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

Percentage Accurate: 99.5% → 99.7%

Time: 11.2s

Alternatives: 13

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: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 51.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+171}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -0.042:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-97}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-109}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-281}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-290}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -3.05e+171)
     (* -6.0 (* z y))
     (if (<= z -0.042)
       t_0
       (if (<= z -1.55e-53)
         (* y 4.0)
         (if (<= z -6.6e-97)
           (* x -3.0)
           (if (<= z -7e-109)
             (* y 4.0)
             (if (<= z -1e-145)
               (* x -3.0)
               (if (<= z -9e-281)
                 (* y 4.0)
                 (if (<= z 9.2e-290)
                   (* x -3.0)
                   (if (<= z 1.45e-177)
                     (* y 4.0)
                     (if (<= z 0.5) (* x -3.0) t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.05e+171) {
		tmp = -6.0 * (z * y);
	} else if (z <= -0.042) {
		tmp = t_0;
	} else if (z <= -1.55e-53) {
		tmp = y * 4.0;
	} else if (z <= -6.6e-97) {
		tmp = x * -3.0;
	} else if (z <= -7e-109) {
		tmp = y * 4.0;
	} else if (z <= -1e-145) {
		tmp = x * -3.0;
	} else if (z <= -9e-281) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-290) {
		tmp = x * -3.0;
	} else if (z <= 1.45e-177) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		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 = x * (z * 6.0d0)
    if (z <= (-3.05d+171)) then
        tmp = (-6.0d0) * (z * y)
    else if (z <= (-0.042d0)) then
        tmp = t_0
    else if (z <= (-1.55d-53)) then
        tmp = y * 4.0d0
    else if (z <= (-6.6d-97)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7d-109)) then
        tmp = y * 4.0d0
    else if (z <= (-1d-145)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9d-281)) then
        tmp = y * 4.0d0
    else if (z <= 9.2d-290) then
        tmp = x * (-3.0d0)
    else if (z <= 1.45d-177) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) 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 = x * (z * 6.0);
	double tmp;
	if (z <= -3.05e+171) {
		tmp = -6.0 * (z * y);
	} else if (z <= -0.042) {
		tmp = t_0;
	} else if (z <= -1.55e-53) {
		tmp = y * 4.0;
	} else if (z <= -6.6e-97) {
		tmp = x * -3.0;
	} else if (z <= -7e-109) {
		tmp = y * 4.0;
	} else if (z <= -1e-145) {
		tmp = x * -3.0;
	} else if (z <= -9e-281) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-290) {
		tmp = x * -3.0;
	} else if (z <= 1.45e-177) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -3.05e+171:
		tmp = -6.0 * (z * y)
	elif z <= -0.042:
		tmp = t_0
	elif z <= -1.55e-53:
		tmp = y * 4.0
	elif z <= -6.6e-97:
		tmp = x * -3.0
	elif z <= -7e-109:
		tmp = y * 4.0
	elif z <= -1e-145:
		tmp = x * -3.0
	elif z <= -9e-281:
		tmp = y * 4.0
	elif z <= 9.2e-290:
		tmp = x * -3.0
	elif z <= 1.45e-177:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.05e+171)
		tmp = Float64(-6.0 * Float64(z * y));
	elseif (z <= -0.042)
		tmp = t_0;
	elseif (z <= -1.55e-53)
		tmp = Float64(y * 4.0);
	elseif (z <= -6.6e-97)
		tmp = Float64(x * -3.0);
	elseif (z <= -7e-109)
		tmp = Float64(y * 4.0);
	elseif (z <= -1e-145)
		tmp = Float64(x * -3.0);
	elseif (z <= -9e-281)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.2e-290)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.45e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.05e+171)
		tmp = -6.0 * (z * y);
	elseif (z <= -0.042)
		tmp = t_0;
	elseif (z <= -1.55e-53)
		tmp = y * 4.0;
	elseif (z <= -6.6e-97)
		tmp = x * -3.0;
	elseif (z <= -7e-109)
		tmp = y * 4.0;
	elseif (z <= -1e-145)
		tmp = x * -3.0;
	elseif (z <= -9e-281)
		tmp = y * 4.0;
	elseif (z <= 9.2e-290)
		tmp = x * -3.0;
	elseif (z <= 1.45e-177)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_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, -3.05e+171], N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.042], t$95$0, If[LessEqual[z, -1.55e-53], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6.6e-97], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7e-109], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1e-145], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9e-281], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.2e-290], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.45e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.04999999999999998e171

