-304 < z < 2.55000000000000004e-253 or 2.69999999999999999e-191 < z < 0.185

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. metadata-eval 70.2%

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

      5. distribute-lft-neg-in 70.2%

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

      6. associate-+r+ 70.2%

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

      7. metadata-eval 70.2%

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

      8. metadata-eval 70.2%

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

      9. distribute-rgt-neg-in 70.2%

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

      10. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around 0 68.9%

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

      1. *-commutative 68.9%

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

   10. Simplified 68.9%

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

   if -5.19999999999999973e-102 < z < -1.8e-131 or -4.40000000000000034e-148 < z < -4.3999999999999999e-266 or -1.1200000000000001e-305 < z < 1.54999999999999992e-304 or 2.55000000000000004e-253 < z < 2.69999999999999999e-191

   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 y around inf 76.8%

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

   6. Taylor expanded in z around 0 76.8%

      \[\leadsto y \cdot \color{blue}{4} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-304}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-191}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+146} \lor \neg \left(z \leq 2.7 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-190}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+146} \lor \neg \left(z \leq 9.6 \cdot 10^{+218}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -2.95e+256)
     (* -6.0 (* y z))
     (if (<= z -4.6e+214)
       t_0
       (if (<= z -7.8e+46)
         (* y (* z -6.0))
         (if (<= z -920.0)
           t_0
           (if (<= z -1.42e-102)
             (* x -3.0)
             (if (<= z -1.52e-127)
               (* y 4.0)
               (if (<= z -9e-148)
                 (* x -3.0)
                 (if (<= z -1.52e-263)
                   (* y 4.0)
                   (if (<= z -4e-305)
                     (* x -3.0)
                     (if (<= z 4.2e-306)
                       (* y 4.0)
                       (if (<= z 2.65e-253)
                         (* x -3.0)
                         (if (<= z 7.5e-190)
                           (* y 4.0)
                           (if (<= z 0.185)
                             (* x -3.0)
                             (if (or (<= z 1.4e+146) (not (<= z 9.6e+218)))
                               t_0
                               (* z (* y -6.0))))))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -2.95e+256) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.6e+214) {
		tmp = t_0;
	} else if (z <= -7.8e+46) {
		tmp = y * (z * -6.0);
	} else if (z <= -920.0) {
		tmp = t_0;
	} else if (z <= -1.42e-102) {
		tmp = x * -3.0;
	} else if (z <= -1.52e-127) {
		tmp = y * 4.0;
	} else if (z <= -9e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.52e-263) {
		tmp = y * 4.0;
	} else if (z <= -4e-305) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-306) {
		tmp = y * 4.0;
	} else if (z <= 2.65e-253) {
		tmp = x * -3.0;
	} else if (z <= 7.5e-190) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 1.4e+146) || !(z <= 9.6e+218)) {
		tmp = t_0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-2.95d+256)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-4.6d+214)) then
        tmp = t_0
    else if (z <= (-7.8d+46)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-920.0d0)) then
        tmp = t_0
    else if (z <= (-1.42d-102)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.52d-127)) then
        tmp = y * 4.0d0
    else if (z <= (-9d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.52d-263)) then
        tmp = y * 4.0d0
    else if (z <= (-4d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d-306) then
        tmp = y * 4.0d0
    else if (z <= 2.65d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 7.5d-190) then
        tmp = y * 4.0d0
    else if (z <= 0.185d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 1.4d+146) .or. (.not. (z <= 9.6d+218))) then
        tmp = t_0
    else
        tmp = z * (y * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -2.95e+256) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.6e+214) {
		tmp = t_0;
	} else if (z <= -7.8e+46) {
		tmp = y * (z * -6.0);
	} else if (z <= -920.0) {
		tmp = t_0;
	} else if (z <= -1.42e-102) {
		tmp = x * -3.0;
	} else if (z <= -1.52e-127) {
		tmp = y * 4.0;
	} else if (z <= -9e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.52e-263) {
		tmp = y * 4.0;
	} else if (z <= -4e-305) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-306) {
		tmp = y * 4.0;
	} else if (z <= 2.65e-253) {
		tmp = x * -3.0;
	} else if (z <= 7.5e-190) {
		tmp = y * 4.0;
	} else if (z <= 0.185) {
		tmp = x * -3.0;
	} else if ((z <= 1.4e+146) || !(z <= 9.6e+218)) {
		tmp = t_0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -2.95e+256:
		tmp = -6.0 * (y * z)
	elif z <= -4.6e+214:
		tmp = t_0
	elif z <= -7.8e+46:
		tmp = y * (z * -6.0)
	elif z <= -920.0:
		tmp = t_0
	elif z <= -1.42e-102:
		tmp = x * -3.0
	elif z <= -1.52e-127:
		tmp = y * 4.0
	elif z <= -9e-148:
		tmp = x * -3.0
	elif z <= -1.52e-263:
		tmp = y * 4.0
	elif z <= -4e-305:
		tmp = x * -3.0
	elif z <= 4.2e-306:
		tmp = y * 4.0
	elif z <= 2.65e-253:
		tmp = x * -3.0
	elif z <= 7.5e-190:
		tmp = y * 4.0
	elif z <= 0.185:
		tmp = x * -3.0
	elif (z <= 1.4e+146) or not (z <= 9.6e+218):
		tmp = t_0
	else:
		tmp = z * (y * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -2.95e+256)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -4.6e+214)
		tmp = t_0;
	elseif (z <= -7.8e+46)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -920.0)
		tmp = t_0;
	elseif (z <= -1.42e-102)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.52e-127)
		tmp = Float64(y * 4.0);
	elseif (z <= -9e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.52e-263)
		tmp = Float64(y * 4.0);
	elseif (z <= -4e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e-306)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.65e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.5e-190)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.185)
		tmp = Float64(x * -3.0);
	elseif ((z <= 1.4e+146) || !(z <= 9.6e+218))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -2.95e+256)
		tmp = -6.0 * (y * z);
	elseif (z <= -4.6e+214)
		tmp = t_0;
	elseif (z <= -7.8e+46)
		tmp = y * (z * -6.0);
	elseif (z <= -920.0)
		tmp = t_0;
	elseif (z <= -1.42e-102)
		tmp = x * -3.0;
	elseif (z <= -1.52e-127)
		tmp = y * 4.0;
	elseif (z <= -9e-148)
		tmp = x * -3.0;
	elseif (z <= -1.52e-263)
		tmp = y * 4.0;
	elseif (z <= -4e-305)
		tmp = x * -3.0;
	elseif (z <= 4.2e-306)
		tmp = y * 4.0;
	elseif (z <= 2.65e-253)
		tmp = x * -3.0;
	elseif (z <= 7.5e-190)
		tmp = y * 4.0;
	elseif (z <= 0.185)
		tmp = x * -3.0;
	elseif ((z <= 1.4e+146) || ~((z <= 9.6e+218)))
		tmp = t_0;
	else
		tmp = z * (y * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.95e+256], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e+214], t$95$0, If[LessEqual[z, -7.8e+46], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -920.0], t$95$0, If[LessEqual[z, -1.42e-102], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.52e-127], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -9e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.52e-263], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e-306], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.65e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.5e-190], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.185], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 1.4e+146], N[Not[LessEqual[z, 9.6e+218]], $MachinePrecision]], t$95$0, N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.95000000000000012e256

