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

Percentage Accurate: 99.5% → 99.8%

Time: 11.6s

Alternatives: 15

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.7%

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

   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 99.7%

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

   7. distribute-rgt-neg-out 99.7%

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

   8. distribute-lft-neg-in 99.7%

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

   9. *-commutative 99.7%

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

   10. fma-def 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.7%

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

   3. fma-def 99.7%

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

   4. sub-neg 99.7%

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

   5. distribute-rgt-in 99.7%

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

   6. metadata-eval 99.7%

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

   7. metadata-eval 99.7%

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

   8. distribute-lft-neg-out 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 3: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+174} \lor \neg \left(z \leq 2.35 \cdot 10^{+201}\right) \land z \leq 5.2 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -3.5e+226)
     t_0
     (if (<= z -6.5e+176)
       t_1
       (if (<= z -7.4e+141)
         t_0
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -4.2e-255)
             (* y 4.0)
             (if (<= z 2.85e-220)
               (* x -3.0)
               (if (<= z 1.65e-188)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (or (<= z 2.8e+174)
                           (and (not (<= z 2.35e+201)) (<= z 5.2e+238)))
                     t_1
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -3.5e+226) {
		tmp = t_0;
	} else if (z <= -6.5e+176) {
		tmp = t_1;
	} else if (z <= -7.4e+141) {
		tmp = t_0;
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -4.2e-255) {
		tmp = y * 4.0;
	} else if (z <= 2.85e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.65e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if ((z <= 2.8e+174) || (!(z <= 2.35e+201) && (z <= 5.2e+238))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-3.5d+226)) then
        tmp = t_0
    else if (z <= (-6.5d+176)) then
        tmp = t_1
    else if (z <= (-7.4d+141)) then
        tmp = t_0
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-4.2d-255)) then
        tmp = y * 4.0d0
    else if (z <= 2.85d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 1.65d-188) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if ((z <= 2.8d+174) .or. (.not. (z <= 2.35d+201)) .and. (z <= 5.2d+238)) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -3.5e+226) {
		tmp = t_0;
	} else if (z <= -6.5e+176) {
		tmp = t_1;
	} else if (z <= -7.4e+141) {
		tmp = t_0;
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -4.2e-255) {
		tmp = y * 4.0;
	} else if (z <= 2.85e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.65e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if ((z <= 2.8e+174) || (!(z <= 2.35e+201) && (z <= 5.2e+238))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -3.5e+226:
		tmp = t_0
	elif z <= -6.5e+176:
		tmp = t_1
	elif z <= -7.4e+141:
		tmp = t_0
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -4.2e-255:
		tmp = y * 4.0
	elif z <= 2.85e-220:
		tmp = x * -3.0
	elif z <= 1.65e-188:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif (z <= 2.8e+174) or (not (z <= 2.35e+201) and (z <= 5.2e+238)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.5e+226)
		tmp = t_0;
	elseif (z <= -6.5e+176)
		tmp = t_1;
	elseif (z <= -7.4e+141)
		tmp = t_0;
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -4.2e-255)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.85e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.65e-188)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 2.8e+174) || (!(z <= 2.35e+201) && (z <= 5.2e+238)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.5e+226)
		tmp = t_0;
	elseif (z <= -6.5e+176)
		tmp = t_1;
	elseif (z <= -7.4e+141)
		tmp = t_0;
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -4.2e-255)
		tmp = y * 4.0;
	elseif (z <= 2.85e-220)
		tmp = x * -3.0;
	elseif (z <= 1.65e-188)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif ((z <= 2.8e+174) || (~((z <= 2.35e+201)) && (z <= 5.2e+238)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+226], t$95$0, If[LessEqual[z, -6.5e+176], t$95$1, If[LessEqual[z, -7.4e+141], t$95$0, If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -4.2e-255], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.85e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.65e-188], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 2.8e+174], And[N[Not[LessEqual[z, 2.35e+201]], $MachinePrecision], LessEqual[z, 5.2e+238]]], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999998e226 or -6.49999999999999949e176 < z < -7.4000000000000006e141 or 2.7999999999999999e174 < z < 2.3499999999999999e201 or 5.1999999999999999e238 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 91.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 99.8%

