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

Percentage Accurate: 99.5% → 99.7%

Time: 13.1s

Alternatives: 20

Speedup: 1.2×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. sub-neg 99.8%

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

   5. +-commutative 99.8%

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

   6. distribute-lft-in 99.8%

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

   7. neg-mul-1 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   8. associate-*r* 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

   9. *-commutative 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   10. fma-def 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-265}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.42)
     t_0
     (if (<= z -1.75e-134)
       (* y 4.0)
       (if (<= z -3.4e-265)
         (* x -3.0)
         (if (<= z -1.9e-284)
           (* y 4.0)
           (if (<= z 3.2e-297)
             (* x -3.0)
             (if (<= z 2e-284)
               (* y 4.0)
               (if (<= z 4.8e-232)
                 (* x -3.0)
                 (if (<= z 9.5e-94)
                   (* y 4.0)
                   (if (<= z 0.5) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.42) {
		tmp = t_0;
	} else if (z <= -1.75e-134) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-265) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-297) {
		tmp = x * -3.0;
	} else if (z <= 2e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-232) {
		tmp = x * -3.0;
	} else if (z <= 9.5e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.42d0)) then
        tmp = t_0
    else if (z <= (-1.75d-134)) then
        tmp = y * 4.0d0
    else if (z <= (-3.4d-265)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.9d-284)) then
        tmp = y * 4.0d0
    else if (z <= 3.2d-297) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-284) then
        tmp = y * 4.0d0
    else if (z <= 4.8d-232) then
        tmp = x * (-3.0d0)
    else if (z <= 9.5d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.42) {
		tmp = t_0;
	} else if (z <= -1.75e-134) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-265) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-297) {
		tmp = x * -3.0;
	} else if (z <= 2e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.8e-232) {
		tmp = x * -3.0;
	} else if (z <= 9.5e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.42:
		tmp = t_0
	elif z <= -1.75e-134:
		tmp = y * 4.0
	elif z <= -3.4e-265:
		tmp = x * -3.0
	elif z <= -1.9e-284:
		tmp = y * 4.0
	elif z <= 3.2e-297:
		tmp = x * -3.0
	elif z <= 2e-284:
		tmp = y * 4.0
	elif z <= 4.8e-232:
		tmp = x * -3.0
	elif z <= 9.5e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.42)
		tmp = t_0;
	elseif (z <= -1.75e-134)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.4e-265)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.9e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.2e-297)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.8e-232)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.5e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.42)
		tmp = t_0;
	elseif (z <= -1.75e-134)
		tmp = y * 4.0;
	elseif (z <= -3.4e-265)
		tmp = x * -3.0;
	elseif (z <= -1.9e-284)
		tmp = y * 4.0;
	elseif (z <= 3.2e-297)
		tmp = x * -3.0;
	elseif (z <= 2e-284)
		tmp = y * 4.0;
	elseif (z <= 4.8e-232)
		tmp = x * -3.0;
	elseif (z <= 9.5e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.42], t$95$0, If[LessEqual[z, -1.75e-134], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.4e-265], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.9e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.2e-297], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.8e-232], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.5e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.419999999999999984 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.0%

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

   if -0.419999999999999984 < z < -1.7499999999999999e-134 or -3.4000000000000001e-265 < z < -1.8999999999999999e-284 or 3.19999999999999972e-297 < z < 2.00000000000000007e-284 or 4.79999999999999998e-232 < z < 9.4999999999999997e-94

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.2%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if -1.7499999999999999e-134 < z < -3.4000000000000001e-265 or -1.8999999999999999e-284 < z < 3.19999999999999972e-297 or 2.00000000000000007e-284 < z < 4.79999999999999998e-232 or 9.4999999999999997e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-265}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 4: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-134}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.95 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -150000000000.0)
     t_0
     (if (<= z -1.04e-134)
       (* 6.0 (* y (- 0.6666666666666666 z)))
       (if (<= z -3e-266)
         (* x -3.0)
         (if (<= z -1.9e-284)
           (* y 4.0)
           (if (<= z 5.5e-297)
             (* x -3.0)
             (if (<= z 4.95e-284)
               (* y 4.0)
               (if (<= z 1.65e-229)
                 (* x -3.0)
                 (if (<= z 8.6e-94)
                   (* y 4.0)
                   (if (<= z 0.5) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -150000000000.0) {
		tmp = t_0;
	} else if (z <= -1.04e-134) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -3e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-297) {
		tmp = x * -3.0;
	} else if (z <= 4.95e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.65e-229) {
		tmp = x * -3.0;
	} else if (z <= 8.6e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-150000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.04d-134)) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (z <= (-3d-266)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.9d-284)) then
        tmp = y * 4.0d0
    else if (z <= 5.5d-297) then
        tmp = x * (-3.0d0)
    else if (z <= 4.95d-284) then
        tmp = y * 4.0d0
    else if (z <= 1.65d-229) then
        tmp = x * (-3.0d0)
    else if (z <= 8.6d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -150000000000.0) {
		tmp = t_0;
	} else if (z <= -1.04e-134) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -3e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-297) {
		tmp = x * -3.0;
	} else if (z <= 4.95e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.65e-229) {
		tmp = x * -3.0;
	} else if (z <= 8.6e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -150000000000.0:
		tmp = t_0
	elif z <= -1.04e-134:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif z <= -3e-266:
		tmp = x * -3.0
	elif z <= -1.9e-284:
		tmp = y * 4.0
	elif z <= 5.5e-297:
		tmp = x * -3.0
	elif z <= 4.95e-284:
		tmp = y * 4.0
	elif z <= 1.65e-229:
		tmp = x * -3.0
	elif z <= 8.6e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -150000000000.0)
		tmp = t_0;
	elseif (z <= -1.04e-134)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (z <= -3e-266)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.9e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.5e-297)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.95e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.65e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.6e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -150000000000.0)
		tmp = t_0;
	elseif (z <= -1.04e-134)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (z <= -3e-266)
		tmp = x * -3.0;
	elseif (z <= -1.9e-284)
		tmp = y * 4.0;
	elseif (z <= 5.5e-297)
		tmp = x * -3.0;
	elseif (z <= 4.95e-284)
		tmp = y * 4.0;
	elseif (z <= 1.65e-229)
		tmp = x * -3.0;
	elseif (z <= 8.6e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -150000000000.0], t$95$0, If[LessEqual[z, -1.04e-134], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-266], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.9e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.5e-297], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.95e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.65e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.6e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e11 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.2%