   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* 96.9%

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

      3. fma-def 96.9%

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

      4. sub-neg 96.9%

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

      5. distribute-rgt-in 96.9%

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

      6. metadata-eval 96.9%

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

      7. metadata-eval 96.9%

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

      8. distribute-lft-neg-out 96.9%

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

      9. distribute-rgt-neg-in 96.9%

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

      10. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 58.8%

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

   6. Taylor expanded in z around inf 61.6%

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

   if -3.04999999999999998e171 < z < -0.0420000000000000026 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 63.7%

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

      1. sub-neg 63.7%

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

      2. distribute-rgt-in 63.7%

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

      3. metadata-eval 63.7%

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

      4. metadata-eval 63.7%

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

      5. distribute-lft-neg-in 63.7%

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

      6. associate-+r+ 63.7%

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

      7. metadata-eval 63.7%

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

      8. metadata-eval 63.7%

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

      9. distribute-rgt-neg-in 63.7%

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

      10. metadata-eval 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in z around inf 61.7%

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

   if -0.0420000000000000026 < z < -1.55000000000000008e-53 or -6.6000000000000002e-97 < z < -7e-109 or -9.99999999999999915e-146 < z < -8.99999999999999986e-281 or 9.2000000000000003e-290 < z < 1.44999999999999999e-177

   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 68.2%

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

   6. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if -1.55000000000000008e-53 < z < -6.6000000000000002e-97 or -7e-109 < z < -9.99999999999999915e-146 or -8.99999999999999986e-281 < z < 9.2000000000000003e-290 or 1.44999999999999999e-177 < z < 0.5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 65.8%

