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

Percentage Accurate: 99.5% → 99.8%

Time: 10.3s

Alternatives: 13

Speedup: 1.2×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. +-commutative 99.3%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 51.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+236}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-159}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-198}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1.06e+236)
     t_0
     (if (<= z -7.2e+68)
       t_1
       (if (<= z -0.072)
         t_0
         (if (<= z -3e-127)
           (* y 4.0)
           (if (<= z -1.2e-159)
             (* x -3.0)
             (if (<= z 1.22e-253)
               (* y 4.0)
               (if (<= z 9.6e-198)
                 (* x -3.0)
                 (if (<= z 0.5) (* y 4.0) t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.06e+236) {
		tmp = t_0;
	} else if (z <= -7.2e+68) {
		tmp = t_1;
	} else if (z <= -0.072) {
		tmp = t_0;
	} else if (z <= -3e-127) {
		tmp = y * 4.0;
	} else if (z <= -1.2e-159) {
		tmp = x * -3.0;
	} else if (z <= 1.22e-253) {
		tmp = y * 4.0;
	} else if (z <= 9.6e-198) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1.06d+236)) then
        tmp = t_0
    else if (z <= (-7.2d+68)) then
        tmp = t_1
    else if (z <= (-0.072d0)) then
        tmp = t_0
    else if (z <= (-3d-127)) then
        tmp = y * 4.0d0
    else if (z <= (-1.2d-159)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.22d-253) then
        tmp = y * 4.0d0
    else if (z <= 9.6d-198) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.06e+236) {
		tmp = t_0;
	} else if (z <= -7.2e+68) {
		tmp = t_1;
	} else if (z <= -0.072) {
		tmp = t_0;
	} else if (z <= -3e-127) {
		tmp = y * 4.0;
	} else if (z <= -1.2e-159) {
		tmp = x * -3.0;
	} else if (z <= 1.22e-253) {
		tmp = y * 4.0;
	} else if (z <= 9.6e-198) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.06e+236:
		tmp = t_0
	elif z <= -7.2e+68:
		tmp = t_1
	elif z <= -0.072:
		tmp = t_0
	elif z <= -3e-127:
		tmp = y * 4.0
	elif z <= -1.2e-159:
		tmp = x * -3.0
	elif z <= 1.22e-253:
		tmp = y * 4.0
	elif z <= 9.6e-198:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.06e+236)
		tmp = t_0;
	elseif (z <= -7.2e+68)
		tmp = t_1;
	elseif (z <= -0.072)
		tmp = t_0;
	elseif (z <= -3e-127)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.2e-159)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.22e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.6e-198)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.06e+236)
		tmp = t_0;
	elseif (z <= -7.2e+68)
		tmp = t_1;
	elseif (z <= -0.072)
		tmp = t_0;
	elseif (z <= -3e-127)
		tmp = y * 4.0;
	elseif (z <= -1.2e-159)
		tmp = x * -3.0;
	elseif (z <= 1.22e-253)
		tmp = y * 4.0;
	elseif (z <= 9.6e-198)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.06e+236], t$95$0, If[LessEqual[z, -7.2e+68], t$95$1, If[LessEqual[z, -0.072], t$95$0, If[LessEqual[z, -3e-127], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.2e-159], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.22e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.6e-198], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05999999999999991e236 or -7.1999999999999998e68 < z < -0.0719999999999999946

   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* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 69.8%

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

   6. Taylor expanded in z around inf 65.1%

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

   if -1.05999999999999991e236 < z < -7.1999999999999998e68 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 58.2%

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

      1. +-commutative 58.2%

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

      2. sub-neg 58.2%

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

      3. distribute-rgt-in 58.2%

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

      4. metadata-eval 58.2%

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

      5. distribute-lft-neg-in 58.2%

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

      6. metadata-eval 58.2%

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

      7. neg-mul-1 58.2%

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

      8. distribute-lft-in 58.2%

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

      9. *-commutative 58.2%

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

      10. +-commutative 58.2%

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

      11. mul-1-neg 58.2%

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

      12. *-commutative 58.2%

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

      13. distribute-neg-in 58.2%

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

      14. metadata-eval 58.2%

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

      15. associate-+r+ 58.2%

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

      16. metadata-eval 58.2%

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

      17. distribute-rgt-neg-in 58.2%

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

      18. metadata-eval 58.2%

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

   7. Simplified 58.2%

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

   8. Taylor expanded in z around inf 56.7%

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

   if -0.0719999999999999946 < z < -3.00000000000000009e-127 or -1.19999999999999999e-159 < z < 1.22e-253 or 9.59999999999999946e-198 < z < 0.5