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

   if -1.5e11 < z < -1.04000000000000002e-134

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 98.9%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. fma-def 99.4%

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

      2. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 62.7%

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

   if -1.04000000000000002e-134 < z < -3e-266 or -1.8999999999999999e-284 < z < 5.5000000000000003e-297 or 4.9499999999999998e-284 < z < 1.65000000000000011e-229 or 8.5999999999999997e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   if -3e-266 < z < -1.8999999999999999e-284 or 5.5000000000000003e-297 < z < 4.9499999999999998e-284 or 1.65000000000000011e-229 < z < 8.5999999999999997e-94

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.3%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-134}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.95 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-133}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -150000000000.0)
     t_0
     (if (<= z -1.32e-133)
       (* 6.0 (* y (- 0.6666666666666666 z)))
       (if (<= z -3.8e-266)
         (* x -3.0)
         (if (<= z -1.8e-284)
           (* y 4.0)
           (if (<= z 2.15e-298)
             (* x -3.0)
             (if (<= z 2.55e-284)
               (* y 4.0)
               (if (<= z 1.85e-230)
                 (* x -3.0)
                 (if (<= z 9.5e-94)
                   (* y 4.0)
                   (if (<= z 0.5) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -150000000000.0) {
		tmp = t_0;
	} else if (z <= -1.32e-133) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -3.8e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-298) {
		tmp = x * -3.0;
	} else if (z <= 2.55e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.85e-230) {
		tmp = x * -3.0;
	} else if (z <= 9.5e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-150000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.32d-133)) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (z <= (-3.8d-266)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.8d-284)) then
        tmp = y * 4.0d0
    else if (z <= 2.15d-298) then
        tmp = x * (-3.0d0)
    else if (z <= 2.55d-284) then
        tmp = y * 4.0d0
    else if (z <= 1.85d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 9.5d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -150000000000.0) {
		tmp = t_0;
	} else if (z <= -1.32e-133) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -3.8e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-298) {
		tmp = x * -3.0;
	} else if (z <= 2.55e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.85e-230) {
		tmp = x * -3.0;
	} else if (z <= 9.5e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -150000000000.0:
		tmp = t_0
	elif z <= -1.32e-133:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif z <= -3.8e-266:
		tmp = x * -3.0
	elif z <= -1.8e-284:
		tmp = y * 4.0
	elif z <= 2.15e-298:
		tmp = x * -3.0
	elif z <= 2.55e-284:
		tmp = y * 4.0
	elif z <= 1.85e-230:
		tmp = x * -3.0
	elif z <= 9.5e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -150000000000.0)
		tmp = t_0;
	elseif (z <= -1.32e-133)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (z <= -3.8e-266)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.8e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.15e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.55e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.85e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.5e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -150000000000.0)
		tmp = t_0;
	elseif (z <= -1.32e-133)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (z <= -3.8e-266)
		tmp = x * -3.0;
	elseif (z <= -1.8e-284)
		tmp = y * 4.0;
	elseif (z <= 2.15e-298)
		tmp = x * -3.0;
	elseif (z <= 2.55e-284)
		tmp = y * 4.0;
	elseif (z <= 1.85e-230)
		tmp = x * -3.0;
	elseif (z <= 9.5e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -150000000000.0], t$95$0, If[LessEqual[z, -1.32e-133], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-266], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.8e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.15e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.55e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.85e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.5e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e11 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*l* 99.3%

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

   5. Simplified 99.3%

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

   if -1.5e11 < z < -1.32000000000000008e-133

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 98.9%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. fma-def 99.4%

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

      2. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 62.7%

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

   if -1.32000000000000008e-133 < z < -3.79999999999999994e-266 or -1.8000000000000001e-284 < z < 2.15e-298 or 2.5500000000000001e-284 < z < 1.84999999999999991e-230 or 9.4999999999999997e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   if -3.79999999999999994e-266 < z < -1.8000000000000001e-284 or 2.15e-298 < z < 2.5500000000000001e-284 or 1.84999999999999991e-230 < z < 9.4999999999999997e-94