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.9%

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

   6. Taylor expanded in z around inf 88.9%

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

   if -2.95000000000000012e256 < z < -4.5999999999999998e214 or -7.7999999999999999e46 < z < -920 or 0.185 < z < 1.4e146 or 9.59999999999999923e218 < z

   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 69.9%

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

      1. sub-neg 69.9%

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

      2. distribute-rgt-in 69.9%

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

      3. metadata-eval 69.9%

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

      4. metadata-eval 69.9%

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

      5. distribute-lft-neg-in 69.9%

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

      6. associate-+r+ 69.9%

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

      7. metadata-eval 69.9%

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

      8. metadata-eval 69.9%

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

      9. distribute-rgt-neg-in 69.9%

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

      10. metadata-eval 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in z around inf 68.1%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r* 68.3%

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

      4. *-commutative 68.3%

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

   10. Simplified 68.3%

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

   if -4.5999999999999998e214 < z < -7.7999999999999999e46

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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 y around inf 67.5%

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

   6. Taylor expanded in z around inf 67.5%

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

   if -920 < z < -1.42000000000000009e-102 or -1.5200000000000001e-127 < z < -9.00000000000000029e-148 or -1.52000000000000005e-263 < z < -3.99999999999999999e-305 or 4.2000000000000002e-306 < z < 2.6500000000000001e-253 or 7.5e-190 < z < 0.185

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. metadata-eval 70.2%

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

      5. distribute-lft-neg-in 70.2%

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

      6. associate-+r+ 70.2%

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

      7. metadata-eval 70.2%

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

      8. metadata-eval 70.2%

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

      9. distribute-rgt-neg-in 70.2%

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

      10. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around 0 68.9%

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

      1. *-commutative 68.9%

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

   10. Simplified 68.9%

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

   if -1.42000000000000009e-102 < z < -1.5200000000000001e-127 or -9.00000000000000029e-148 < z < -1.52000000000000005e-263 or -3.99999999999999999e-305 < z < 4.2000000000000002e-306 or 2.6500000000000001e-253 < z < 7.5e-190

   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 y around inf 76.8%

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

   6. Taylor expanded in z around 0 76.8%

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

   if 1.4e146 < z < 9.59999999999999923e218

   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* 99.5%

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

      3. fma-def 99.5%

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

      4. sub-neg 99.5%

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

      5. distribute-rgt-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-neg-out 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 70.1%