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      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-define 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 63.3%

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

   6. Taylor expanded in z around 0 61.5%

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

   if -3.00000000000000009e-127 < z < -1.19999999999999999e-159 or 1.22e-253 < z < 9.59999999999999946e-198

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. sub-neg 85.4%

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

      3. distribute-rgt-in 85.4%

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

      4. metadata-eval 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. neg-mul-1 85.4%

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

      8. distribute-lft-in 85.4%

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

      9. *-commutative 85.4%

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

      10. +-commutative 85.4%

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

      11. mul-1-neg 85.4%

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

      12. *-commutative 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. metadata-eval 85.4%

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

      15. associate-+r+ 85.4%

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

      16. metadata-eval 85.4%

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

      17. distribute-rgt-neg-in 85.4%

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

      18. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

   10. Simplified 85.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+236}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+68}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-159}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-198}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-124}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-193}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -1.26e+237)
     t_0
     (if (<= z -9.5e+65)
       t_1
       (if (<= z -0.072)
         t_0
         (if (<= z -6.2e-124)
           (* y 4.0)
           (if (<= z -8.2e-151)
             (* x -3.0)
             (if (<= z 2.65e-253)
               (* y 4.0)
               (if (<= z 3.3e-193)
                 (* x -3.0)
                 (if (<= z 0.62) (* y 4.0) t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.26e+237) {
		tmp = t_0;
	} else if (z <= -9.5e+65) {
		tmp = t_1;
	} else if (z <= -0.072) {
		tmp = t_0;
	} else if (z <= -6.2e-124) {
		tmp = y * 4.0;
	} else if (z <= -8.2e-151) {
		tmp = x * -3.0;
	} else if (z <= 2.65e-253) {
		tmp = y * 4.0;
	} else if (z <= 3.3e-193) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = x * (z * 6.0d0)
    if (z <= (-1.26d+237)) then
        tmp = t_0
    else if (z <= (-9.5d+65)) then
        tmp = t_1
    else if (z <= (-0.072d0)) then
        tmp = t_0
    else if (z <= (-6.2d-124)) then
        tmp = y * 4.0d0
    else if (z <= (-8.2d-151)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.65d-253) then
        tmp = y * 4.0d0
    else if (z <= 3.3d-193) then
        tmp = x * (-3.0d0)
    else if (z <= 0.62d0) then
        tmp = y * 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.26e+237) {
		tmp = t_0;
	} else if (z <= -9.5e+65) {
		tmp = t_1;
	} else if (z <= -0.072) {
		tmp = t_0;
	} else if (z <= -6.2e-124) {
		tmp = y * 4.0;
	} else if (z <= -8.2e-151) {
		tmp = x * -3.0;
	} else if (z <= 2.65e-253) {
		tmp = y * 4.0;
	} else if (z <= 3.3e-193) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -1.26e+237:
		tmp = t_0
	elif z <= -9.5e+65:
		tmp = t_1
	elif z <= -0.072:
		tmp = t_0
	elif z <= -6.2e-124:
		tmp = y * 4.0
	elif z <= -8.2e-151:
		tmp = x * -3.0
	elif z <= 2.65e-253:
		tmp = y * 4.0
	elif z <= 3.3e-193:
		tmp = x * -3.0
	elif z <= 0.62:
		tmp = y * 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -1.26e+237)
		tmp = t_0;
	elseif (z <= -9.5e+65)
		tmp = t_1;
	elseif (z <= -0.072)
		tmp = t_0;
	elseif (z <= -6.2e-124)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.2e-151)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.65e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.3e-193)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.62)
		tmp = Float64(y * 4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -1.26e+237)
		tmp = t_0;
	elseif (z <= -9.5e+65)
		tmp = t_1;
	elseif (z <= -0.072)
		tmp = t_0;
	elseif (z <= -6.2e-124)
		tmp = y * 4.0;
	elseif (z <= -8.2e-151)
		tmp = x * -3.0;
	elseif (z <= 2.65e-253)
		tmp = y * 4.0;
	elseif (z <= 3.3e-193)
		tmp = x * -3.0;
	elseif (z <= 0.62)
		tmp = y * 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+237], t$95$0, If[LessEqual[z, -9.5e+65], t$95$1, If[LessEqual[z, -0.072], t$95$0, If[LessEqual[z, -6.2e-124], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.2e-151], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.65e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.3e-193], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(y * 4.0), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2599999999999999e237 or -9.5000000000000005e65 < z < -0.0719999999999999946