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.3%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-133}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-264}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (* z -6.0))))
   (if (<= z -150000000000.0)
     t_0
     (if (<= z -1.15e-134)
       (* 6.0 (* y (- 0.6666666666666666 z)))
       (if (<= z -1.56e-264)
         (* x -3.0)
         (if (<= z -2.1e-284)
           (* y 4.0)
           (if (<= z 7.2e-299)
             (* x -3.0)
             (if (<= z 4.2e-284)
               (* y 4.0)
               (if (<= z 3.8e-230)
                 (* x -3.0)
                 (if (<= z 8.8e-94)
                   (* y 4.0)
                   (if (<= z 0.5) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -150000000000.0) {
		tmp = t_0;
	} else if (z <= -1.15e-134) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -1.56e-264) {
		tmp = x * -3.0;
	} else if (z <= -2.1e-284) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-299) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.8e-230) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - x) * (z * (-6.0d0))
    if (z <= (-150000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.15d-134)) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (z <= (-1.56d-264)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.1d-284)) then
        tmp = y * 4.0d0
    else if (z <= 7.2d-299) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d-284) then
        tmp = y * 4.0d0
    else if (z <= 3.8d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -150000000000.0) {
		tmp = t_0;
	} else if (z <= -1.15e-134) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -1.56e-264) {
		tmp = x * -3.0;
	} else if (z <= -2.1e-284) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-299) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.8e-230) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z * -6.0)
	tmp = 0
	if z <= -150000000000.0:
		tmp = t_0
	elif z <= -1.15e-134:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif z <= -1.56e-264:
		tmp = x * -3.0
	elif z <= -2.1e-284:
		tmp = y * 4.0
	elif z <= 7.2e-299:
		tmp = x * -3.0
	elif z <= 4.2e-284:
		tmp = y * 4.0
	elif z <= 3.8e-230:
		tmp = x * -3.0
	elif z <= 8.8e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -150000000000.0)
		tmp = t_0;
	elseif (z <= -1.15e-134)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (z <= -1.56e-264)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.1e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.2e-299)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.8e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * (z * -6.0);
	tmp = 0.0;
	if (z <= -150000000000.0)
		tmp = t_0;
	elseif (z <= -1.15e-134)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (z <= -1.56e-264)
		tmp = x * -3.0;
	elseif (z <= -2.1e-284)
		tmp = y * 4.0;
	elseif (z <= 7.2e-299)
		tmp = x * -3.0;
	elseif (z <= 4.2e-284)
		tmp = y * 4.0;
	elseif (z <= 3.8e-230)
		tmp = x * -3.0;
	elseif (z <= 8.8e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -150000000000.0], t$95$0, If[LessEqual[z, -1.15e-134], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.56e-264], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.1e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.2e-299], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.8e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e11 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   if -1.5e11 < z < -1.15e-134

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 98.9%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. fma-def 99.4%

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

      2. associate-*r* 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around 0 62.7%

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

   if -1.15e-134 < z < -1.5599999999999999e-264 or -2.09999999999999991e-284 < z < 7.2e-299 or 4.19999999999999982e-284 < z < 3.7999999999999998e-230 or 8.80000000000000004e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   if -1.5599999999999999e-264 < z < -2.09999999999999991e-284 or 7.2e-299 < z < 4.19999999999999982e-284 or 3.7999999999999998e-230 < z < 8.80000000000000004e-94

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.3%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150000000000:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-264}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 7: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (* z -6.0))))
   (if (<= z -6e+15)
     t_0
     (if (<= z -5.3e-132)
       (* y (+ 4.0 (* z -6.0)))
       (if (<= z -5.1e-266)
         (* x -3.0)
         (if (<= z -2.3e-284)
           (* y 4.0)
           (if (<= z 1.1e-298)
             (* x -3.0)
             (if (<= z 3.4e-284)
               (* y 4.0)
               (if (<= z 1.45e-231)
                 (* x -3.0)
                 (if (<= z 8.8e-94)
                   (* y 4.0)
                   (if (<= z 0.5) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -6e+15) {
		tmp = t_0;
	} else if (z <= -5.3e-132) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (z <= -5.1e-266) {
		tmp = x * -3.0;
	} else if (z <= -2.3e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-298) {
		tmp = x * -3.0;
	} else if (z <= 3.4e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.45e-231) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y - x) * (z * (-6.0d0))
    if (z <= (-6d+15)) then
        tmp = t_0
    else if (z <= (-5.3d-132)) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else if (z <= (-5.1d-266)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.3d-284)) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-298) then
        tmp = x * (-3.0d0)
    else if (z <= 3.4d-284) then
        tmp = y * 4.0d0
    else if (z <= 1.45d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -6e+15) {
		tmp = t_0;
	} else if (z <= -5.3e-132) {
		tmp = y * (4.0 + (z * -6.0));
	} else if (z <= -5.1e-266) {
		tmp = x * -3.0;
	} else if (z <= -2.3e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-298) {
		tmp = x * -3.0;
	} else if (z <= 3.4e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.45e-231) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z * -6.0)
	tmp = 0
	if z <= -6e+15:
		tmp = t_0
	elif z <= -5.3e-132:
		tmp = y * (4.0 + (z * -6.0))
	elif z <= -5.1e-266:
		tmp = x * -3.0
	elif z <= -2.3e-284:
		tmp = y * 4.0
	elif z <= 1.1e-298:
		tmp = x * -3.0
	elif z <= 3.4e-284:
		tmp = y * 4.0
	elif z <= 1.45e-231:
		tmp = x * -3.0
	elif z <= 8.8e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -6e+15)
		tmp = t_0;
	elseif (z <= -5.3e-132)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	elseif (z <= -5.1e-266)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.3e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.4e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.45e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * (z * -6.0);
	tmp = 0.0;
	if (z <= -6e+15)
		tmp = t_0;
	elseif (z <= -5.3e-132)
		tmp = y * (4.0 + (z * -6.0));
	elseif (z <= -5.1e-266)
		tmp = x * -3.0;
	elseif (z <= -2.3e-284)
		tmp = y * 4.0;
	elseif (z <= 1.1e-298)
		tmp = x * -3.0;
	elseif (z <= 3.4e-284)
		tmp = y * 4.0;
	elseif (z <= 1.45e-231)
		tmp = x * -3.0;
	elseif (z <= 8.8e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+15], t$95$0, If[LessEqual[z, -5.3e-132], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-266], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.3e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.4e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.45e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e15 or 0.5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   if -6e15 < z < -5.3000000000000003e-132