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

      1. sub-neg 65.8%

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

      2. distribute-rgt-in 65.8%

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

      3. metadata-eval 65.8%

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

      4. metadata-eval 65.8%

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

      5. distribute-lft-neg-in 65.8%

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

      6. associate-+r+ 65.8%

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

      7. metadata-eval 65.8%

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

      8. metadata-eval 65.8%

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

      9. distribute-rgt-neg-in 65.8%

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

      10. metadata-eval 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 64.6%

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

      1. *-commutative 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+171}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -0.042:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-97}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-109}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-281}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-290}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -0.06:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-97}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-287}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -3.05e+171)
     (* z (* -6.0 y))
     (if (<= z -0.06)
       t_0
       (if (<= z -1.15e-53)
         (* y 4.0)
         (if (<= z -1.3e-97)
           (* x -3.0)
           (if (<= z -1.3e-107)
             (* y 4.0)
             (if (<= z -1.26e-145)
               (* x -3.0)
               (if (<= z -5.4e-280)
                 (* y 4.0)
                 (if (<= z 4.8e-287)
                   (* x -3.0)
                   (if (<= z 3.7e-178)
                     (* y 4.0)
                     (if (<= z 0.5) (* x -3.0) t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -3.05e+171) {
		tmp = z * (-6.0 * y);
	} else if (z <= -0.06) {
		tmp = t_0;
	} else if (z <= -1.15e-53) {
		tmp = y * 4.0;
	} else if (z <= -1.3e-97) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-107) {
		tmp = y * 4.0;
	} else if (z <= -1.26e-145) {
		tmp = x * -3.0;
	} else if (z <= -5.4e-280) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-287) {
		tmp = x * -3.0;
	} else if (z <= 3.7e-178) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		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 = x * (z * 6.0d0)
    if (z <= (-3.05d+171)) then
        tmp = z * ((-6.0d0) * y)
    else if (z <= (-0.06d0)) then
        tmp = t_0
    else if (z <= (-1.15d-53)) then
        tmp = y * 4.0d0
    else if (z <= (-1.3d-97)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.3d-107)) then
        tmp = y * 4.0d0
    else if (z <= (-1.26d-145)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.4d-280)) then
        tmp = y * 4.0d0
    else if (z <= 4.8d-287) then
        tmp = x * (-3.0d0)
    else if (z <= 3.7d-178) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) 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 = x * (z * 6.0);
	double tmp;
	if (z <= -3.05e+171) {
		tmp = z * (-6.0 * y);
	} else if (z <= -0.06) {
		tmp = t_0;
	} else if (z <= -1.15e-53) {
		tmp = y * 4.0;
	} else if (z <= -1.3e-97) {
		tmp = x * -3.0;
	} else if (z <= -1.3e-107) {
		tmp = y * 4.0;
	} else if (z <= -1.26e-145) {
		tmp = x * -3.0;
	} else if (z <= -5.4e-280) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-287) {
		tmp = x * -3.0;
	} else if (z <= 3.7e-178) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -3.05e+171:
		tmp = z * (-6.0 * y)
	elif z <= -0.06:
		tmp = t_0
	elif z <= -1.15e-53:
		tmp = y * 4.0
	elif z <= -1.3e-97:
		tmp = x * -3.0
	elif z <= -1.3e-107:
		tmp = y * 4.0
	elif z <= -1.26e-145:
		tmp = x * -3.0
	elif z <= -5.4e-280:
		tmp = y * 4.0
	elif z <= 4.8e-287:
		tmp = x * -3.0
	elif z <= 3.7e-178:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -3.05e+171)
		tmp = Float64(z * Float64(-6.0 * y));
	elseif (z <= -0.06)
		tmp = t_0;
	elseif (z <= -1.15e-53)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.3e-97)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.3e-107)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.26e-145)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.4e-280)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.8e-287)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.7e-178)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -3.05e+171)
		tmp = z * (-6.0 * y);
	elseif (z <= -0.06)
		tmp = t_0;
	elseif (z <= -1.15e-53)
		tmp = y * 4.0;
	elseif (z <= -1.3e-97)
		tmp = x * -3.0;
	elseif (z <= -1.3e-107)
		tmp = y * 4.0;
	elseif (z <= -1.26e-145)
		tmp = x * -3.0;
	elseif (z <= -5.4e-280)
		tmp = y * 4.0;
	elseif (z <= 4.8e-287)
		tmp = x * -3.0;
	elseif (z <= 3.7e-178)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_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, -3.05e+171], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.06], t$95$0, If[LessEqual[z, -1.15e-53], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.3e-97], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.3e-107], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.26e-145], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.4e-280], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.8e-287], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.7e-178], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.04999999999999998e171

   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* 96.9%

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

      3. fma-def 96.9%

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

      4. sub-neg 96.9%

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

      5. distribute-rgt-in 96.9%

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

      6. metadata-eval 96.9%

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

      7. metadata-eval 96.9%

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

      8. distribute-lft-neg-out 96.9%

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

      9. distribute-rgt-neg-in 96.9%

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

      10. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 58.8%

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

   6. Taylor expanded in z around inf 61.6%

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

      1. associate-*r* 61.7%

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

      2. *-commutative 61.7%

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

   8. Simplified 61.7%

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

   if -3.04999999999999998e171 < z < -0.059999999999999998 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 63.7%

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

      1. sub-neg 63.7%

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

      2. distribute-rgt-in 63.7%

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

      3. metadata-eval 63.7%

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

      4. metadata-eval 63.7%

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

      5. distribute-lft-neg-in 63.7%

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

      6. associate-+r+ 63.7%

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

      7. metadata-eval 63.7%

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

      8. metadata-eval 63.7%

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

      9. distribute-rgt-neg-in 63.7%

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

      10. metadata-eval 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in z around inf 61.7%

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

   if -0.059999999999999998 < z < -1.1500000000000001e-53 or -1.30000000000000003e-97 < z < -1.3e-107 or -1.2599999999999999e-145 < z < -5.39999999999999967e-280 or 4.79999999999999999e-287 < z < 3.70000000000000004e-178

   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 68.2%

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

   6. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if -1.1500000000000001e-53 < z < -1.30000000000000003e-97 or -1.3e-107 < z < -1.2599999999999999e-145 or -5.39999999999999967e-280 < z < 4.79999999999999999e-287 or 3.70000000000000004e-178 < z < 0.5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 65.8%