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

   8. Taylor expanded in x around 0 78.0%

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

   if -3.4999999999999998e226 < z < -6.49999999999999949e176 or -7.4000000000000006e141 < z < -7.7999999999999999e-10 or 1.1e-5 < z < 2.7999999999999999e174 or 2.3499999999999999e201 < z < 5.1999999999999999e238

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around inf 93.5%

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

   8. Taylor expanded in x around inf 68.2%

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

   if -7.7999999999999999e-10 < z < -4.1999999999999999e-255 or 2.8499999999999999e-220 < z < 1.6500000000000001e-188

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 65.0%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -4.1999999999999999e-255 < z < 2.8499999999999999e-220 or 1.6500000000000001e-188 < z < 1.1e-5

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 64.0%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. distribute-lft1-in 64.1%

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

      2. metadata-eval 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+226}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+176}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+141}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+174} \lor \neg \left(z \leq 2.35 \cdot 10^{+201}\right) \land z \leq 5.2 \cdot 10^{+238}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+173} \lor \neg \left(z \leq 9 \cdot 10^{+201}\right) \land z \leq 5.1 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -3.4e+230)
     t_0
     (if (<= z -1.75e+177)
       t_1
       (if (<= z -9.5e+141)
         (* z (* y -6.0))
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -1.18e-268)
             (* y 4.0)
             (if (<= z 2.9e-219)
               (* x -3.0)
               (if (<= z 1e-188)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (or (<= z 4.4e+173)
                           (and (not (<= z 9e+201)) (<= z 5.1e+238)))
                     t_1
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -3.4e+230) {
		tmp = t_0;
	} else if (z <= -1.75e+177) {
		tmp = t_1;
	} else if (z <= -9.5e+141) {
		tmp = z * (y * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -1.18e-268) {
		tmp = y * 4.0;
	} else if (z <= 2.9e-219) {
		tmp = x * -3.0;
	} else if (z <= 1e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if ((z <= 4.4e+173) || (!(z <= 9e+201) && (z <= 5.1e+238))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-3.4d+230)) then
        tmp = t_0
    else if (z <= (-1.75d+177)) then
        tmp = t_1
    else if (z <= (-9.5d+141)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-1.18d-268)) then
        tmp = y * 4.0d0
    else if (z <= 2.9d-219) then
        tmp = x * (-3.0d0)
    else if (z <= 1d-188) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if ((z <= 4.4d+173) .or. (.not. (z <= 9d+201)) .and. (z <= 5.1d+238)) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -3.4e+230) {
		tmp = t_0;
	} else if (z <= -1.75e+177) {
		tmp = t_1;
	} else if (z <= -9.5e+141) {
		tmp = z * (y * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -1.18e-268) {
		tmp = y * 4.0;
	} else if (z <= 2.9e-219) {
		tmp = x * -3.0;
	} else if (z <= 1e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if ((z <= 4.4e+173) || (!(z <= 9e+201) && (z <= 5.1e+238))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -3.4e+230:
		tmp = t_0
	elif z <= -1.75e+177:
		tmp = t_1
	elif z <= -9.5e+141:
		tmp = z * (y * -6.0)
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -1.18e-268:
		tmp = y * 4.0
	elif z <= 2.9e-219:
		tmp = x * -3.0
	elif z <= 1e-188:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif (z <= 4.4e+173) or (not (z <= 9e+201) and (z <= 5.1e+238)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.4e+230)
		tmp = t_0;
	elseif (z <= -1.75e+177)
		tmp = t_1;
	elseif (z <= -9.5e+141)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -1.18e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.9e-219)
		tmp = Float64(x * -3.0);
	elseif (z <= 1e-188)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 4.4e+173) || (!(z <= 9e+201) && (z <= 5.1e+238)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.4e+230)
		tmp = t_0;
	elseif (z <= -1.75e+177)
		tmp = t_1;
	elseif (z <= -9.5e+141)
		tmp = z * (y * -6.0);
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -1.18e-268)
		tmp = y * 4.0;
	elseif (z <= 2.9e-219)
		tmp = x * -3.0;
	elseif (z <= 1e-188)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif ((z <= 4.4e+173) || (~((z <= 9e+201)) && (z <= 5.1e+238)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+230], t$95$0, If[LessEqual[z, -1.75e+177], t$95$1, If[LessEqual[z, -9.5e+141], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -1.18e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.9e-219], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1e-188], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 4.4e+173], And[N[Not[LessEqual[z, 9e+201]], $MachinePrecision], LessEqual[z, 5.1e+238]]], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.39999999999999986e230 or 4.4e173 < z < 9.0000000000000002e201 or 5.1000000000000002e238 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 89.5%