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-*l* 99.5%

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

      3. fma-def 99.6%

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

      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. +-commutative 99.6%

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

      6. distribute-lft-in 99.6%

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

      7. neg-mul-1 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.6%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 64.2%

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

   if -5.3000000000000003e-132 < z < -5.10000000000000027e-266 or -2.3e-284 < z < 1.1e-298 or 3.39999999999999991e-284 < z < 1.45e-231 or 8.80000000000000004e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   if -5.10000000000000027e-266 < z < -2.3e-284 or 1.1e-298 < z < 3.39999999999999991e-284 or 1.45e-231 < z < 8.80000000000000004e-94

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.3%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+15}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 8: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-264}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.68)
     t_0
     (if (<= z -3.6e-131)
       (* y 4.0)
       (if (<= z -2.9e-264)
         (* x -3.0)
         (if (<= z -1.9e-284)
           (* y 4.0)
           (if (<= z 3.5e-298)
             (* x -3.0)
             (if (<= z 6.9e-284)
               (* y 4.0)
               (if (<= z 4.1e-231)
                 (* x -3.0)
                 (if (<= z 7.2e-94)
                   (* y 4.0)
                   (if (<= z 0.55) (* x -3.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.68) {
		tmp = t_0;
	} else if (z <= -3.6e-131) {
		tmp = y * 4.0;
	} else if (z <= -2.9e-264) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-298) {
		tmp = x * -3.0;
	} else if (z <= 6.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-231) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.68d0)) then
        tmp = t_0
    else if (z <= (-3.6d-131)) then
        tmp = y * 4.0d0
    else if (z <= (-2.9d-264)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.9d-284)) then
        tmp = y * 4.0d0
    else if (z <= 3.5d-298) then
        tmp = x * (-3.0d0)
    else if (z <= 6.9d-284) then
        tmp = y * 4.0d0
    else if (z <= 4.1d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.68) {
		tmp = t_0;
	} else if (z <= -3.6e-131) {
		tmp = y * 4.0;
	} else if (z <= -2.9e-264) {
		tmp = x * -3.0;
	} else if (z <= -1.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-298) {
		tmp = x * -3.0;
	} else if (z <= 6.9e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-231) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.68:
		tmp = t_0
	elif z <= -3.6e-131:
		tmp = y * 4.0
	elif z <= -2.9e-264:
		tmp = x * -3.0
	elif z <= -1.9e-284:
		tmp = y * 4.0
	elif z <= 3.5e-298:
		tmp = x * -3.0
	elif z <= 6.9e-284:
		tmp = y * 4.0
	elif z <= 4.1e-231:
		tmp = x * -3.0
	elif z <= 7.2e-94:
		tmp = y * 4.0
	elif z <= 0.55:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.68)
		tmp = t_0;
	elseif (z <= -3.6e-131)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.9e-264)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.9e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.5e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.9e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.1e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.68)
		tmp = t_0;
	elseif (z <= -3.6e-131)
		tmp = y * 4.0;
	elseif (z <= -2.9e-264)
		tmp = x * -3.0;
	elseif (z <= -1.9e-284)
		tmp = y * 4.0;
	elseif (z <= 3.5e-298)
		tmp = x * -3.0;
	elseif (z <= 6.9e-284)
		tmp = y * 4.0;
	elseif (z <= 4.1e-231)
		tmp = x * -3.0;
	elseif (z <= 7.2e-94)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.68], t$95$0, If[LessEqual[z, -3.6e-131], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.9e-264], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.9e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.5e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.9e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.1e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.680000000000000049 or 0.55000000000000004 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in x around 0 97.1%

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

      1. fma-def 98.8%

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

      2. associate-*r* 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around inf 99.1%