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

      1. sub-neg 65.8%

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

      2. distribute-rgt-in 65.8%

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

      3. metadata-eval 65.8%

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

      4. metadata-eval 65.8%

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

      5. distribute-lft-neg-in 65.8%

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

      6. associate-+r+ 65.8%

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

      7. metadata-eval 65.8%

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

      8. metadata-eval 65.8%

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

      9. distribute-rgt-neg-in 65.8%

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

      10. metadata-eval 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 64.6%

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

      1. *-commutative 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -0.06:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-97}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-287}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-178}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.00135:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-97}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-286}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -0.00135)
     t_0
     (if (<= z -6.5e-53)
       (* y 4.0)
       (if (<= z -4.3e-97)
         (* x -3.0)
         (if (<= z -1.95e-112)
           (* y 4.0)
           (if (<= z -2.6e-145)
             (* x -3.0)
             (if (<= z -5.1e-280)
               (* y 4.0)
               (if (<= z 3.9e-286)
                 (* x -3.0)
                 (if (<= z 2.6e-175)
                   (* y 4.0)
                   (if (<= z 0.5) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.00135) {
		tmp = t_0;
	} else if (z <= -6.5e-53) {
		tmp = y * 4.0;
	} else if (z <= -4.3e-97) {
		tmp = x * -3.0;
	} else if (z <= -1.95e-112) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-145) {
		tmp = x * -3.0;
	} else if (z <= -5.1e-280) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-286) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-175) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		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) * (z * (y - x))
    if (z <= (-0.00135d0)) then
        tmp = t_0
    else if (z <= (-6.5d-53)) then
        tmp = y * 4.0d0
    else if (z <= (-4.3d-97)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.95d-112)) then
        tmp = y * 4.0d0
    else if (z <= (-2.6d-145)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.1d-280)) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-286) then
        tmp = x * (-3.0d0)
    else if (z <= 2.6d-175) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) 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 * (z * (y - x));
	double tmp;
	if (z <= -0.00135) {
		tmp = t_0;
	} else if (z <= -6.5e-53) {
		tmp = y * 4.0;
	} else if (z <= -4.3e-97) {
		tmp = x * -3.0;
	} else if (z <= -1.95e-112) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-145) {
		tmp = x * -3.0;
	} else if (z <= -5.1e-280) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-286) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-175) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.00135:
		tmp = t_0
	elif z <= -6.5e-53:
		tmp = y * 4.0
	elif z <= -4.3e-97:
		tmp = x * -3.0
	elif z <= -1.95e-112:
		tmp = y * 4.0
	elif z <= -2.6e-145:
		tmp = x * -3.0
	elif z <= -5.1e-280:
		tmp = y * 4.0
	elif z <= 3.9e-286:
		tmp = x * -3.0
	elif z <= 2.6e-175:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.00135)
		tmp = t_0;
	elseif (z <= -6.5e-53)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.3e-97)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.95e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.6e-145)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.1e-280)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-286)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.6e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		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 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.00135)
		tmp = t_0;
	elseif (z <= -6.5e-53)
		tmp = y * 4.0;
	elseif (z <= -4.3e-97)
		tmp = x * -3.0;
	elseif (z <= -1.95e-112)
		tmp = y * 4.0;
	elseif (z <= -2.6e-145)
		tmp = x * -3.0;
	elseif (z <= -5.1e-280)
		tmp = y * 4.0;
	elseif (z <= 3.9e-286)
		tmp = x * -3.0;
	elseif (z <= 2.6e-175)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		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[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00135], t$95$0, If[LessEqual[z, -6.5e-53], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.3e-97], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.95e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.6e-145], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.1e-280], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-286], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.6e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0013500000000000001 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 97.3%

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

   if -0.0013500000000000001 < z < -6.4999999999999997e-53 or -4.3e-97 < z < -1.9500000000000001e-112 or -2.6e-145 < z < -5.0999999999999996e-280 or 3.89999999999999995e-286 < z < 2.6e-175

   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 68.2%

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

   6. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if -6.4999999999999997e-53 < z < -4.3e-97 or -1.9500000000000001e-112 < z < -2.6e-145 or -5.0999999999999996e-280 < z < 3.89999999999999995e-286 or 2.6e-175 < z < 0.5