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

      1. fma-def 99.9%

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

      2. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 99.8%

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

   8. Taylor expanded in x around 0 78.3%

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

   if -3.39999999999999986e230 < z < -1.74999999999999996e177 or -9.49999999999999974e141 < z < -7.7999999999999999e-10 or 1.1e-5 < z < 4.4e173 or 9.0000000000000002e201 < z < 5.1000000000000002e238

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around inf 93.5%

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

   8. Taylor expanded in x around inf 68.2%

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

   if -1.74999999999999996e177 < z < -9.49999999999999974e141

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 99.8%

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

   8. Taylor expanded in x around 0 76.8%

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

   if -7.7999999999999999e-10 < z < -1.18e-268 or 2.89999999999999984e-219 < z < 9.9999999999999995e-189

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 65.0%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -1.18e-268 < z < 2.89999999999999984e-219 or 9.9999999999999995e-189 < z < 1.1e-5

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 64.0%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. distribute-lft1-in 64.1%

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

      2. metadata-eval 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+230}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+177}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+173} \lor \neg \left(z \leq 9 \cdot 10^{+201}\right) \land z \leq 5.1 \cdot 10^{+238}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-259}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+173}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+199} \lor \neg \left(z \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* z (* x 6.0))))
   (if (<= z -4.8e+229)
     t_0
     (if (<= z -2.25e+176)
       t_1
       (if (<= z -1.45e+141)
         (* z (* y -6.0))
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -8.8e-259)
             (* y 4.0)
             (if (<= z 3.9e-219)
               (* x -3.0)
               (if (<= z 5e-189)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (<= z 6e+173)
                     (* 6.0 (* x z))
                     (if (or (<= z 5.8e+199) (not (<= z 5e+235)))
                       t_0
                       t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -4.8e+229) {
		tmp = t_0;
	} else if (z <= -2.25e+176) {
		tmp = t_1;
	} else if (z <= -1.45e+141) {
		tmp = z * (y * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -8.8e-259) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-219) {
		tmp = x * -3.0;
	} else if (z <= 5e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 6e+173) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 5.8e+199) || !(z <= 5e+235)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = z * (x * 6.0d0)
    if (z <= (-4.8d+229)) then
        tmp = t_0
    else if (z <= (-2.25d+176)) then
        tmp = t_1
    else if (z <= (-1.45d+141)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-8.8d-259)) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-219) then
        tmp = x * (-3.0d0)
    else if (z <= 5d-189) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if (z <= 6d+173) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= 5.8d+199) .or. (.not. (z <= 5d+235))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -4.8e+229) {
		tmp = t_0;
	} else if (z <= -2.25e+176) {
		tmp = t_1;
	} else if (z <= -1.45e+141) {
		tmp = z * (y * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -8.8e-259) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-219) {
		tmp = x * -3.0;
	} else if (z <= 5e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 6e+173) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 5.8e+199) || !(z <= 5e+235)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = z * (x * 6.0)
	tmp = 0
	if z <= -4.8e+229:
		tmp = t_0
	elif z <= -2.25e+176:
		tmp = t_1
	elif z <= -1.45e+141:
		tmp = z * (y * -6.0)
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -8.8e-259:
		tmp = y * 4.0
	elif z <= 3.9e-219:
		tmp = x * -3.0
	elif z <= 5e-189:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif z <= 6e+173:
		tmp = 6.0 * (x * z)
	elif (z <= 5.8e+199) or not (z <= 5e+235):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -4.8e+229)
		tmp = t_0;
	elseif (z <= -2.25e+176)
		tmp = t_1;
	elseif (z <= -1.45e+141)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -8.8e-259)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-219)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif (z <= 6e+173)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= 5.8e+199) || !(z <= 5e+235))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -4.8e+229)
		tmp = t_0;
	elseif (z <= -2.25e+176)
		tmp = t_1;
	elseif (z <= -1.45e+141)
		tmp = z * (y * -6.0);
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -8.8e-259)
		tmp = y * 4.0;
	elseif (z <= 3.9e-219)
		tmp = x * -3.0;
	elseif (z <= 5e-189)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif (z <= 6e+173)
		tmp = 6.0 * (x * z);
	elseif ((z <= 5.8e+199) || ~((z <= 5e+235)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+229], t$95$0, If[LessEqual[z, -2.25e+176], t$95$1, If[LessEqual[z, -1.45e+141], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -8.8e-259], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-219], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6e+173], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 5.8e+199], N[Not[LessEqual[z, 5e+235]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.8000000000000002e229 or 5.9999999999999995e173 < z < 5.7999999999999998e199 or 5.00000000000000027e235 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 89.5%