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

   7. Taylor expanded in x around 0 51.9%

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

   if -0.680000000000000049 < z < -3.5999999999999999e-131 or -2.8999999999999999e-264 < z < -1.8999999999999999e-284 or 3.4999999999999998e-298 < z < 6.9e-284 or 4.1000000000000002e-231 < z < 7.2e-94

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.2%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if -3.5999999999999999e-131 < z < -2.8999999999999999e-264 or -1.8999999999999999e-284 < z < 3.4999999999999998e-298 or 6.9e-284 < z < 4.1000000000000002e-231 or 7.2e-94 < z < 0.55000000000000004

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-264}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-132}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.68)
   (* -6.0 (* y z))
   (if (<= z -8.4e-132)
     (* y 4.0)
     (if (<= z -2e-266)
       (* x -3.0)
       (if (<= z -1.85e-284)
         (* y 4.0)
         (if (<= z 4.4e-298)
           (* x -3.0)
           (if (<= z 1.85e-284)
             (* y 4.0)
             (if (<= z 3.5e-232)
               (* x -3.0)
               (if (<= z 8.6e-94)
                 (* y 4.0)
                 (if (<= z 0.5) (* x -3.0) (* 6.0 (* x z))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = -6.0 * (y * z);
	} else if (z <= -8.4e-132) {
		tmp = y * 4.0;
	} else if (z <= -2e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.85e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.4e-298) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-232) {
		tmp = x * -3.0;
	} else if (z <= 8.6e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (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 <= (-0.68d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-8.4d-132)) then
        tmp = y * 4.0d0
    else if (z <= (-2d-266)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.85d-284)) then
        tmp = y * 4.0d0
    else if (z <= 4.4d-298) then
        tmp = x * (-3.0d0)
    else if (z <= 1.85d-284) then
        tmp = y * 4.0d0
    else if (z <= 3.5d-232) then
        tmp = x * (-3.0d0)
    else if (z <= 8.6d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = -6.0 * (y * z);
	} else if (z <= -8.4e-132) {
		tmp = y * 4.0;
	} else if (z <= -2e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.85e-284) {
		tmp = y * 4.0;
	} else if (z <= 4.4e-298) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-232) {
		tmp = x * -3.0;
	} else if (z <= 8.6e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.68:
		tmp = -6.0 * (y * z)
	elif z <= -8.4e-132:
		tmp = y * 4.0
	elif z <= -2e-266:
		tmp = x * -3.0
	elif z <= -1.85e-284:
		tmp = y * 4.0
	elif z <= 4.4e-298:
		tmp = x * -3.0
	elif z <= 1.85e-284:
		tmp = y * 4.0
	elif z <= 3.5e-232:
		tmp = x * -3.0
	elif z <= 8.6e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -8.4e-132)
		tmp = Float64(y * 4.0);
	elseif (z <= -2e-266)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.85e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.4e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.85e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.5e-232)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.6e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.68)
		tmp = -6.0 * (y * z);
	elseif (z <= -8.4e-132)
		tmp = y * 4.0;
	elseif (z <= -2e-266)
		tmp = x * -3.0;
	elseif (z <= -1.85e-284)
		tmp = y * 4.0;
	elseif (z <= 4.4e-298)
		tmp = x * -3.0;
	elseif (z <= 1.85e-284)
		tmp = y * 4.0;
	elseif (z <= 3.5e-232)
		tmp = x * -3.0;
	elseif (z <= 8.6e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.68], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.4e-132], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2e-266], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.85e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.4e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.85e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.5e-232], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.6e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.680000000000000049

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.6%

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

   3. Taylor expanded in x around 0 94.3%

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

      1. fma-def 97.8%

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

      2. associate-*r* 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in z around inf 99.3%

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

   7. Taylor expanded in x around 0 55.4%

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

   if -0.680000000000000049 < z < -8.4000000000000004e-132 or -2e-266 < z < -1.85e-284 or 4.4e-298 < z < 1.85e-284 or 3.4999999999999998e-232 < z < 8.5999999999999997e-94