   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* 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. distribute-rgt-in 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 71.0%

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

   6. Taylor expanded in z around inf 66.0%

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

   if -1.2599999999999999e237 < z < -9.5000000000000005e65 or 0.619999999999999996 < 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 58.1%

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

      1. +-commutative 58.1%

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

      2. sub-neg 58.1%

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

      3. distribute-rgt-in 58.1%

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

      4. metadata-eval 58.1%

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

      5. distribute-lft-neg-in 58.1%

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

      6. metadata-eval 58.1%

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

      7. neg-mul-1 58.1%

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

      8. distribute-lft-in 58.1%

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

      9. *-commutative 58.1%

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

      10. +-commutative 58.1%

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

      11. mul-1-neg 58.1%

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

      12. *-commutative 58.1%

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

      13. distribute-neg-in 58.1%

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

      14. metadata-eval 58.1%

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

      15. associate-+r+ 58.1%

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

      16. metadata-eval 58.1%

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

      17. distribute-rgt-neg-in 58.1%

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

      18. metadata-eval 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in z around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-*r* 56.7%

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

   10. Simplified 56.7%

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

   if -0.0719999999999999946 < z < -6.1999999999999996e-124 or -8.2000000000000002e-151 < z < 2.6500000000000001e-253 or 3.2999999999999999e-193 < z < 0.619999999999999996

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      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-define 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 63.3%

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

   6. Taylor expanded in z around 0 61.5%

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

   if -6.1999999999999996e-124 < z < -8.2000000000000002e-151 or 2.6500000000000001e-253 < z < 3.2999999999999999e-193

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. sub-neg 85.4%

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

      3. distribute-rgt-in 85.4%

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

      4. metadata-eval 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. neg-mul-1 85.4%

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

      8. distribute-lft-in 85.4%

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

      9. *-commutative 85.4%

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

      10. +-commutative 85.4%

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

      11. mul-1-neg 85.4%

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

      12. *-commutative 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. metadata-eval 85.4%

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

      15. associate-+r+ 85.4%

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

      16. metadata-eval 85.4%

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

      17. distribute-rgt-neg-in 85.4%

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

      18. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

   10. Simplified 85.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+237}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-124}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-193}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+228}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-157}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-197}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -6.5e+228)
     (* -6.0 (* y z))
     (if (<= z -4.1e+73)
       t_0
       (if (<= z -0.072)
         (* y (* z -6.0))
         (if (<= z -3.9e-127)
           (* y 4.0)
           (if (<= z -2.75e-157)
             (* x -3.0)
             (if (<= z 2.5e-253)
               (* y 4.0)
               (if (<= z 1.75e-197)
                 (* x -3.0)
                 (if (<= z 0.5) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -6.5e+228) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.1e+73) {
		tmp = t_0;
	} else if (z <= -0.072) {
		tmp = y * (z * -6.0);
	} else if (z <= -3.9e-127) {
		tmp = y * 4.0;
	} else if (z <= -2.75e-157) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-253) {
		tmp = y * 4.0;
	} else if (z <= 1.75e-197) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-6.5d+228)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-4.1d+73)) then
        tmp = t_0
    else if (z <= (-0.072d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-3.9d-127)) then
        tmp = y * 4.0d0
    else if (z <= (-2.75d-157)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-253) then
        tmp = y * 4.0d0
    else if (z <= 1.75d-197) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -6.5e+228) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.1e+73) {
		tmp = t_0;
	} else if (z <= -0.072) {
		tmp = y * (z * -6.0);
	} else if (z <= -3.9e-127) {
		tmp = y * 4.0;
	} else if (z <= -2.75e-157) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-253) {
		tmp = y * 4.0;
	} else if (z <= 1.75e-197) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -6.5e+228:
		tmp = -6.0 * (y * z)
	elif z <= -4.1e+73:
		tmp = t_0
	elif z <= -0.072:
		tmp = y * (z * -6.0)
	elif z <= -3.9e-127:
		tmp = y * 4.0
	elif z <= -2.75e-157:
		tmp = x * -3.0
	elif z <= 2.5e-253:
		tmp = y * 4.0
	elif z <= 1.75e-197:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	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 <= -6.5e+228)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -4.1e+73)
		tmp = t_0;
	elseif (z <= -0.072)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -3.9e-127)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.75e-157)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.75e-197)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	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 <= -6.5e+228)
		tmp = -6.0 * (y * z);
	elseif (z <= -4.1e+73)
		tmp = t_0;
	elseif (z <= -0.072)
		tmp = y * (z * -6.0);
	elseif (z <= -3.9e-127)
		tmp = y * 4.0;
	elseif (z <= -2.75e-157)
		tmp = x * -3.0;
	elseif (z <= 2.5e-253)
		tmp = y * 4.0;
	elseif (z <= 1.75e-197)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	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, -6.5e+228], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e+73], t$95$0, If[LessEqual[z, -0.072], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-127], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.75e-157], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.75e-197], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5e228