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

      1. fma-def 99.9%

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

      2. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 99.8%

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

   8. Taylor expanded in x around 0 78.3%

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

   if -4.8000000000000002e229 < z < -2.25000000000000002e176 or -1.45000000000000003e141 < z < -7.7999999999999999e-10 or 5.7999999999999998e199 < z < 5.00000000000000027e235

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 94.8%

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

   8. Taylor expanded in x around inf 72.0%

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

   if -2.25000000000000002e176 < z < -1.45000000000000003e141

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 99.8%

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

   8. Taylor expanded in x around 0 76.8%

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

   if -7.7999999999999999e-10 < z < -8.80000000000000038e-259 or 3.89999999999999987e-219 < z < 4.9999999999999997e-189

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 65.0%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -8.80000000000000038e-259 < z < 3.89999999999999987e-219 or 4.9999999999999997e-189 < z < 1.1e-5

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 64.0%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. distribute-lft1-in 64.1%

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

      2. metadata-eval 64.1%

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

   7. Simplified 64.1%

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

   if 1.1e-5 < z < 5.9999999999999995e173

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 99.4%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in z around inf 91.6%

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

   8. Taylor expanded in x around inf 63.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+229}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-259}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+173}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+199} \lor \neg \left(z \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 6: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-274}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+174}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+201} \lor \neg \left(z \leq 4.2 \cdot 10^{+237}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* z (* x 6.0))))
   (if (<= z -1.55e+230)
     t_0
     (if (<= z -2.9e+178)
       t_1
       (if (<= z -6.5e+141)
         (* y (* z -6.0))
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -8.8e-274)
             (* y 4.0)
             (if (<= z 3.15e-220)
               (* x -3.0)
               (if (<= z 3.4e-189)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (<= z 3.5e+174)
                     (* 6.0 (* x z))
                     (if (or (<= z 1.6e+201) (not (<= z 4.2e+237)))
                       t_0
                       t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -1.55e+230) {
		tmp = t_0;
	} else if (z <= -2.9e+178) {
		tmp = t_1;
	} else if (z <= -6.5e+141) {
		tmp = y * (z * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -8.8e-274) {
		tmp = y * 4.0;
	} else if (z <= 3.15e-220) {
		tmp = x * -3.0;
	} else if (z <= 3.4e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 3.5e+174) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 1.6e+201) || !(z <= 4.2e+237)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = z * (x * 6.0d0)
    if (z <= (-1.55d+230)) then
        tmp = t_0
    else if (z <= (-2.9d+178)) then
        tmp = t_1
    else if (z <= (-6.5d+141)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-8.8d-274)) then
        tmp = y * 4.0d0
    else if (z <= 3.15d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 3.4d-189) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if (z <= 3.5d+174) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= 1.6d+201) .or. (.not. (z <= 4.2d+237))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -1.55e+230) {
		tmp = t_0;
	} else if (z <= -2.9e+178) {
		tmp = t_1;
	} else if (z <= -6.5e+141) {
		tmp = y * (z * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -8.8e-274) {
		tmp = y * 4.0;
	} else if (z <= 3.15e-220) {
		tmp = x * -3.0;
	} else if (z <= 3.4e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 3.5e+174) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 1.6e+201) || !(z <= 4.2e+237)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = z * (x * 6.0)
	tmp = 0
	if z <= -1.55e+230:
		tmp = t_0
	elif z <= -2.9e+178:
		tmp = t_1
	elif z <= -6.5e+141:
		tmp = y * (z * -6.0)
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -8.8e-274:
		tmp = y * 4.0
	elif z <= 3.15e-220:
		tmp = x * -3.0
	elif z <= 3.4e-189:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif z <= 3.5e+174:
		tmp = 6.0 * (x * z)
	elif (z <= 1.6e+201) or not (z <= 4.2e+237):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -1.55e+230)
		tmp = t_0;
	elseif (z <= -2.9e+178)
		tmp = t_1;
	elseif (z <= -6.5e+141)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -8.8e-274)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.15e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.4e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.5e+174)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= 1.6e+201) || !(z <= 4.2e+237))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -1.55e+230)
		tmp = t_0;
	elseif (z <= -2.9e+178)
		tmp = t_1;
	elseif (z <= -6.5e+141)
		tmp = y * (z * -6.0);
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -8.8e-274)
		tmp = y * 4.0;
	elseif (z <= 3.15e-220)
		tmp = x * -3.0;
	elseif (z <= 3.4e-189)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif (z <= 3.5e+174)
		tmp = 6.0 * (x * z);
	elseif ((z <= 1.6e+201) || ~((z <= 4.2e+237)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+230], t$95$0, If[LessEqual[z, -2.9e+178], t$95$1, If[LessEqual[z, -6.5e+141], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -8.8e-274], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.15e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.4e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.5e+174], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.6e+201], N[Not[LessEqual[z, 4.2e+237]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.54999999999999991e230 or 3.5000000000000001e174 < z < 1.6e201 or 4.20000000000000029e237 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 89.5%