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.2%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if -8.4000000000000004e-132 < z < -2e-266 or -1.85e-284 < z < 4.4e-298 or 1.85e-284 < z < 3.4999999999999998e-232 or 8.5999999999999997e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   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. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 57.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-132}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 10: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.68)
   (* z (* y -6.0))
   (if (<= z -8e-131)
     (* y 4.0)
     (if (<= z -5.4e-266)
       (* x -3.0)
       (if (<= z -2.05e-284)
         (* y 4.0)
         (if (<= z 7.2e-298)
           (* x -3.0)
           (if (<= z 6.4e-284)
             (* y 4.0)
             (if (<= z 5.6e-230)
               (* x -3.0)
               (if (<= z 7.4e-94)
                 (* y 4.0)
                 (if (<= z 0.5) (* x -3.0) (* 6.0 (* x z))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = z * (y * -6.0);
	} else if (z <= -8e-131) {
		tmp = y * 4.0;
	} else if (z <= -5.4e-266) {
		tmp = x * -3.0;
	} else if (z <= -2.05e-284) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-298) {
		tmp = x * -3.0;
	} else if (z <= 6.4e-284) {
		tmp = y * 4.0;
	} else if (z <= 5.6e-230) {
		tmp = x * -3.0;
	} else if (z <= 7.4e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (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 <= (-0.68d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-8d-131)) then
        tmp = y * 4.0d0
    else if (z <= (-5.4d-266)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.05d-284)) then
        tmp = y * 4.0d0
    else if (z <= 7.2d-298) then
        tmp = x * (-3.0d0)
    else if (z <= 6.4d-284) then
        tmp = y * 4.0d0
    else if (z <= 5.6d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 7.4d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = z * (y * -6.0);
	} else if (z <= -8e-131) {
		tmp = y * 4.0;
	} else if (z <= -5.4e-266) {
		tmp = x * -3.0;
	} else if (z <= -2.05e-284) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-298) {
		tmp = x * -3.0;
	} else if (z <= 6.4e-284) {
		tmp = y * 4.0;
	} else if (z <= 5.6e-230) {
		tmp = x * -3.0;
	} else if (z <= 7.4e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.68:
		tmp = z * (y * -6.0)
	elif z <= -8e-131:
		tmp = y * 4.0
	elif z <= -5.4e-266:
		tmp = x * -3.0
	elif z <= -2.05e-284:
		tmp = y * 4.0
	elif z <= 7.2e-298:
		tmp = x * -3.0
	elif z <= 6.4e-284:
		tmp = y * 4.0
	elif z <= 5.6e-230:
		tmp = x * -3.0
	elif z <= 7.4e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -8e-131)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.4e-266)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.05e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.2e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.4e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.6e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.4e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.68)
		tmp = z * (y * -6.0);
	elseif (z <= -8e-131)
		tmp = y * 4.0;
	elseif (z <= -5.4e-266)
		tmp = x * -3.0;
	elseif (z <= -2.05e-284)
		tmp = y * 4.0;
	elseif (z <= 7.2e-298)
		tmp = x * -3.0;
	elseif (z <= 6.4e-284)
		tmp = y * 4.0;
	elseif (z <= 5.6e-230)
		tmp = x * -3.0;
	elseif (z <= 7.4e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.68], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-131], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.4e-266], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.05e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.2e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.4e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.6e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.4e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.680000000000000049

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.6%

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

   3. Taylor expanded in x around 0 94.3%

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

      1. fma-def 97.8%

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

      2. associate-*r* 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in z around inf 99.3%

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

   7. Taylor expanded in x around 0 55.5%

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

   if -0.680000000000000049 < z < -7.9999999999999999e-131 or -5.39999999999999992e-266 < z < -2.04999999999999999e-284 or 7.20000000000000005e-298 < z < 6.40000000000000047e-284 or 5.6000000000000002e-230 < z < 7.3999999999999996e-94

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.2%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if -7.9999999999999999e-131 < z < -5.39999999999999992e-266 or -2.04999999999999999e-284 < z < 7.20000000000000005e-298 or 6.40000000000000047e-284 < z < 5.6000000000000002e-230 or 7.3999999999999996e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   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. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 98.8%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 57.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-131}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 11: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{-133}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.68)
   (* z (* y -6.0))
   (if (<= z -1.38e-133)
     (* y 4.0)
     (if (<= z -9e-266)
       (* x -3.0)
       (if (<= z -1.8e-284)
         (* y 4.0)
         (if (<= z 2.65e-297)
           (* x -3.0)
           (if (<= z 5.2e-284)
             (* y 4.0)
             (if (<= z 2.5e-230)
               (* x -3.0)
               (if (<= z 7.6e-94)
                 (* y 4.0)
                 (if (<= z 0.5) (* x -3.0) (* z (* x 6.0))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = z * (y * -6.0);
	} else if (z <= -1.38e-133) {
		tmp = y * 4.0;
	} else if (z <= -9e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.65e-297) {
		tmp = x * -3.0;
	} else if (z <= 5.2e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-230) {
		tmp = x * -3.0;
	} else if (z <= 7.6e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 <= (-0.68d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-1.38d-133)) then
        tmp = y * 4.0d0
    else if (z <= (-9d-266)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.8d-284)) then
        tmp = y * 4.0d0
    else if (z <= 2.65d-297) then
        tmp = x * (-3.0d0)
    else if (z <= 5.2d-284) then
        tmp = y * 4.0d0
    else if (z <= 2.5d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 7.6d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 <= -0.68) {
		tmp = z * (y * -6.0);
	} else if (z <= -1.38e-133) {
		tmp = y * 4.0;
	} else if (z <= -9e-266) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.65e-297) {
		tmp = x * -3.0;
	} else if (z <= 5.2e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.5e-230) {
		tmp = x * -3.0;
	} else if (z <= 7.6e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.68:
		tmp = z * (y * -6.0)
	elif z <= -1.38e-133:
		tmp = y * 4.0
	elif z <= -9e-266:
		tmp = x * -3.0
	elif z <= -1.8e-284:
		tmp = y * 4.0
	elif z <= 2.65e-297:
		tmp = x * -3.0
	elif z <= 5.2e-284:
		tmp = y * 4.0
	elif z <= 2.5e-230:
		tmp = x * -3.0
	elif z <= 7.6e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -1.38e-133)
		tmp = Float64(y * 4.0);
	elseif (z <= -9e-266)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.8e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.65e-297)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.2e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.5e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.6e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	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 <= -0.68)
		tmp = z * (y * -6.0);
	elseif (z <= -1.38e-133)
		tmp = y * 4.0;
	elseif (z <= -9e-266)
		tmp = x * -3.0;
	elseif (z <= -1.8e-284)
		tmp = y * 4.0;
	elseif (z <= 2.65e-297)
		tmp = x * -3.0;
	elseif (z <= 5.2e-284)
		tmp = y * 4.0;
	elseif (z <= 2.5e-230)
		tmp = x * -3.0;
	elseif (z <= 7.6e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.68], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.38e-133], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -9e-266], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.8e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.65e-297], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.2e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.5e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.6e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.680000000000000049