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 65.8%

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

      1. sub-neg 65.8%

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

      2. distribute-rgt-in 65.8%

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

      3. metadata-eval 65.8%

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

      4. metadata-eval 65.8%

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

      5. distribute-lft-neg-in 65.8%

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

      6. associate-+r+ 65.8%

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

      7. metadata-eval 65.8%

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

      8. metadata-eval 65.8%

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

      9. distribute-rgt-neg-in 65.8%

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

      10. metadata-eval 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 64.6%

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

      1. *-commutative 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00135:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-97}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-286}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ t_1 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.0115:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-98}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-281}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))) (t_1 (* x (+ -3.0 (* z 6.0)))))
   (if (<= z -0.0115)
     t_0
     (if (<= z -9e-52)
       (* y 4.0)
       (if (<= z -1.36e-98)
         (* x -3.0)
         (if (<= z -1.62e-112)
           (* y 4.0)
           (if (<= z -1.55e-145)
             t_1
             (if (<= z -1.05e-281)
               (* y 4.0)
               (if (<= z 1.5e-289)
                 (* x -3.0)
                 (if (<= z 1.85e-176)
                   (* y 4.0)
                   (if (<= z 4.2e+14) t_1 t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -0.0115) {
		tmp = t_0;
	} else if (z <= -9e-52) {
		tmp = y * 4.0;
	} else if (z <= -1.36e-98) {
		tmp = x * -3.0;
	} else if (z <= -1.62e-112) {
		tmp = y * 4.0;
	} else if (z <= -1.55e-145) {
		tmp = t_1;
	} else if (z <= -1.05e-281) {
		tmp = y * 4.0;
	} else if (z <= 1.5e-289) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-176) {
		tmp = y * 4.0;
	} else if (z <= 4.2e+14) {
		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) * (z * (y - x))
    t_1 = x * ((-3.0d0) + (z * 6.0d0))
    if (z <= (-0.0115d0)) then
        tmp = t_0
    else if (z <= (-9d-52)) then
        tmp = y * 4.0d0
    else if (z <= (-1.36d-98)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.62d-112)) then
        tmp = y * 4.0d0
    else if (z <= (-1.55d-145)) then
        tmp = t_1
    else if (z <= (-1.05d-281)) then
        tmp = y * 4.0d0
    else if (z <= 1.5d-289) then
        tmp = x * (-3.0d0)
    else if (z <= 1.85d-176) then
        tmp = y * 4.0d0
    else if (z <= 4.2d+14) 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 * (z * (y - x));
	double t_1 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (z <= -0.0115) {
		tmp = t_0;
	} else if (z <= -9e-52) {
		tmp = y * 4.0;
	} else if (z <= -1.36e-98) {
		tmp = x * -3.0;
	} else if (z <= -1.62e-112) {
		tmp = y * 4.0;
	} else if (z <= -1.55e-145) {
		tmp = t_1;
	} else if (z <= -1.05e-281) {
		tmp = y * 4.0;
	} else if (z <= 1.5e-289) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-176) {
		tmp = y * 4.0;
	} else if (z <= 4.2e+14) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	t_1 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if z <= -0.0115:
		tmp = t_0
	elif z <= -9e-52:
		tmp = y * 4.0
	elif z <= -1.36e-98:
		tmp = x * -3.0
	elif z <= -1.62e-112:
		tmp = y * 4.0
	elif z <= -1.55e-145:
		tmp = t_1
	elif z <= -1.05e-281:
		tmp = y * 4.0
	elif z <= 1.5e-289:
		tmp = x * -3.0
	elif z <= 1.85e-176:
		tmp = y * 4.0
	elif z <= 4.2e+14:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	t_1 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (z <= -0.0115)
		tmp = t_0;
	elseif (z <= -9e-52)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.36e-98)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.62e-112)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.55e-145)
		tmp = t_1;
	elseif (z <= -1.05e-281)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.5e-289)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.85e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.2e+14)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	t_1 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (z <= -0.0115)
		tmp = t_0;
	elseif (z <= -9e-52)
		tmp = y * 4.0;
	elseif (z <= -1.36e-98)
		tmp = x * -3.0;
	elseif (z <= -1.62e-112)
		tmp = y * 4.0;
	elseif (z <= -1.55e-145)
		tmp = t_1;
	elseif (z <= -1.05e-281)
		tmp = y * 4.0;
	elseif (z <= 1.5e-289)
		tmp = x * -3.0;
	elseif (z <= 1.85e-176)
		tmp = y * 4.0;
	elseif (z <= 4.2e+14)
		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[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0115], t$95$0, If[LessEqual[z, -9e-52], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.36e-98], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.62e-112], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.55e-145], t$95$1, If[LessEqual[z, -1.05e-281], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.5e-289], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.85e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.2e+14], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0115 or 4.2e14 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.7%