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

   6. Taylor expanded in z around inf 70.1%

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

      1. associate-*r* 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -920:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-190}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.185:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+146} \lor \neg \left(z \leq 9.6 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.08:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-128}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-191}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.08)
     t_0
     (if (<= z -6e-102)
       (* x -3.0)
       (if (<= z -4.4e-128)
         (* y 4.0)
         (if (<= z -1.2e-148)
           (* x -3.0)
           (if (<= z -1.7e-263)
             (* y 4.0)
             (if (<= z -3.1e-305)
               (* x -3.0)
               (if (<= z 4e-306)
                 (* y 4.0)
                 (if (<= z 8.8e-253)
                   (* x -3.0)
                   (if (<= z 1.6e-191)
                     (* y 4.0)
                     (if (<= z 0.52) (* x -3.0) t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.08) {
		tmp = t_0;
	} else if (z <= -6e-102) {
		tmp = x * -3.0;
	} else if (z <= -4.4e-128) {
		tmp = y * 4.0;
	} else if (z <= -1.2e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.7e-263) {
		tmp = y * 4.0;
	} else if (z <= -3.1e-305) {
		tmp = x * -3.0;
	} else if (z <= 4e-306) {
		tmp = y * 4.0;
	} else if (z <= 8.8e-253) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-191) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} 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 <= (-0.08d0)) then
        tmp = t_0
    else if (z <= (-6d-102)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.4d-128)) then
        tmp = y * 4.0d0
    else if (z <= (-1.2d-148)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.7d-263)) then
        tmp = y * 4.0d0
    else if (z <= (-3.1d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 4d-306) then
        tmp = y * 4.0d0
    else if (z <= 8.8d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-191) then
        tmp = y * 4.0d0
    else if (z <= 0.52d0) then
        tmp = x * (-3.0d0)
    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 <= -0.08) {
		tmp = t_0;
	} else if (z <= -6e-102) {
		tmp = x * -3.0;
	} else if (z <= -4.4e-128) {
		tmp = y * 4.0;
	} else if (z <= -1.2e-148) {
		tmp = x * -3.0;
	} else if (z <= -1.7e-263) {
		tmp = y * 4.0;
	} else if (z <= -3.1e-305) {
		tmp = x * -3.0;
	} else if (z <= 4e-306) {
		tmp = y * 4.0;
	} else if (z <= 8.8e-253) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-191) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.08:
		tmp = t_0
	elif z <= -6e-102:
		tmp = x * -3.0
	elif z <= -4.4e-128:
		tmp = y * 4.0
	elif z <= -1.2e-148:
		tmp = x * -3.0
	elif z <= -1.7e-263:
		tmp = y * 4.0
	elif z <= -3.1e-305:
		tmp = x * -3.0
	elif z <= 4e-306:
		tmp = y * 4.0
	elif z <= 8.8e-253:
		tmp = x * -3.0
	elif z <= 1.6e-191:
		tmp = y * 4.0
	elif z <= 0.52:
		tmp = x * -3.0
	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 <= -0.08)
		tmp = t_0;
	elseif (z <= -6e-102)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.4e-128)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.2e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.7e-263)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.1e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 4e-306)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.8e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-191)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.52)
		tmp = Float64(x * -3.0);
	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 <= -0.08)
		tmp = t_0;
	elseif (z <= -6e-102)
		tmp = x * -3.0;
	elseif (z <= -4.4e-128)
		tmp = y * 4.0;
	elseif (z <= -1.2e-148)
		tmp = x * -3.0;
	elseif (z <= -1.7e-263)
		tmp = y * 4.0;
	elseif (z <= -3.1e-305)
		tmp = x * -3.0;
	elseif (z <= 4e-306)
		tmp = y * 4.0;
	elseif (z <= 8.8e-253)
		tmp = x * -3.0;
	elseif (z <= 1.6e-191)
		tmp = y * 4.0;
	elseif (z <= 0.52)
		tmp = x * -3.0;
	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, -0.08], t$95$0, If[LessEqual[z, -6e-102], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.4e-128], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.2e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.7e-263], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.1e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4e-306], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.8e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-191], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0800000000000000017 or 0.52000000000000002 < z

   1. Initial program 99.7%

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

      1. +-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* 99.7%

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

      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 99.7%

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

      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 y around inf 49.6%

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

   6. Taylor expanded in z around inf 47.9%

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

   if -0.0800000000000000017 < z < -6e-102 or -4.40000000000000019e-128 < z < -1.2000000000000001e-148 or -1.70000000000000002e-263 < z < -3.0999999999999998e-305 or 4.00000000000000011e-306 < z < 8.79999999999999983e-253 or 1.6000000000000002e-191 < z < 0.52000000000000002

   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 71.0%

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

      1. sub-neg 71.0%

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

      2. distribute-rgt-in 71.0%

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

      3. metadata-eval 71.0%

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

      4. metadata-eval 71.0%

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

      5. distribute-lft-neg-in 71.0%

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

      6. associate-+r+ 71.0%

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

      7. metadata-eval 71.0%

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

      8. metadata-eval 71.0%

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

      9. distribute-rgt-neg-in 71.0%

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

      10. metadata-eval 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in z around 0 69.7%

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

      1. *-commutative 69.7%

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

   10. Simplified 69.7%

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

   if -6e-102 < z < -4.40000000000000019e-128 or -1.2000000000000001e-148 < z < -1.70000000000000002e-263 or -3.0999999999999998e-305 < z < 4.00000000000000011e-306 or 8.79999999999999983e-253 < z < 1.6000000000000002e-191