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

      1. fma-def 99.9%

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

      2. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 99.8%

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

   8. Taylor expanded in x around 0 78.3%

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

   if -1.54999999999999991e230 < z < -2.9e178 or -6.50000000000000053e141 < z < -7.7999999999999999e-10 or 1.6e201 < z < 4.20000000000000029e237

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 94.8%

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

   8. Taylor expanded in x around inf 72.0%

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

   if -2.9e178 < z < -6.50000000000000053e141

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 76.9%

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

   5. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -7.7999999999999999e-10 < z < -8.7999999999999998e-274 or 3.15000000000000008e-220 < z < 3.4000000000000001e-189

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 65.0%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -8.7999999999999998e-274 < z < 3.15000000000000008e-220 or 3.4000000000000001e-189 < z < 1.1e-5

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 64.0%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. distribute-lft1-in 64.1%

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

      2. metadata-eval 64.1%

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

   7. Simplified 64.1%

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

   if 1.1e-5 < z < 3.5000000000000001e174

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 99.4%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in z around inf 91.6%

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

   8. Taylor expanded in x around inf 63.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+230}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+178}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-274}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+174}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+201} \lor \neg \left(z \leq 4.2 \cdot 10^{+237}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-261}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-53}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5800000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -7.8e-10)
     t_1
     (if (<= z -7.8e-261)
       t_0
       (if (<= z 3.7e-219)
         (* x -3.0)
         (if (<= z 9.8e-189)
           (* y 4.0)
           (if (<= z 1.12e-53) (* x -3.0) (if (<= z 5800000.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -7.8e-261) {
		tmp = t_0;
	} else if (z <= 3.7e-219) {
		tmp = x * -3.0;
	} else if (z <= 9.8e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.12e-53) {
		tmp = x * -3.0;
	} else if (z <= 5800000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-7.8d-261)) then
        tmp = t_0
    else if (z <= 3.7d-219) then
        tmp = x * (-3.0d0)
    else if (z <= 9.8d-189) then
        tmp = y * 4.0d0
    else if (z <= 1.12d-53) then
        tmp = x * (-3.0d0)
    else if (z <= 5800000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -7.8e-261) {
		tmp = t_0;
	} else if (z <= 3.7e-219) {
		tmp = x * -3.0;
	} else if (z <= 9.8e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.12e-53) {
		tmp = x * -3.0;
	} else if (z <= 5800000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -7.8e-10:
		tmp = t_1
	elif z <= -7.8e-261:
		tmp = t_0
	elif z <= 3.7e-219:
		tmp = x * -3.0
	elif z <= 9.8e-189:
		tmp = y * 4.0
	elif z <= 1.12e-53:
		tmp = x * -3.0
	elif z <= 5800000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -7.8e-261)
		tmp = t_0;
	elseif (z <= 3.7e-219)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.8e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.12e-53)
		tmp = Float64(x * -3.0);
	elseif (z <= 5800000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -7.8e-261)
		tmp = t_0;
	elseif (z <= 3.7e-219)
		tmp = x * -3.0;
	elseif (z <= 9.8e-189)
		tmp = y * 4.0;
	elseif (z <= 1.12e-53)
		tmp = x * -3.0;
	elseif (z <= 5800000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -7.8e-261], t$95$0, If[LessEqual[z, 3.7e-219], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.8e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.12e-53], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5800000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.7999999999999999e-10 or 5.8e6 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 96.5%