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 75.4%

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

   6. Taylor expanded in z around inf 75.4%

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

   if -6.5e228 < z < -4.0999999999999998e73 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 58.2%

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

      1. +-commutative 58.2%

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

      2. sub-neg 58.2%

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

      3. distribute-rgt-in 58.2%

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

      4. metadata-eval 58.2%

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

      5. distribute-lft-neg-in 58.2%

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

      6. metadata-eval 58.2%

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

      7. neg-mul-1 58.2%

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

      8. distribute-lft-in 58.2%

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

      9. *-commutative 58.2%

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

      10. +-commutative 58.2%

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

      11. mul-1-neg 58.2%

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

      12. *-commutative 58.2%

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

      13. distribute-neg-in 58.2%

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

      14. metadata-eval 58.2%

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

      15. associate-+r+ 58.2%

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

      16. metadata-eval 58.2%

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

      17. distribute-rgt-neg-in 58.2%

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

      18. metadata-eval 58.2%

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

   7. Simplified 58.2%

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

   8. Taylor expanded in z around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-*r* 56.8%

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

   10. Simplified 56.8%

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

   if -4.0999999999999998e73 < z < -0.0719999999999999946

   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* 99.4%

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

      3. fma-define 99.4%

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

      4. sub-neg 99.4%

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

      5. distribute-rgt-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-neg-out 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 64.9%

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

   6. Taylor expanded in z around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*r* 56.1%

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

      3. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   if -0.0719999999999999946 < z < -3.89999999999999966e-127 or -2.7499999999999999e-157 < z < 2.49999999999999986e-253 or 1.7499999999999999e-197 < z < 0.5

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      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-define 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 63.3%

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

   6. Taylor expanded in z around 0 61.5%

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

   if -3.89999999999999966e-127 < z < -2.7499999999999999e-157 or 2.49999999999999986e-253 < z < 1.7499999999999999e-197

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. sub-neg 85.4%

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

      3. distribute-rgt-in 85.4%

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

      4. metadata-eval 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. neg-mul-1 85.4%

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

      8. distribute-lft-in 85.4%

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

      9. *-commutative 85.4%

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

      10. +-commutative 85.4%

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

      11. mul-1-neg 85.4%

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

      12. *-commutative 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. metadata-eval 85.4%