   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 y around inf 76.8%

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

   6. Taylor expanded in z around 0 76.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.08:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-102}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-128}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-191}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(-3 + z \cdot 6\right)\\ t_2 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.19:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+223}:\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z)))
        (t_1 (* x (+ -3.0 (* z 6.0))))
        (t_2 (* x (* z 6.0))))
   (if (<= z -4.2e+256)
     t_0
     (if (<= z -2.9e+215)
       t_2
       (if (<= z -2e+46)
         (* y (* z -6.0))
         (if (<= z -1.3e-10)
           t_1
           (if (<= z 0.19)
             (+ x (* (- y x) 4.0))
             (if (<= z 3.4e+146) t_1 (if (<= z 3.2e+223) (+ x t_0) t_2)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (-3.0 + (z * 6.0));
	double t_2 = x * (z * 6.0);
	double tmp;
	if (z <= -4.2e+256) {
		tmp = t_0;
	} else if (z <= -2.9e+215) {
		tmp = t_2;
	} else if (z <= -2e+46) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.3e-10) {
		tmp = t_1;
	} else if (z <= 0.19) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 3.4e+146) {
		tmp = t_1;
	} else if (z <= 3.2e+223) {
		tmp = x + t_0;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * ((-3.0d0) + (z * 6.0d0))
    t_2 = x * (z * 6.0d0)
    if (z <= (-4.2d+256)) then
        tmp = t_0
    else if (z <= (-2.9d+215)) then
        tmp = t_2
    else if (z <= (-2d+46)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1.3d-10)) then
        tmp = t_1
    else if (z <= 0.19d0) then
        tmp = x + ((y - x) * 4.0d0)
    else if (z <= 3.4d+146) then
        tmp = t_1
    else if (z <= 3.2d+223) then
        tmp = x + t_0
    else
        tmp = t_2
    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 * (-3.0 + (z * 6.0));
	double t_2 = x * (z * 6.0);
	double tmp;
	if (z <= -4.2e+256) {
		tmp = t_0;
	} else if (z <= -2.9e+215) {
		tmp = t_2;
	} else if (z <= -2e+46) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.3e-10) {
		tmp = t_1;
	} else if (z <= 0.19) {
		tmp = x + ((y - x) * 4.0);
	} else if (z <= 3.4e+146) {
		tmp = t_1;
	} else if (z <= 3.2e+223) {
		tmp = x + t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (-3.0 + (z * 6.0))
	t_2 = x * (z * 6.0)
	tmp = 0
	if z <= -4.2e+256:
		tmp = t_0
	elif z <= -2.9e+215:
		tmp = t_2
	elif z <= -2e+46:
		tmp = y * (z * -6.0)
	elif z <= -1.3e-10:
		tmp = t_1
	elif z <= 0.19:
		tmp = x + ((y - x) * 4.0)
	elif z <= 3.4e+146:
		tmp = t_1
	elif z <= 3.2e+223:
		tmp = x + t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_2 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -4.2e+256)
		tmp = t_0;
	elseif (z <= -2.9e+215)
		tmp = t_2;
	elseif (z <= -2e+46)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1.3e-10)
		tmp = t_1;
	elseif (z <= 0.19)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	elseif (z <= 3.4e+146)
		tmp = t_1;
	elseif (z <= 3.2e+223)
		tmp = Float64(x + t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x * (-3.0 + (z * 6.0));
	t_2 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -4.2e+256)
		tmp = t_0;
	elseif (z <= -2.9e+215)
		tmp = t_2;
	elseif (z <= -2e+46)
		tmp = y * (z * -6.0);
	elseif (z <= -1.3e-10)
		tmp = t_1;
	elseif (z <= 0.19)
		tmp = x + ((y - x) * 4.0);
	elseif (z <= 3.4e+146)
		tmp = t_1;
	elseif (z <= 3.2e+223)
		tmp = x + t_0;
	else
		tmp = t_2;
	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[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+256], t$95$0, If[LessEqual[z, -2.9e+215], t$95$2, If[LessEqual[z, -2e+46], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-10], t$95$1, If[LessEqual[z, 0.19], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+146], t$95$1, If[LessEqual[z, 3.2e+223], N[(x + t$95$0), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.2e256

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.9%

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

   6. Taylor expanded in z around inf 88.9%

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

   if -4.2e256 < z < -2.8999999999999999e215 or 3.2000000000000001e223 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. sub-neg 75.9%

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

      2. distribute-rgt-in 75.9%

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

      3. metadata-eval 75.9%

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

      4. metadata-eval 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. associate-+r+ 75.9%

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

      7. metadata-eval 75.9%

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

      8. metadata-eval 75.9%

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

      9. distribute-rgt-neg-in 75.9%

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

      10. metadata-eval 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in z around inf 75.7%

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

      1. associate-*r* 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

   10. Simplified 75.9%

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

   if -2.8999999999999999e215 < z < -2e46

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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 y around inf 67.5%

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

   6. Taylor expanded in z around inf 67.5%

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

   if -2e46 < z < -1.29999999999999991e-10 or 0.19 < z < 3.39999999999999991e146

   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 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. distribute-lft-neg-in 64.4%

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

      6. associate-+r+ 64.4%

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

      7. metadata-eval 64.4%

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

      8. metadata-eval 64.4%

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

      9. distribute-rgt-neg-in 64.4%

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

      10. metadata-eval 64.4%

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

   7. Simplified 64.4%

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

   if -1.29999999999999991e-10 < z < 0.19

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 98.5%

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

   if 3.39999999999999991e146 < z < 3.2000000000000001e223

   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 y around inf 70.2%

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

      1. associate-*r* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in z around inf 70.2%