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

      1. fma-def 99.7%

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

      2. associate-*r* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 97.8%

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

   8. Taylor expanded in x around 0 94.5%

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

      1. +-commutative 94.5%

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

      2. metadata-eval 94.5%

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

      3. distribute-lft-neg-in 94.5%

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

      4. associate-*r* 94.5%

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

      5. *-commutative 94.5%

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

      6. distribute-lft-neg-out 94.5%

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

      7. *-commutative 94.5%

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

      8. associate-*l* 94.5%

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

      9. distribute-lft-out 94.6%

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

      10. *-commutative 94.6%

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

      11. distribute-lft-in 97.8%

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

      12. sub-neg 97.8%

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

   10. Simplified 97.8%

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

   if -7.7999999999999999e-10 < z < -7.80000000000000035e-261 or 1.12000000000000008e-53 < z < 5.8e6

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 66.1%

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

   if -7.80000000000000035e-261 < z < 3.7e-219 or 9.7999999999999994e-189 < z < 1.12000000000000008e-53

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 68.3%

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

   5. Taylor expanded in z around 0 68.5%

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

      1. distribute-lft1-in 68.5%

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

      2. metadata-eval 68.5%

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

   7. Simplified 68.5%

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

   if 3.7e-219 < z < 9.7999999999999994e-189

   1. Initial program 98.9%

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

      1. +-commutative 98.9%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 71.1%

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

   5. Taylor expanded in z around 0 71.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-53}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5800000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -7.8e-10)
     t_0
     (if (<= z -4.6e-263)
       (* y 4.0)
       (if (<= z 2.15e-219)
         (* x -3.0)
         (if (<= z 1.25e-188) (* 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 <= -7.8e-10) {
		tmp = t_0;
	} else if (z <= -4.6e-263) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-219) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-188) {
		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 <= (-7.8d-10)) then
        tmp = t_0
    else if (z <= (-4.6d-263)) then
        tmp = y * 4.0d0
    else if (z <= 2.15d-219) then
        tmp = x * (-3.0d0)
    else if (z <= 1.25d-188) 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 <= -7.8e-10) {
		tmp = t_0;
	} else if (z <= -4.6e-263) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-219) {
		tmp = x * -3.0;
	} else if (z <= 1.25e-188) {
		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 <= -7.8e-10:
		tmp = t_0
	elif z <= -4.6e-263:
		tmp = y * 4.0
	elif z <= 2.15e-219:
		tmp = x * -3.0
	elif z <= 1.25e-188:
		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 <= -7.8e-10)
		tmp = t_0;
	elseif (z <= -4.6e-263)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.15e-219)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.25e-188)
		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 <= -7.8e-10)
		tmp = t_0;
	elseif (z <= -4.6e-263)
		tmp = y * 4.0;
	elseif (z <= 2.15e-219)
		tmp = x * -3.0;
	elseif (z <= 1.25e-188)
		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, -7.8e-10], t$95$0, If[LessEqual[z, -4.6e-263], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.15e-219], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.25e-188], 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 < -7.7999999999999999e-10 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 96.5%