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

      15. associate-+r+ 85.4%

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

      16. metadata-eval 85.4%

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

      17. distribute-rgt-neg-in 85.4%

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

      18. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

   10. Simplified 85.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+228}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-127}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-157}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-197}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+228}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-123}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-196}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.12e+228)
   (* -6.0 (* y z))
   (if (<= z -4.9e+71)
     (* x (* z 6.0))
     (if (<= z -0.072)
       (* y (* z -6.0))
       (if (<= z -1.7e-123)
         (* y 4.0)
         (if (<= z -2.95e-151)
           (* x -3.0)
           (if (<= z 2.7e-253)
             (* y 4.0)
             (if (<= z 5.6e-196)
               (* x -3.0)
               (if (<= z 0.65) (* y 4.0) (* z (* x 6.0)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.12e+228) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.9e+71) {
		tmp = x * (z * 6.0);
	} else if (z <= -0.072) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.7e-123) {
		tmp = y * 4.0;
	} else if (z <= -2.95e-151) {
		tmp = x * -3.0;
	} else if (z <= 2.7e-253) {
		tmp = y * 4.0;
	} else if (z <= 5.6e-196) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.12d+228)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-4.9d+71)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-0.072d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1.7d-123)) then
        tmp = y * 4.0d0
    else if (z <= (-2.95d-151)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.7d-253) then
        tmp = y * 4.0d0
    else if (z <= 5.6d-196) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = z * (x * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.12e+228) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.9e+71) {
		tmp = x * (z * 6.0);
	} else if (z <= -0.072) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.7e-123) {
		tmp = y * 4.0;
	} else if (z <= -2.95e-151) {
		tmp = x * -3.0;
	} else if (z <= 2.7e-253) {
		tmp = y * 4.0;
	} else if (z <= 5.6e-196) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.12e+228:
		tmp = -6.0 * (y * z)
	elif z <= -4.9e+71:
		tmp = x * (z * 6.0)
	elif z <= -0.072:
		tmp = y * (z * -6.0)
	elif z <= -1.7e-123:
		tmp = y * 4.0
	elif z <= -2.95e-151:
		tmp = x * -3.0
	elif z <= 2.7e-253:
		tmp = y * 4.0
	elif z <= 5.6e-196:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.12e+228)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -4.9e+71)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -0.072)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1.7e-123)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.95e-151)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.7e-253)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.6e-196)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(z * Float64(x * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.12e+228)
		tmp = -6.0 * (y * z);
	elseif (z <= -4.9e+71)
		tmp = x * (z * 6.0);
	elseif (z <= -0.072)
		tmp = y * (z * -6.0);
	elseif (z <= -1.7e-123)
		tmp = y * 4.0;
	elseif (z <= -2.95e-151)
		tmp = x * -3.0;
	elseif (z <= 2.7e-253)
		tmp = y * 4.0;
	elseif (z <= 5.6e-196)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.12e+228], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e+71], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.072], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-123], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.95e-151], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.7e-253], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.6e-196], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.11999999999999994e228

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 75.4%

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

   6. Taylor expanded in z around inf 75.4%

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

   if -1.11999999999999994e228 < z < -4.8999999999999997e71

   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 63.8%

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

      1. +-commutative 63.8%

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

      2. sub-neg 63.8%

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

      3. distribute-rgt-in 63.8%

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

      4. metadata-eval 63.8%

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

      5. distribute-lft-neg-in 63.8%

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

      6. metadata-eval 63.8%

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

      7. neg-mul-1 63.8%

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

      8. distribute-lft-in 63.8%

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

      9. *-commutative 63.8%

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

      10. +-commutative 63.8%

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

      11. mul-1-neg 63.8%

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

      12. *-commutative 63.8%

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

      13. distribute-neg-in 63.8%

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

      14. metadata-eval 63.8%

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

      15. associate-+r+ 63.8%

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

      16. metadata-eval 63.8%

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

      17. distribute-rgt-neg-in 63.8%

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

      18. metadata-eval 63.8%

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

   7. Simplified 63.8%

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

   8. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. associate-*r* 63.8%

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

   10. Simplified 63.8%

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

   if -4.8999999999999997e71 < z < -0.0719999999999999946

   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* 99.4%

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

      3. fma-define 99.4%

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

      4. sub-neg 99.4%

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

      5. distribute-rgt-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-neg-out 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 64.9%

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

   6. Taylor expanded in z around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*r* 56.1%

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

      3. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   if -0.0719999999999999946 < z < -1.7e-123 or -2.95e-151 < z < 2.69999999999999999e-253 or 5.5999999999999997e-196 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      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-define 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 63.3%

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

   6. Taylor expanded in z around 0 61.5%

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

   if -1.7e-123 < z < -2.95e-151 or 2.69999999999999999e-253 < z < 5.5999999999999997e-196

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. sub-neg 85.4%

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

      3. distribute-rgt-in 85.4%

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

      4. metadata-eval 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. neg-mul-1 85.4%

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

      8. distribute-lft-in 85.4%

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

      9. *-commutative 85.4%

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

      10. +-commutative 85.4%

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

      11. mul-1-neg 85.4%

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

      12. *-commutative 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. metadata-eval 85.4%