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

      1. *-commutative 70.2%

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

   10. Simplified 70.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.19:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+223}:\\ \;\;\;\;x + -6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(-3 + z \cdot 6\right)\\ t_2 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.19:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+221}:\\ \;\;\;\;x + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z)))
        (t_1 (* x (+ -3.0 (* z 6.0))))
        (t_2 (* x (* z 6.0))))
   (if (<= z -4.6e+256)
     t_0
     (if (<= z -1.22e+213)
       t_2
       (if (<= z -2.7e+47)
         (* y (* z -6.0))
         (if (<= z -1.7e-9)
           t_1
           (if (<= z 0.19)
             (+ (* x -3.0) (* y 4.0))
             (if (<= z 4.6e+146) t_1 (if (<= z 3.2e+221) (+ x t_0) t_2)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (-3.0 + (z * 6.0));
	double t_2 = x * (z * 6.0);
	double tmp;
	if (z <= -4.6e+256) {
		tmp = t_0;
	} else if (z <= -1.22e+213) {
		tmp = t_2;
	} else if (z <= -2.7e+47) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.7e-9) {
		tmp = t_1;
	} else if (z <= 0.19) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if (z <= 4.6e+146) {
		tmp = t_1;
	} else if (z <= 3.2e+221) {
		tmp = x + t_0;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * ((-3.0d0) + (z * 6.0d0))
    t_2 = x * (z * 6.0d0)
    if (z <= (-4.6d+256)) then
        tmp = t_0
    else if (z <= (-1.22d+213)) then
        tmp = t_2
    else if (z <= (-2.7d+47)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1.7d-9)) then
        tmp = t_1
    else if (z <= 0.19d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else if (z <= 4.6d+146) then
        tmp = t_1
    else if (z <= 3.2d+221) then
        tmp = x + t_0
    else
        tmp = t_2
    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 * (-3.0 + (z * 6.0));
	double t_2 = x * (z * 6.0);
	double tmp;
	if (z <= -4.6e+256) {
		tmp = t_0;
	} else if (z <= -1.22e+213) {
		tmp = t_2;
	} else if (z <= -2.7e+47) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.7e-9) {
		tmp = t_1;
	} else if (z <= 0.19) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if (z <= 4.6e+146) {
		tmp = t_1;
	} else if (z <= 3.2e+221) {
		tmp = x + t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (-3.0 + (z * 6.0))
	t_2 = x * (z * 6.0)
	tmp = 0
	if z <= -4.6e+256:
		tmp = t_0
	elif z <= -1.22e+213:
		tmp = t_2
	elif z <= -2.7e+47:
		tmp = y * (z * -6.0)
	elif z <= -1.7e-9:
		tmp = t_1
	elif z <= 0.19:
		tmp = (x * -3.0) + (y * 4.0)
	elif z <= 4.6e+146:
		tmp = t_1
	elif z <= 3.2e+221:
		tmp = x + t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_2 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -4.6e+256)
		tmp = t_0;
	elseif (z <= -1.22e+213)
		tmp = t_2;
	elseif (z <= -2.7e+47)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1.7e-9)
		tmp = t_1;
	elseif (z <= 0.19)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	elseif (z <= 4.6e+146)
		tmp = t_1;
	elseif (z <= 3.2e+221)
		tmp = Float64(x + t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x * (-3.0 + (z * 6.0));
	t_2 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -4.6e+256)
		tmp = t_0;
	elseif (z <= -1.22e+213)
		tmp = t_2;
	elseif (z <= -2.7e+47)
		tmp = y * (z * -6.0);
	elseif (z <= -1.7e-9)
		tmp = t_1;
	elseif (z <= 0.19)
		tmp = (x * -3.0) + (y * 4.0);
	elseif (z <= 4.6e+146)
		tmp = t_1;
	elseif (z <= 3.2e+221)
		tmp = x + t_0;
	else
		tmp = t_2;
	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[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+256], t$95$0, If[LessEqual[z, -1.22e+213], t$95$2, If[LessEqual[z, -2.7e+47], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-9], t$95$1, If[LessEqual[z, 0.19], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+146], t$95$1, If[LessEqual[z, 3.2e+221], N[(x + t$95$0), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.5999999999999997e256

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.9%

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

   6. Taylor expanded in z around inf 88.9%

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

   if -4.5999999999999997e256 < z < -1.2199999999999999e213 or 3.2e221 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. sub-neg 75.9%

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

      2. distribute-rgt-in 75.9%

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

      3. metadata-eval 75.9%

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

      4. metadata-eval 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. associate-+r+ 75.9%

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

      7. metadata-eval 75.9%

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

      8. metadata-eval 75.9%

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

      9. distribute-rgt-neg-in 75.9%

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

      10. metadata-eval 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in z around inf 75.7%

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

      1. associate-*r* 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

   10. Simplified 75.9%

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

   if -1.2199999999999999e213 < z < -2.69999999999999996e47

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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 y around inf 67.5%

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

   6. Taylor expanded in z around inf 67.5%

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

   if -2.69999999999999996e47 < z < -1.6999999999999999e-9 or 0.19 < z < 4.60000000000000001e146

   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 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. distribute-lft-neg-in 64.4%

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

      6. associate-+r+ 64.4%

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

      7. metadata-eval 64.4%

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

      8. metadata-eval 64.4%

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

      9. distribute-rgt-neg-in 64.4%

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

      10. metadata-eval 64.4%

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

   7. Simplified 64.4%

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

   if -1.6999999999999999e-9 < z < 0.19

   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 0 99.7%

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

   6. Taylor expanded in z around 0 98.5%

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

   if 4.60000000000000001e146 < z < 3.2e221

   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 y around inf 70.2%

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

      1. associate-*r* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in z around inf 70.2%