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

      1. fma-def 99.7%

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

      2. associate-*r* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 97.8%

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

   8. Taylor expanded in x around 0 94.5%

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

      1. +-commutative 94.5%

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

      2. metadata-eval 94.5%

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

      3. distribute-lft-neg-in 94.5%

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

      4. associate-*r* 94.5%

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

      5. *-commutative 94.5%

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

      6. distribute-lft-neg-out 94.5%

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

      7. *-commutative 94.5%

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

      8. associate-*l* 94.5%

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

      9. distribute-lft-out 94.6%

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

      10. *-commutative 94.6%

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

      11. distribute-lft-in 97.8%

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

      12. sub-neg 97.8%

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

   10. Simplified 97.8%

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

   if -7.7999999999999999e-10 < z < -4.60000000000000006e-263 or 2.1500000000000001e-219 < z < 1.25e-188

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 65.0%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -4.60000000000000006e-263 < z < 2.1500000000000001e-219 or 1.25e-188 < z < 0.5

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 60.1%

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

   5. Taylor expanded in z around 0 60.3%

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

      1. distribute-lft1-in 60.3%

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

      2. metadata-eval 60.3%

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

   7. Simplified 60.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-263}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 9: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-261}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3.15e+15)
     t_0
     (if (<= z -1.75e-261)
       (* y 4.0)
       (if (<= z 8e-220)
         (* x -3.0)
         (if (<= z 4.4e-189) (* 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 * z);
	double tmp;
	if (z <= -3.15e+15) {
		tmp = t_0;
	} else if (z <= -1.75e-261) {
		tmp = y * 4.0;
	} else if (z <= 8e-220) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-189) {
		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 * z)
    if (z <= (-3.15d+15)) then
        tmp = t_0
    else if (z <= (-1.75d-261)) then
        tmp = y * 4.0d0
    else if (z <= 8d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d-189) 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 * z);
	double tmp;
	if (z <= -3.15e+15) {
		tmp = t_0;
	} else if (z <= -1.75e-261) {
		tmp = y * 4.0;
	} else if (z <= 8e-220) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-189) {
		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 * z)
	tmp = 0
	if z <= -3.15e+15:
		tmp = t_0
	elif z <= -1.75e-261:
		tmp = y * 4.0
	elif z <= 8e-220:
		tmp = x * -3.0
	elif z <= 4.4e-189:
		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(y * z))
	tmp = 0.0
	if (z <= -3.15e+15)
		tmp = t_0;
	elseif (z <= -1.75e-261)
		tmp = Float64(y * 4.0);
	elseif (z <= 8e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e-189)
		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 * z);
	tmp = 0.0;
	if (z <= -3.15e+15)
		tmp = t_0;
	elseif (z <= -1.75e-261)
		tmp = y * 4.0;
	elseif (z <= 8e-220)
		tmp = x * -3.0;
	elseif (z <= 4.4e-189)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.15e+15], t$95$0, If[LessEqual[z, -1.75e-261], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e-189], 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 < -3.15e15 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 96.4%

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

      1. fma-def 99.7%

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

      2. associate-*r* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 99.6%

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

   8. Taylor expanded in x around 0 52.8%

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

   if -3.15e15 < z < -1.7499999999999999e-261 or 7.99999999999999994e-220 < z < 4.40000000000000038e-189

   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. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 59.7%

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

   5. Taylor expanded in z around 0 59.7%

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

   if -1.7499999999999999e-261 < z < 7.99999999999999994e-220 or 4.40000000000000038e-189 < z < 0.5

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 60.1%

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

   5. Taylor expanded in z around 0 60.3%

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

      1. distribute-lft1-in 60.3%

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

      2. metadata-eval 60.3%

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

   7. Simplified 60.3%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+15}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-261}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.64\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.64)))
   (* -6.0 (* (- y x) z))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.64)) {
		tmp = -6.0 * ((y - x) * z);
	} 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 <= 0.64d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    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 <= 0.64)) {
		tmp = -6.0 * ((y - x) * z);
	} 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 <= 0.64):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.64))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	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 <= 0.64)))
		tmp = -6.0 * ((y - x) * z);
	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, 0.64]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $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 0.640000000000000013 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 96.4%