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

      15. associate-+r+ 85.4%

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

      16. metadata-eval 85.4%

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

      17. distribute-rgt-neg-in 85.4%

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

      18. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

   10. Simplified 85.4%

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

   if 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 56.1%

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

      1. +-commutative 56.1%

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

      2. sub-neg 56.1%

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

      3. distribute-rgt-in 56.1%

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

      4. metadata-eval 56.1%

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

      5. distribute-lft-neg-in 56.1%

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

      6. metadata-eval 56.1%

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

      7. neg-mul-1 56.1%

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

      8. distribute-lft-in 56.1%

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

      9. *-commutative 56.1%

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

      10. +-commutative 56.1%

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

      11. mul-1-neg 56.1%

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

      12. *-commutative 56.1%

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

      13. distribute-neg-in 56.1%

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

      14. metadata-eval 56.1%

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

      15. associate-+r+ 56.1%

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

      16. metadata-eval 56.1%

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

      17. distribute-rgt-neg-in 56.1%

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

      18. metadata-eval 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in z around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-*r* 54.1%

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

   10. Simplified 54.1%

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

   11. Taylor expanded in x around 0 54.1%

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

       1. associate-*r* 54.1%

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

       2. *-commutative 54.1%

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

   13. Simplified 54.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+228}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.072:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-123}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-151}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-253}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-196}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.04:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-254}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-197}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.04)
     t_0
     (if (<= z -7.5e-128)
       (* y 4.0)
       (if (<= z -1.52e-161)
         (* x -3.0)
         (if (<= z 9.8e-254)
           (* y 4.0)
           (if (<= z 2.95e-197) (* x -3.0) (if (<= z 0.5) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.04) {
		tmp = t_0;
	} else if (z <= -7.5e-128) {
		tmp = y * 4.0;
	} else if (z <= -1.52e-161) {
		tmp = x * -3.0;
	} else if (z <= 9.8e-254) {
		tmp = y * 4.0;
	} else if (z <= 2.95e-197) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.04d0)) then
        tmp = t_0
    else if (z <= (-7.5d-128)) then
        tmp = y * 4.0d0
    else if (z <= (-1.52d-161)) then
        tmp = x * (-3.0d0)
    else if (z <= 9.8d-254) then
        tmp = y * 4.0d0
    else if (z <= 2.95d-197) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.04) {
		tmp = t_0;
	} else if (z <= -7.5e-128) {
		tmp = y * 4.0;
	} else if (z <= -1.52e-161) {
		tmp = x * -3.0;
	} else if (z <= 9.8e-254) {
		tmp = y * 4.0;
	} else if (z <= 2.95e-197) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.04:
		tmp = t_0
	elif z <= -7.5e-128:
		tmp = y * 4.0
	elif z <= -1.52e-161:
		tmp = x * -3.0
	elif z <= 9.8e-254:
		tmp = y * 4.0
	elif z <= 2.95e-197:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.04)
		tmp = t_0;
	elseif (z <= -7.5e-128)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.52e-161)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.8e-254)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.95e-197)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.04)
		tmp = t_0;
	elseif (z <= -7.5e-128)
		tmp = y * 4.0;
	elseif (z <= -1.52e-161)
		tmp = x * -3.0;
	elseif (z <= 9.8e-254)
		tmp = y * 4.0;
	elseif (z <= 2.95e-197)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.04], t$95$0, If[LessEqual[z, -7.5e-128], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.52e-161], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.8e-254], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.95e-197], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0400000000000000008 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 inf 96.3%

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

   6. Taylor expanded in z around inf 96.4%

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

   if -0.0400000000000000008 < z < -7.50000000000000021e-128 or -1.52000000000000002e-161 < z < 9.79999999999999959e-254 or 2.95000000000000024e-197 < z < 0.5

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      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-define 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 63.3%

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

   6. Taylor expanded in z around 0 61.5%

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

   if -7.50000000000000021e-128 < z < -1.52000000000000002e-161 or 9.79999999999999959e-254 < z < 2.95000000000000024e-197

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. sub-neg 85.4%

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

      3. distribute-rgt-in 85.4%

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

      4. metadata-eval 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. neg-mul-1 85.4%

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

      8. distribute-lft-in 85.4%

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

      9. *-commutative 85.4%

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

      10. +-commutative 85.4%

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

      11. mul-1-neg 85.4%

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

      12. *-commutative 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. metadata-eval 85.4%