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

      1. *-commutative 70.2%

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

   10. Simplified 70.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.19:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+221}:\\ \;\;\;\;x + -6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.19:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+221}:\\ \;\;\;\;x - z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* x (* z 6.0))))
   (if (<= z -3.3e+256)
     (* -6.0 (* y z))
     (if (<= z -1.5e+214)
       t_1
       (if (<= z -1.7e+47)
         (* y (* z -6.0))
         (if (<= z -1.4e-10)
           t_0
           (if (<= z 0.19)
             (+ (* x -3.0) (* y 4.0))
             (if (<= z 3e+146)
               t_0
               (if (<= z 2.4e+221) (- x (* z (* y 6.0))) t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -3.3e+256) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.5e+214) {
		tmp = t_1;
	} else if (z <= -1.7e+47) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.4e-10) {
		tmp = t_0;
	} else if (z <= 0.19) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if (z <= 3e+146) {
		tmp = t_0;
	} else if (z <= 2.4e+221) {
		tmp = x - (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 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = x * (z * 6.0d0)
    if (z <= (-3.3d+256)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-1.5d+214)) then
        tmp = t_1
    else if (z <= (-1.7d+47)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1.4d-10)) then
        tmp = t_0
    else if (z <= 0.19d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else if (z <= 3d+146) then
        tmp = t_0
    else if (z <= 2.4d+221) then
        tmp = x - (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 = x * (-3.0 + (z * 6.0));
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -3.3e+256) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.5e+214) {
		tmp = t_1;
	} else if (z <= -1.7e+47) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.4e-10) {
		tmp = t_0;
	} else if (z <= 0.19) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if (z <= 3e+146) {
		tmp = t_0;
	} else if (z <= 2.4e+221) {
		tmp = x - (z * (y * 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -3.3e+256:
		tmp = -6.0 * (y * z)
	elif z <= -1.5e+214:
		tmp = t_1
	elif z <= -1.7e+47:
		tmp = y * (z * -6.0)
	elif z <= -1.4e-10:
		tmp = t_0
	elif z <= 0.19:
		tmp = (x * -3.0) + (y * 4.0)
	elif z <= 3e+146:
		tmp = t_0
	elif z <= 2.4e+221:
		tmp = x - (z * (y * 6.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.3e+256)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -1.5e+214)
		tmp = t_1;
	elseif (z <= -1.7e+47)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1.4e-10)
		tmp = t_0;
	elseif (z <= 0.19)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	elseif (z <= 3e+146)
		tmp = t_0;
	elseif (z <= 2.4e+221)
		tmp = Float64(x - Float64(z * Float64(y * 6.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.3e+256)
		tmp = -6.0 * (y * z);
	elseif (z <= -1.5e+214)
		tmp = t_1;
	elseif (z <= -1.7e+47)
		tmp = y * (z * -6.0);
	elseif (z <= -1.4e-10)
		tmp = t_0;
	elseif (z <= 0.19)
		tmp = (x * -3.0) + (y * 4.0);
	elseif (z <= 3e+146)
		tmp = t_0;
	elseif (z <= 2.4e+221)
		tmp = x - (z * (y * 6.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+256], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e+214], t$95$1, If[LessEqual[z, -1.7e+47], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-10], t$95$0, If[LessEqual[z, 0.19], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+146], t$95$0, If[LessEqual[z, 2.4e+221], N[(x - N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.2999999999999999e256

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 88.9%

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

   6. Taylor expanded in z around inf 88.9%

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

   if -3.2999999999999999e256 < z < -1.5000000000000001e214 or 2.40000000000000019e221 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. sub-neg 75.9%

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

      2. distribute-rgt-in 75.9%

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

      3. metadata-eval 75.9%

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

      4. metadata-eval 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. associate-+r+ 75.9%

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

      7. metadata-eval 75.9%

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

      8. metadata-eval 75.9%

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

      9. distribute-rgt-neg-in 75.9%

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

      10. metadata-eval 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in z around inf 75.7%

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

      1. associate-*r* 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

   10. Simplified 75.9%

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

   if -1.5000000000000001e214 < z < -1.6999999999999999e47

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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 y around inf 67.5%

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

   6. Taylor expanded in z around inf 67.5%

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

   if -1.6999999999999999e47 < z < -1.40000000000000008e-10 or 0.19 < z < 3.00000000000000002e146

   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 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. distribute-lft-neg-in 64.4%

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

      6. associate-+r+ 64.4%

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

      7. metadata-eval 64.4%

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

      8. metadata-eval 64.4%

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

      9. distribute-rgt-neg-in 64.4%

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

      10. metadata-eval 64.4%

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

   7. Simplified 64.4%

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

   if -1.40000000000000008e-10 < z < 0.19

   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 0 99.7%

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

   6. Taylor expanded in z around 0 98.5%

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

   if 3.00000000000000002e146 < z < 2.40000000000000019e221

   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 y around inf 70.2%

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

      1. associate-*r* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in z around inf 70.3%