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

   if -0.0115 < z < -9.0000000000000001e-52 or -1.36000000000000003e-98 < z < -1.62000000000000009e-112 or -1.55e-145 < z < -1.0499999999999999e-281 or 1.4999999999999999e-289 < z < 1.84999999999999992e-176

   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 68.2%

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

   6. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if -9.0000000000000001e-52 < z < -1.36000000000000003e-98 or -1.0499999999999999e-281 < z < 1.4999999999999999e-289

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 79.5%

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

      1. sub-neg 79.5%

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

      2. distribute-rgt-in 79.5%

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

      3. metadata-eval 79.5%

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

      4. metadata-eval 79.5%

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

      5. distribute-lft-neg-in 79.5%

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

      6. associate-+r+ 79.5%

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

      7. metadata-eval 79.5%

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

      8. metadata-eval 79.5%

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

      9. distribute-rgt-neg-in 79.5%

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

      10. metadata-eval 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in z around 0 79.5%

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

      1. *-commutative 79.5%

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

   10. Simplified 79.5%

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

   if -1.62000000000000009e-112 < z < -1.55e-145 or 1.84999999999999992e-176 < z < 4.2e14

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 62.0%

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

      1. sub-neg 62.0%

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

      2. distribute-rgt-in 62.1%

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

      3. metadata-eval 62.1%

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

      4. metadata-eval 62.1%

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

      5. distribute-lft-neg-in 62.1%

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

      6. associate-+r+ 62.1%

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

      7. metadata-eval 62.1%

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

      8. metadata-eval 62.1%

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

      9. distribute-rgt-neg-in 62.1%

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

      10. metadata-eval 62.1%

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

   7. Simplified 62.1%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0115:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-98}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-112}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-281}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -0.066:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-96}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -0.066)
     t_0
     (if (<= z -4.2e-52)
       (* y 4.0)
       (if (<= z -1e-96)
         (* x -3.0)
         (if (<= z -2.2e-107)
           (* y 4.0)
           (if (<= z -2.3e-145)
             (* x -3.0)
             (if (<= z -6.3e-280)
               (* y 4.0)
               (if (<= z 2.5e-287)
                 (* x -3.0)
                 (if (<= z 3.1e-176)
                   (* y 4.0)
                   (if (<= z 0.55) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -0.066) {
		tmp = t_0;
	} else if (z <= -4.2e-52) {
		tmp = y * 4.0;
	} else if (z <= -1e-96) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-107) {
		tmp = y * 4.0;
	} else if (z <= -2.3e-145) {
		tmp = x * -3.0;
	} else if (z <= -6.3e-280) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-287) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-176) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		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) * (z * y)
    if (z <= (-0.066d0)) then
        tmp = t_0
    else if (z <= (-4.2d-52)) then
        tmp = y * 4.0d0
    else if (z <= (-1d-96)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.2d-107)) then
        tmp = y * 4.0d0
    else if (z <= (-2.3d-145)) then
        tmp = x * (-3.0d0)
    else if (z <= (-6.3d-280)) then
        tmp = y * 4.0d0
    else if (z <= 2.5d-287) then
        tmp = x * (-3.0d0)
    else if (z <= 3.1d-176) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) 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 * (z * y);
	double tmp;
	if (z <= -0.066) {
		tmp = t_0;
	} else if (z <= -4.2e-52) {
		tmp = y * 4.0;
	} else if (z <= -1e-96) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-107) {
		tmp = y * 4.0;
	} else if (z <= -2.3e-145) {
		tmp = x * -3.0;
	} else if (z <= -6.3e-280) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-287) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-176) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -0.066:
		tmp = t_0
	elif z <= -4.2e-52:
		tmp = y * 4.0
	elif z <= -1e-96:
		tmp = x * -3.0
	elif z <= -2.2e-107:
		tmp = y * 4.0
	elif z <= -2.3e-145:
		tmp = x * -3.0
	elif z <= -6.3e-280:
		tmp = y * 4.0
	elif z <= 2.5e-287:
		tmp = x * -3.0
	elif z <= 3.1e-176:
		tmp = y * 4.0
	elif z <= 0.55:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -0.066)
		tmp = t_0;
	elseif (z <= -4.2e-52)
		tmp = Float64(y * 4.0);
	elseif (z <= -1e-96)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.2e-107)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.3e-145)
		tmp = Float64(x * -3.0);
	elseif (z <= -6.3e-280)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.5e-287)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.1e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -0.066)
		tmp = t_0;
	elseif (z <= -4.2e-52)
		tmp = y * 4.0;
	elseif (z <= -1e-96)
		tmp = x * -3.0;
	elseif (z <= -2.2e-107)
		tmp = y * 4.0;
	elseif (z <= -2.3e-145)
		tmp = x * -3.0;
	elseif (z <= -6.3e-280)
		tmp = y * 4.0;
	elseif (z <= 2.5e-287)
		tmp = x * -3.0;
	elseif (z <= 3.1e-176)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.066], t$95$0, If[LessEqual[z, -4.2e-52], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1e-96], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.2e-107], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.3e-145], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -6.3e-280], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.5e-287], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.1e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.066000000000000003 or 0.55000000000000004 < z