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

      15. associate-+r+ 85.4%

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

      16. metadata-eval 85.4%

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

      17. distribute-rgt-neg-in 85.4%

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

      18. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

   10. Simplified 85.4%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.04:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-128}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-161}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-254}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-197}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.072:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-154}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-254}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 42000:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.072)
     t_0
     (if (<= z -2e-126)
       (* y 4.0)
       (if (<= z -8.8e-154)
         (* x -3.0)
         (if (<= z 1.75e-254)
           (* y 4.0)
           (if (<= z 2.5e-197)
             (* x -3.0)
             (if (<= z 42000.0) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.072) {
		tmp = t_0;
	} else if (z <= -2e-126) {
		tmp = y * 4.0;
	} else if (z <= -8.8e-154) {
		tmp = x * -3.0;
	} else if (z <= 1.75e-254) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-197) {
		tmp = x * -3.0;
	} else if (z <= 42000.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.072d0)) then
        tmp = t_0
    else if (z <= (-2d-126)) then
        tmp = y * 4.0d0
    else if (z <= (-8.8d-154)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.75d-254) then
        tmp = y * 4.0d0
    else if (z <= 2.5d-197) then
        tmp = x * (-3.0d0)
    else if (z <= 42000.0d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.072) {
		tmp = t_0;
	} else if (z <= -2e-126) {
		tmp = y * 4.0;
	} else if (z <= -8.8e-154) {
		tmp = x * -3.0;
	} else if (z <= 1.75e-254) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-197) {
		tmp = x * -3.0;
	} else if (z <= 42000.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.072:
		tmp = t_0
	elif z <= -2e-126:
		tmp = y * 4.0
	elif z <= -8.8e-154:
		tmp = x * -3.0
	elif z <= 1.75e-254:
		tmp = y * 4.0
	elif z <= 2.5e-197:
		tmp = x * -3.0
	elif z <= 42000.0:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.072)
		tmp = t_0;
	elseif (z <= -2e-126)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.8e-154)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.75e-254)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.5e-197)
		tmp = Float64(x * -3.0);
	elseif (z <= 42000.0)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.072)
		tmp = t_0;
	elseif (z <= -2e-126)
		tmp = y * 4.0;
	elseif (z <= -8.8e-154)
		tmp = x * -3.0;
	elseif (z <= 1.75e-254)
		tmp = y * 4.0;
	elseif (z <= 2.5e-197)
		tmp = x * -3.0;
	elseif (z <= 42000.0)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.072], t$95$0, If[LessEqual[z, -2e-126], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.8e-154], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.75e-254], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.5e-197], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 42000.0], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0719999999999999946 or 42000 < 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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 52.7%

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

   6. Taylor expanded in z around inf 51.1%

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

   if -0.0719999999999999946 < z < -1.9999999999999999e-126 or -8.80000000000000029e-154 < z < 1.75000000000000004e-254 or 2.5000000000000001e-197 < z < 42000

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      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-define 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 62.7%

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

   6. Taylor expanded in z around 0 60.9%

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

   if -1.9999999999999999e-126 < z < -8.80000000000000029e-154 or 1.75000000000000004e-254 < z < 2.5000000000000001e-197

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. sub-neg 85.4%

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

      3. distribute-rgt-in 85.4%

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

      4. metadata-eval 85.4%

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

      5. distribute-lft-neg-in 85.4%

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

      6. metadata-eval 85.4%

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

      7. neg-mul-1 85.4%

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

      8. distribute-lft-in 85.4%

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

      9. *-commutative 85.4%

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

      10. +-commutative 85.4%

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

      11. mul-1-neg 85.4%

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

      12. *-commutative 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. metadata-eval 85.4%

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

      15. associate-+r+ 85.4%

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

      16. metadata-eval 85.4%

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

      17. distribute-rgt-neg-in 85.4%

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

      18. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in z around 0 85.4%

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

      1. *-commutative 85.4%

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

   10. Simplified 85.4%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.072:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-154}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-254}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-197}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 42000:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1040000 \lor \neg \left(x \leq 1.6 \cdot 10^{+53}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1040000.0) (not (<= x 1.6e+53)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1040000.0) || !(x <= 1.6e+53)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1040000.0d0)) .or. (.not. (x <= 1.6d+53))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1040000.0) || !(x <= 1.6e+53)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1040000.0) or not (x <= 1.6e+53):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1040000.0) || !(x <= 1.6e+53))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1040000.0) || ~((x <= 1.6e+53)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1040000.0], N[Not[LessEqual[x, 1.6e+53]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04e6 or 1.6e53 < x