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.6%

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

   3. Taylor expanded in x around 0 94.3%

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

      1. fma-def 97.8%

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

      2. associate-*r* 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in z around inf 99.3%

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

   7. Taylor expanded in x around 0 55.5%

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

   if -0.680000000000000049 < z < -1.38e-133 or -9.0000000000000006e-266 < z < -1.8000000000000001e-284 or 2.6500000000000001e-297 < z < 5.2e-284 or 2.50000000000000017e-230 < z < 7.59999999999999999e-94

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.2%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if -1.38e-133 < z < -9.0000000000000006e-266 or -1.8000000000000001e-284 < z < 2.6500000000000001e-297 or 5.2e-284 < z < 2.50000000000000017e-230 or 7.59999999999999999e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   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. Taylor expanded in y around 0 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

      1. fma-def 99.8%

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

      2. associate-*r* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 98.9%

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

   7. Taylor expanded in x around inf 57.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{-133}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-266}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 12: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-132}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-265}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.68)
   (* y (* z -6.0))
   (if (<= z -6.2e-132)
     (* y 4.0)
     (if (<= z -5.6e-265)
       (* x -3.0)
       (if (<= z -1.8e-284)
         (* y 4.0)
         (if (<= z 3.5e-298)
           (* x -3.0)
           (if (<= z 1.95e-284)
             (* y 4.0)
             (if (<= z 2.05e-230)
               (* x -3.0)
               (if (<= z 8.8e-94)
                 (* y 4.0)
                 (if (<= z 0.5) (* x -3.0) (* z (* x 6.0))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = y * (z * -6.0);
	} else if (z <= -6.2e-132) {
		tmp = y * 4.0;
	} else if (z <= -5.6e-265) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-298) {
		tmp = x * -3.0;
	} else if (z <= 1.95e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.05e-230) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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 <= (-0.68d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-6.2d-132)) then
        tmp = y * 4.0d0
    else if (z <= (-5.6d-265)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.8d-284)) then
        tmp = y * 4.0d0
    else if (z <= 3.5d-298) then
        tmp = x * (-3.0d0)
    else if (z <= 1.95d-284) then
        tmp = y * 4.0d0
    else if (z <= 2.05d-230) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-94) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 <= -0.68) {
		tmp = y * (z * -6.0);
	} else if (z <= -6.2e-132) {
		tmp = y * 4.0;
	} else if (z <= -5.6e-265) {
		tmp = x * -3.0;
	} else if (z <= -1.8e-284) {
		tmp = y * 4.0;
	} else if (z <= 3.5e-298) {
		tmp = x * -3.0;
	} else if (z <= 1.95e-284) {
		tmp = y * 4.0;
	} else if (z <= 2.05e-230) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-94) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.68:
		tmp = y * (z * -6.0)
	elif z <= -6.2e-132:
		tmp = y * 4.0
	elif z <= -5.6e-265:
		tmp = x * -3.0
	elif z <= -1.8e-284:
		tmp = y * 4.0
	elif z <= 3.5e-298:
		tmp = x * -3.0
	elif z <= 1.95e-284:
		tmp = y * 4.0
	elif z <= 2.05e-230:
		tmp = x * -3.0
	elif z <= 8.8e-94:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -6.2e-132)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.6e-265)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.8e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.5e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.95e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.05e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-94)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	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 <= -0.68)
		tmp = y * (z * -6.0);
	elseif (z <= -6.2e-132)
		tmp = y * 4.0;
	elseif (z <= -5.6e-265)
		tmp = x * -3.0;
	elseif (z <= -1.8e-284)
		tmp = y * 4.0;
	elseif (z <= 3.5e-298)
		tmp = x * -3.0;
	elseif (z <= 1.95e-284)
		tmp = y * 4.0;
	elseif (z <= 2.05e-230)
		tmp = x * -3.0;
	elseif (z <= 8.8e-94)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.68], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-132], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.6e-265], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.8e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.5e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.95e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.05e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-94], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.680000000000000049

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 56.0%

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

   5. Taylor expanded in z around inf 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   if -0.680000000000000049 < z < -6.20000000000000016e-132 or -5.60000000000000047e-265 < z < -1.8000000000000001e-284 or 3.4999999999999998e-298 < z < 1.9499999999999999e-284 or 2.0500000000000001e-230 < z < 8.80000000000000004e-94

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 72.2%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if -6.20000000000000016e-132 < z < -5.60000000000000047e-265 or -1.8000000000000001e-284 < z < 3.4999999999999998e-298 or 1.9499999999999999e-284 < z < 2.0500000000000001e-230 or 8.80000000000000004e-94 < z < 0.5