   1. Initial program 99.8%

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

      1. +-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* 99.0%

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

      3. fma-def 99.0%

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

      4. sub-neg 99.0%

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

      5. distribute-rgt-in 99.0%

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

      6. metadata-eval 99.0%

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

      7. metadata-eval 99.0%

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

      8. distribute-lft-neg-out 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around inf 43.9%

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

   6. Taylor expanded in z around inf 43.9%

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

   if -0.066000000000000003 < z < -4.1999999999999997e-52 or -9.9999999999999991e-97 < z < -2.20000000000000012e-107 or -2.30000000000000007e-145 < z < -6.2999999999999998e-280 or 2.50000000000000013e-287 < z < 3.09999999999999992e-176

   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 68.2%

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

   6. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   if -4.1999999999999997e-52 < z < -9.9999999999999991e-97 or -2.20000000000000012e-107 < z < -2.30000000000000007e-145 or -6.2999999999999998e-280 < z < 2.50000000000000013e-287 or 3.09999999999999992e-176 < z < 0.55000000000000004

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 65.8%

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

      1. sub-neg 65.8%

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

      2. distribute-rgt-in 65.8%

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

      3. metadata-eval 65.8%

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

      4. metadata-eval 65.8%

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

      5. distribute-lft-neg-in 65.8%

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

      6. associate-+r+ 65.8%

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

      7. metadata-eval 65.8%

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

      8. metadata-eval 65.8%

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

      9. distribute-rgt-neg-in 65.8%

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

      10. metadata-eval 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in z around 0 64.6%

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

      1. *-commutative 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.066:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-52}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-96}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-280}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+76} \lor \neg \left(y \leq 5.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.02e+76) (not (<= y 5.2e-18)))
   (* y (+ 4.0 (* -6.0 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e+76) || !(y <= 5.2e-18)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.02d+76)) .or. (.not. (y <= 5.2d-18))) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e+76) || !(y <= 5.2e-18)) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.02e+76) or not (y <= 5.2e-18):
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.02e+76) || !(y <= 5.2e-18))
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.02e+76) || ~((y <= 5.2e-18)))
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.02e+76], N[Not[LessEqual[y, 5.2e-18]], $MachinePrecision]], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000007e76 or 5.2000000000000001e-18 < 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 79.4%