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

      1. fma-def 99.7%

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

      2. associate-*r* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around inf 98.9%

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

   8. Taylor expanded in x around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. metadata-eval 95.6%

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

      3. distribute-lft-neg-in 95.6%

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

      4. associate-*r* 95.6%

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

      5. *-commutative 95.6%

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

      6. distribute-lft-neg-out 95.6%

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

      7. *-commutative 95.6%

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

      8. associate-*l* 95.6%

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

      9. distribute-lft-out 95.6%

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

      10. *-commutative 95.6%

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

      11. distribute-lft-in 98.9%

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

      12. sub-neg 98.9%

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

   10. Simplified 98.9%

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

   if -0.599999999999999978 < z < 0.640000000000000013

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around 0 96.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.64\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 11: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* z (+ (* x 6.0) (* y -6.0)))
   (if (<= z 0.55) (+ (* x -3.0) (* y 4.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((x * 6.0) + (y * -6.0));
	} else if (z <= 0.55) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.6d0)) then
        tmp = z * ((x * 6.0d0) + (y * (-6.0d0)))
    else if (z <= 0.55d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((x * 6.0) + (y * -6.0));
	} else if (z <= 0.55) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((x * 6.0) + (y * -6.0))
	elif z <= 0.55:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(z * Float64(Float64(x * 6.0) + Float64(y * -6.0)));
	elseif (z <= 0.55)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = z * ((x * 6.0) + (y * -6.0));
	elseif (z <= 0.55)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(z * N[(N[(x * 6.0), $MachinePrecision] + N[(y * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 96.3%

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

      1. fma-def 99.9%

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

      2. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 98.6%

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

   if -0.599999999999999978 < 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. Step-by-step derivation

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in z around 0 96.3%

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

   if 0.55000000000000004 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 96.6%

      \[\leadsto \color{blue}{\left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right) \cdot x + 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. 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* 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in z around inf 99.3%

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

   8. Taylor expanded in x around 0 96.4%

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

      1. +-commutative 96.4%

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

      2. metadata-eval 96.4%

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

      3. distribute-lft-neg-in 96.4%

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

      4. associate-*r* 96.2%

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

      5. *-commutative 96.2%

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

      6. distribute-lft-neg-out 96.2%

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

      7. *-commutative 96.2%

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

      8. associate-*l* 96.4%

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

      9. distribute-lft-out 96.4%

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

      10. *-commutative 96.4%

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

      11. distribute-lft-in 99.4%

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

      12. sub-neg 99.4%

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

   10. Simplified 99.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 12: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 13: 38.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.2e-37) (* x -3.0) (if (<= x 4.5e-31) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e-37) {
		tmp = x * -3.0;
	} else if (x <= 4.5e-31) {
		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 <= (-2.2d-37)) then
        tmp = x * (-3.0d0)
    else if (x <= 4.5d-31) 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 <= -2.2e-37) {
		tmp = x * -3.0;
	} else if (x <= 4.5e-31) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.2e-37:
		tmp = x * -3.0
	elif x <= 4.5e-31:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.2e-37)
		tmp = Float64(x * -3.0);
	elseif (x <= 4.5e-31)
		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 <= -2.2e-37)
		tmp = x * -3.0;
	elseif (x <= 4.5e-31)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.2e-37], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 4.5e-31], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000002e-37 or 4.5000000000000004e-31 < x

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 81.1%

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

   5. Taylor expanded in z around 0 32.4%

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

      1. distribute-lft1-in 32.4%

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

      2. metadata-eval 32.4%

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

   7. Simplified 32.4%

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

   if -2.20000000000000002e-37 < x < 4.5000000000000004e-31

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 81.2%

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

   5. Taylor expanded in z around 0 40.3%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 14: 26.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in y around 0 53.4%

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

5. Taylor expanded in z around 0 21.1%

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

   1. distribute-lft1-in 21.1%

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

   2. metadata-eval 21.1%

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

7. Simplified 21.1%

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

8. Final simplification 21.1%

   \[\leadsto x \cdot -3 \]

Alternative 15: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around inf 59.7%

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

5. Taylor expanded in z around 0 2.6%

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

6. Final simplification 2.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(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))))