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in y around 0 68.6%

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

   4. Taylor expanded in z around 0 68.1%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 68.1%

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

      2. metadata-eval 68.1%

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

   6. Simplified 68.1%

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

   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. Taylor expanded in y around 0 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

      1. fma-def 99.8%

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

      2. associate-*r* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 98.9%

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

   7. Taylor expanded in x around inf 57.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-132}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-265}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 13: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* (- y x) (* z -6.0))
   (if (<= z 0.56) (+ (* x -3.0) (* y 4.0)) (* z (+ (* x 6.0) (* y -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.56) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((x * 6.0) + (y * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.56d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * ((x * 6.0d0) + (y * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.56) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((x * 6.0) + (y * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.56:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * ((x * 6.0) + (y * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.56)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(Float64(x * 6.0) + Float64(y * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.56)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * ((x * 6.0) + (y * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.56], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * 6.0), $MachinePrecision] + N[(y * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in z around inf 99.2%

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

      1. associate-*r* 99.4%

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

      2. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if -0.57999999999999996 < z < 0.56000000000000005

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. fma-def 99.6%

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

      2. associate-*r* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0 97.2%

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

   if 0.56000000000000005 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

      1. fma-def 99.8%

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

      2. associate-*r* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 98.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \end{array} \]

Alternative 14: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-55} \lor \neg \left(x \leq 1.7 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e-55) (not (<= x 1.7e+60)))
   (* x (- (* z 6.0) 3.0))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-55) || !(x <= 1.7e+60)) {
		tmp = x * ((z * 6.0) - 3.0);
	} 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 <= (-2.7d-55)) .or. (.not. (x <= 1.7d+60))) then
        tmp = x * ((z * 6.0d0) - 3.0d0)
    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 <= -2.7e-55) || !(x <= 1.7e+60)) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e-55) or not (x <= 1.7e+60):
		tmp = x * ((z * 6.0) - 3.0)
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e-55) || !(x <= 1.7e+60))
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	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 <= -2.7e-55) || ~((x <= 1.7e+60)))
		tmp = x * ((z * 6.0) - 3.0);
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e-55], N[Not[LessEqual[x, 1.7e+60]], $MachinePrecision]], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.70000000000000004e-55 or 1.7e60 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 84.1%

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

   if -2.70000000000000004e-55 < x < 1.7e60

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 78.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-55} \lor \neg \left(x \leq 1.7 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 15: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.65)))
   (* (- y x) (* z -6.0))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.65)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.65)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.65):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.65))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.65)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.0%

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

      1. associate-*r* 99.1%

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

      2. *-commutative 99.1%

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

   5. Simplified 99.1%

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

   if -0.599999999999999978 < z < 0.650000000000000022

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 99.3%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. fma-def 99.6%

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

      2. associate-*r* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0 97.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 16: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.5%

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

   1. neg-mul-1 99.5%

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

   2. +-commutative 99.5%

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

   3. sub-neg 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 17: 99.7% accurate, 1.2× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate-*l* 99.8%

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

   2. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 18: 37.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.8e-60) (* x -3.0) (if (<= x 2.5e-88) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e-60) {
		tmp = x * -3.0;
	} else if (x <= 2.5e-88) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.8d-60)) then
        tmp = x * (-3.0d0)
    else if (x <= 2.5d-88) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e-60) {
		tmp = x * -3.0;
	} else if (x <= 2.5e-88) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.8e-60:
		tmp = x * -3.0
	elif x <= 2.5e-88:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.8e-60)
		tmp = Float64(x * -3.0);
	elseif (x <= 2.5e-88)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.8e-60)
		tmp = x * -3.0;
	elseif (x <= 2.5e-88)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.8e-60], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 2.5e-88], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999995e-60 or 2.50000000000000004e-88 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 99.5%

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

   3. Taylor expanded in y around 0 77.1%

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

   4. Taylor expanded in z around 0 41.2%

      \[\leadsto \color{blue}{-4 \cdot x + x} \]
   5. Step-by-step derivation

      1. distribute-lft1-in 41.2%

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

      2. metadata-eval 41.2%

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

   6. Simplified 41.2%

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

   if -8.7999999999999995e-60 < x < 2.50000000000000004e-88

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.9%

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

      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. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. neg-mul-1 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 82.0%

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

   5. Taylor expanded in z around 0 50.5%

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

      1. *-commutative 50.5%

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

   7. Simplified 50.5%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 19: 25.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in y around 0 99.5%

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

3. Taylor expanded in y around 0 51.6%

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

4. Taylor expanded in z around 0 28.0%

   \[\leadsto \color{blue}{-4 \cdot x + x} \]
5. Step-by-step derivation

   1. distribute-lft1-in 28.0%

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

   2. metadata-eval 28.0%

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

6. Simplified 28.0%

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

7. Final simplification 28.0%

   \[\leadsto x \cdot -3 \]

Alternative 20: 2.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in y around 0 99.5%

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

3. Taylor expanded in z around inf 46.0%

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

   1. neg-mul-1 46.0%

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

5. Simplified 46.0%

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

6. Taylor expanded in z around 0 2.9%

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

7. Final simplification 2.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023185 
(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))))