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

   if -1.02000000000000007e76 < y < 5.2000000000000001e-18

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 75.1%

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

      1. sub-neg 75.1%

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

      2. distribute-rgt-in 75.1%

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

      3. metadata-eval 75.1%

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

      4. metadata-eval 75.1%

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

      5. distribute-lft-neg-in 75.1%

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

      6. associate-+r+ 75.1%

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

      7. metadata-eval 75.1%

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

      8. metadata-eval 75.1%

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

      9. distribute-rgt-neg-in 75.1%

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

      10. metadata-eval 75.1%

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

   7. Simplified 75.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+76} \lor \neg \left(y \leq 5.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.57:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.57)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.52) (+ x (* (- y x) 4.0)) (* (- y x) (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.57) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = (y - x) * (-6.0 * 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 <= (-0.57d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.52d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (y - x) * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.57) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = (y - x) * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.57:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.52:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = (y - x) * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.57)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.52)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(Float64(y - x) * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.57)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.52)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = (y - x) * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.57], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.569999999999999951

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.0%

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

   if -0.569999999999999951 < z < 0.52000000000000002

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 97.3%

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

   if 0.52000000000000002 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 96.8%

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

      1. associate-*r* 96.9%

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

      2. *-commutative 96.9%

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

   8. Simplified 96.9%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.57:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(-6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.5% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.65) (+ (* y 4.0) (* x -3.0)) (* (- y x) (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.65) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = (y - x) * (-6.0 * 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 <= (-0.58d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.65d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (y - x) * ((-6.0d0) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.65) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = (y - x) * (-6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.65:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = (y - x) * (-6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.65)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(Float64(y - x) * Float64(-6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.65)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = (y - x) * (-6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in z around inf 99.0%

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

   if -0.57999999999999996 < z < 0.650000000000000022

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 96.8%

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

   6. Taylor expanded in x around 0 97.3%

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

   if 0.650000000000000022 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 96.8%

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

      1. associate-*r* 96.9%

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

      2. *-commutative 96.9%

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

   8. Simplified 96.9%

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

4. Final simplification 97.7%

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

Alternative 10: 37.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+79} \lor \neg \left(y \leq 1.4 \cdot 10^{-102}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+79) (not (<= y 1.4e-102))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+79) || !(y <= 1.4e-102)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3d+79)) .or. (.not. (y <= 1.4d-102))) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+79) || !(y <= 1.4e-102)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+79) or not (y <= 1.4e-102):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+79) || !(y <= 1.4e-102))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e+79) || ~((y <= 1.4e-102)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+79], N[Not[LessEqual[y, 1.4e-102]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999974e79 or 1.40000000000000006e-102 < 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 99.9%

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

      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 72.8%

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

   6. Taylor expanded in z around 0 38.7%

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

      1. *-commutative 38.7%

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

   8. Simplified 38.7%

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

   if -2.99999999999999974e79 < y < 1.40000000000000006e-102

   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 77.6%

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

      1. sub-neg 77.6%

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

      2. distribute-rgt-in 77.7%

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

      3. metadata-eval 77.7%

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

      4. metadata-eval 77.7%

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

      5. distribute-lft-neg-in 77.7%

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

      6. associate-+r+ 77.7%

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

      7. metadata-eval 77.7%

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

      8. metadata-eval 77.7%

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

      9. distribute-rgt-neg-in 77.7%

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

      10. metadata-eval 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around 0 37.0%

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

      1. *-commutative 37.0%

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

   10. Simplified 37.0%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+79} \lor \neg \left(y \leq 1.4 \cdot 10^{-102}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 12: 26.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 55.2%

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

   1. sub-neg 55.2%

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

   2. distribute-rgt-in 55.2%

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

   3. metadata-eval 55.2%

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

   4. metadata-eval 55.2%

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

   5. distribute-lft-neg-in 55.2%

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

   6. associate-+r+ 55.2%

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

   7. metadata-eval 55.2%

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

   8. metadata-eval 55.2%

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

   9. distribute-rgt-neg-in 55.2%

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

   10. metadata-eval 55.2%

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

7. Simplified 55.2%

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

8. Taylor expanded in z around 0 25.0%

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

   1. *-commutative 25.0%

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

10. Simplified 25.0%

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

11. Final simplification 25.0%

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

Alternative 13: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around inf 52.5%

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

6. Taylor expanded in z around 0 2.7%

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

7. Final simplification 2.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(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))))