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

      1. neg-mul-1 70.3%

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

   10. Simplified 70.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+256}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.19:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+221}:\\ \;\;\;\;x - z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -7.3 \cdot 10^{-104}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-96}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -7.3e-104)
     t_0
     (if (<= y -5.6e-205)
       (* x -3.0)
       (if (<= y -6.2e-277)
         (* x (* z 6.0))
         (if (<= y 1.3e-96) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -7.3e-104) {
		tmp = t_0;
	} else if (y <= -5.6e-205) {
		tmp = x * -3.0;
	} else if (y <= -6.2e-277) {
		tmp = x * (z * 6.0);
	} else if (y <= 1.3e-96) {
		tmp = x * -3.0;
	} 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 * (0.6666666666666666d0 - z))
    if (y <= (-7.3d-104)) then
        tmp = t_0
    else if (y <= (-5.6d-205)) then
        tmp = x * (-3.0d0)
    else if (y <= (-6.2d-277)) then
        tmp = x * (z * 6.0d0)
    else if (y <= 1.3d-96) then
        tmp = x * (-3.0d0)
    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 * (0.6666666666666666 - z));
	double tmp;
	if (y <= -7.3e-104) {
		tmp = t_0;
	} else if (y <= -5.6e-205) {
		tmp = x * -3.0;
	} else if (y <= -6.2e-277) {
		tmp = x * (z * 6.0);
	} else if (y <= 1.3e-96) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	tmp = 0
	if y <= -7.3e-104:
		tmp = t_0
	elif y <= -5.6e-205:
		tmp = x * -3.0
	elif y <= -6.2e-277:
		tmp = x * (z * 6.0)
	elif y <= 1.3e-96:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	tmp = 0.0
	if (y <= -7.3e-104)
		tmp = t_0;
	elseif (y <= -5.6e-205)
		tmp = Float64(x * -3.0);
	elseif (y <= -6.2e-277)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (y <= 1.3e-96)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	tmp = 0.0;
	if (y <= -7.3e-104)
		tmp = t_0;
	elseif (y <= -5.6e-205)
		tmp = x * -3.0;
	elseif (y <= -6.2e-277)
		tmp = x * (z * 6.0);
	elseif (y <= 1.3e-96)
		tmp = x * -3.0;
	else
		tmp = t_0;
	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]}, If[LessEqual[y, -7.3e-104], t$95$0, If[LessEqual[y, -5.6e-205], N[(x * -3.0), $MachinePrecision], If[LessEqual[y, -6.2e-277], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-96], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3e-104 or 1.3000000000000001e-96 < y

   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. +-commutative 99.6%

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

      2. flip-+ 32.2%

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

      3. pow2 32.2%

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

      4. associate-*l* 32.1%

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

      5. pow2 32.1%

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

      6. associate-*l* 32.3%

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

   6. Applied egg-rr 32.3%

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

   7. Taylor expanded in y around inf 90.2%

      \[\leadsto \color{blue}{\left(x + \left(-12 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)\right) - -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]

   8. Taylor expanded in x around 0 69.7%

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

   if -7.3e-104 < y < -5.59999999999999983e-205 or -6.19999999999999958e-277 < y < 1.3000000000000001e-96

   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 86.5%

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

      1. sub-neg 86.5%

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

      2. distribute-rgt-in 86.5%

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

      3. metadata-eval 86.5%

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

      4. metadata-eval 86.5%

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

      5. distribute-lft-neg-in 86.5%

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

      6. associate-+r+ 86.5%

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

      7. metadata-eval 86.5%

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

      8. metadata-eval 86.5%

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

      9. distribute-rgt-neg-in 86.5%

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

      10. metadata-eval 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in z around 0 53.4%

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

      1. *-commutative 53.4%

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

   10. Simplified 53.4%

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

   if -5.59999999999999983e-205 < y < -6.19999999999999958e-277

   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 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. metadata-eval 99.8%

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

      4. metadata-eval 99.8%

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

      5. distribute-lft-neg-in 99.8%

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

      6. associate-+r+ 99.8%

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

      7. metadata-eval 99.8%

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

      8. metadata-eval 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 67.5%

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

      1. associate-*r* 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 67.7%

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

      4. *-commutative 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{-104}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-205}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-96}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.5)))
   (* z (+ (* y -6.0) (* x 6.0)))
   (+ (* x -3.0) (* y 4.0))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.58d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.5):
		tmp = z * ((y * -6.0) + (x * 6.0))
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.5 < z

   1. Initial program 99.7%

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

      1. 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 0 97.1%

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

   6. Taylor expanded in z around inf 97.8%

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

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in z around 0 97.5%

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

4. Final simplification 97.6%

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

Alternative 12: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.52)
   (* z (+ (* y -6.0) (* x 6.0)))
   (if (<= z 0.5) (+ (* x -3.0) (* y 4.0)) (+ x (* -6.0 (* (- y x) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else if (z <= 0.5) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.52d0)) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    else if (z <= 0.5d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = x + ((-6.0d0) * ((y - x) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else if (z <= 0.5) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.52:
		tmp = z * ((y * -6.0) + (x * 6.0))
	elif z <= 0.5:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = x + (-6.0 * ((y - x) * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.52)
		tmp = Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0)));
	elseif (z <= 0.5)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.52)
		tmp = z * ((y * -6.0) + (x * 6.0));
	elseif (z <= 0.5)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = x + (-6.0 * ((y - x) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.52], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.52000000000000002

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 96.3%

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

   6. Taylor expanded in z around inf 97.8%

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

   if -0.52000000000000002 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in z around 0 97.5%