   1. Initial program 98.9%

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

      1. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around inf 84.0%

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

      1. +-commutative 84.0%

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

      2. sub-neg 84.0%

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

      3. distribute-rgt-in 84.0%

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

      4. metadata-eval 84.0%

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

      5. distribute-lft-neg-in 84.0%

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

      6. metadata-eval 84.0%

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

      7. neg-mul-1 84.0%

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

      8. distribute-lft-in 84.0%

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

      9. *-commutative 84.0%

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

      10. +-commutative 84.0%

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

      11. mul-1-neg 84.0%

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

      12. *-commutative 84.0%

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

      13. distribute-neg-in 84.0%

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

      14. metadata-eval 84.0%

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

      15. associate-+r+ 84.0%

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

      16. metadata-eval 84.0%

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

      17. distribute-rgt-neg-in 84.0%

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

      18. metadata-eval 84.0%

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

   7. Simplified 84.0%

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

   if -1.04e6 < x < 1.6e53

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 81.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1040000 \lor \neg \left(x \leq 1.6 \cdot 10^{+53}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.9%

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

   6. Taylor expanded in z around inf 96.9%

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

      1. associate-*r* 97.1%

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

   8. Simplified 97.1%

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

   if -0.599999999999999978 < z < 0.5

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 97.1%

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

   if 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 97.0%

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

   6. Taylor expanded in z around inf 97.0%

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

4. Final simplification 97.1%

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

Alternative 10: 37.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+130} \lor \neg \left(x \leq 6.4 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.8e+130) (not (<= x 6.4e+94))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.8e+130) || !(x <= 6.4e+94)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7.8d+130)) .or. (.not. (x <= 6.4d+94))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.8e+130) || !(x <= 6.4e+94)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.8e+130) or not (x <= 6.4e+94):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.8e+130) || !(x <= 6.4e+94))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.8e+130) || ~((x <= 6.4e+94)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.8e+130], N[Not[LessEqual[x, 6.4e+94]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8000000000000004e130 or 6.40000000000000028e94 < x

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around inf 92.3%

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

      1. +-commutative 92.3%

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

      2. sub-neg 92.3%

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

      3. distribute-rgt-in 92.3%

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

      4. metadata-eval 92.3%

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

      5. distribute-lft-neg-in 92.3%

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

      6. metadata-eval 92.3%

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

      7. neg-mul-1 92.3%

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

      8. distribute-lft-in 92.3%

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

      9. *-commutative 92.3%

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

      10. +-commutative 92.3%

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

      11. mul-1-neg 92.3%

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

      12. *-commutative 92.3%

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

      13. distribute-neg-in 92.3%

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

      14. metadata-eval 92.3%

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

      15. associate-+r+ 92.3%

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

      16. metadata-eval 92.3%

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

      17. distribute-rgt-neg-in 92.3%

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

      18. metadata-eval 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in z around 0 49.8%

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

      1. *-commutative 49.8%

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

   10. Simplified 49.8%

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

   if -7.8000000000000004e130 < x < 6.40000000000000028e94

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 72.7%

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

   6. Taylor expanded in z around 0 37.1%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+130} \lor \neg \left(x \leq 6.4 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
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 99.3%

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

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

Alternative 12: 26.0% 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 99.3%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 48.1%

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

   1. +-commutative 48.1%

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

   2. sub-neg 48.1%

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

   3. distribute-rgt-in 48.1%

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

   4. metadata-eval 48.1%

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

   5. distribute-lft-neg-in 48.1%

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

   6. metadata-eval 48.1%

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

   7. neg-mul-1 48.1%

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

   8. distribute-lft-in 48.1%

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

   9. *-commutative 48.1%

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

   10. +-commutative 48.1%

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

   11. mul-1-neg 48.1%

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

   12. *-commutative 48.1%

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

   13. distribute-neg-in 48.1%

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

   14. metadata-eval 48.1%

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

   15. associate-+r+ 48.1%

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

   16. metadata-eval 48.1%

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

   17. distribute-rgt-neg-in 48.1%

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

   18. metadata-eval 48.1%

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

7. Simplified 48.1%

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

8. Taylor expanded in z around 0 22.1%

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

   1. *-commutative 22.1%

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

10. Simplified 22.1%

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

11. Final simplification 22.1%

    \[\leadsto x \cdot -3 \]
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 99.3%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 inf 51.3%

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

6. Taylor expanded in z around 0 2.8%

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

7. Final simplification 2.8%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024044 
(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))))