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

   if 0.5 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 97.9%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+50} \lor \neg \left(y \leq 9.6 \cdot 10^{+54}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e+50) (not (<= y 9.6e+54)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e+50) || !(y <= 9.6e+54)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.4d+50)) .or. (.not. (y <= 9.6d+54))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e+50) || !(y <= 9.6e+54)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e+50) or not (y <= 9.6e+54):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e+50) || !(y <= 9.6e+54))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e+50) || ~((y <= 9.6e+54)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e+50], N[Not[LessEqual[y, 9.6e+54]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3999999999999998e50 or 9.59999999999999993e54 < y

   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. +-commutative 99.6%

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

      2. flip-+ 21.9%

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

      3. pow2 21.9%

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

      4. associate-*l* 21.9%

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

      5. pow2 21.9%

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

      6. associate-*l* 22.0%

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

   6. Applied egg-rr 22.0%

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

   7. Taylor expanded in y around inf 92.7%

      \[\leadsto \color{blue}{\left(x + \left(-12 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right) + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\right)\right) - -6 \cdot \left(x \cdot \left(0.6666666666666666 - z\right)\right)} \]

   8. Taylor expanded in x around 0 83.1%

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

   if -3.3999999999999998e50 < y < 9.59999999999999993e54

   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 76.1%

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

      1. sub-neg 76.1%

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

      2. distribute-rgt-in 76.1%

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

      3. metadata-eval 76.1%

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

      4. metadata-eval 76.1%

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

      5. distribute-lft-neg-in 76.1%

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

      6. associate-+r+ 76.2%

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

      7. metadata-eval 76.2%

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

      8. metadata-eval 76.2%

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

      9. distribute-rgt-neg-in 76.2%

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

      10. metadata-eval 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+50} \lor \neg \left(y \leq 9.6 \cdot 10^{+54}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+50} \lor \neg \left(y \leq 1.12 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.3e+50) (not (<= y 1.12e+55)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e+50) || !(y <= 1.12e+55)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.3d+50)) .or. (.not. (y <= 1.12d+55))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e+50) || !(y <= 1.12e+55)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.3e+50) or not (y <= 1.12e+55):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.3e+50) || !(y <= 1.12e+55))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.3e+50) || ~((y <= 1.12e+55)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.3e+50], N[Not[LessEqual[y, 1.12e+55]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e50 or 1.12000000000000006e55 < y

   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. Taylor expanded in y around inf 83.2%

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

   if -3.3e50 < y < 1.12000000000000006e55

   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 76.1%

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

      1. sub-neg 76.1%

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

      2. distribute-rgt-in 76.1%

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

      3. metadata-eval 76.1%

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

      4. metadata-eval 76.1%

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

      5. distribute-lft-neg-in 76.1%

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

      6. associate-+r+ 76.2%

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

      7. metadata-eval 76.2%

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

      8. metadata-eval 76.2%

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

      9. distribute-rgt-neg-in 76.2%

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

      10. metadata-eval 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+50} \lor \neg \left(y \leq 1.12 \cdot 10^{+55}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+74} \lor \neg \left(x \leq 1.65 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e+74) (not (<= x 1.65e-59))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e+74) || !(x <= 1.65e-59)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1d+74)) .or. (.not. (x <= 1.65d-59))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e+74) || !(x <= 1.65e-59)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e+74) or not (x <= 1.65e-59):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e+74) || !(x <= 1.65e-59))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e+74) || ~((x <= 1.65e-59)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e+74], N[Not[LessEqual[x, 1.65e-59]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999952e73 or 1.64999999999999991e-59 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 78.8%

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

      1. sub-neg 78.8%

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

      2. distribute-rgt-in 78.8%

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

      3. metadata-eval 78.8%

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

      4. metadata-eval 78.8%

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

      5. distribute-lft-neg-in 78.8%

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

      6. associate-+r+ 78.8%

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

      7. metadata-eval 78.8%

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

      8. metadata-eval 78.8%

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

      9. distribute-rgt-neg-in 78.8%

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

      10. metadata-eval 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around 0 45.4%

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

      1. *-commutative 45.4%

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

   10. Simplified 45.4%

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

   if -9.99999999999999952e73 < x < 1.64999999999999991e-59

   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* 99.7%

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

      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. Taylor expanded in y around inf 76.3%

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

   6. Taylor expanded in z around 0 45.5%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+74} \lor \neg \left(x \leq 1.65 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 17: 25.7% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf 53.7%

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

   1. sub-neg 53.7%

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

   2. distribute-rgt-in 53.7%

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

   3. metadata-eval 53.7%

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

   4. metadata-eval 53.7%

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

   5. distribute-lft-neg-in 53.7%

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

   6. associate-+r+ 53.7%

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

   7. metadata-eval 53.7%

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

   8. metadata-eval 53.7%

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

   9. distribute-rgt-neg-in 53.7%

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

   10. metadata-eval 53.7%

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

7. Simplified 53.7%

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

8. Taylor expanded in z around 0 30.6%

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

   1. *-commutative 30.6%

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

10. Simplified 30.6%

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

11. Final simplification 30.6%

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

Alternative 18: 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 y around inf 48.0%

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

   1. associate-*r* 48.0%

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

7. Simplified 48.0%

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

8. Taylor expanded in x around inf 2.3%

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

9. Final simplification 2.3%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(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))))