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

Percentage Accurate: 99.5% → 99.8%

Time: 11.1s

Alternatives: 16

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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+174} \lor \neg \left(z \leq 1.22 \cdot 10^{+201}\right) \land z \leq 6.6 \cdot 10^{+237}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -4e+225)
     t_0
     (if (<= z -4.2e+178)
       t_1
       (if (<= z -1.95e+141)
         t_0
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -6.5e-257)
             (* y 4.0)
             (if (<= z 3.1e-220)
               (* x -3.0)
               (if (<= z 3.8e-188)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (or (<= z 1.95e+174)
                           (and (not (<= z 1.22e+201)) (<= z 6.6e+237)))
                     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 <= -4e+225) {
		tmp = t_0;
	} else if (z <= -4.2e+178) {
		tmp = t_1;
	} else if (z <= -1.95e+141) {
		tmp = t_0;
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -6.5e-257) {
		tmp = y * 4.0;
	} else if (z <= 3.1e-220) {
		tmp = x * -3.0;
	} else if (z <= 3.8e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if ((z <= 1.95e+174) || (!(z <= 1.22e+201) && (z <= 6.6e+237))) {
		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 <= (-4d+225)) then
        tmp = t_0
    else if (z <= (-4.2d+178)) then
        tmp = t_1
    else if (z <= (-1.95d+141)) then
        tmp = t_0
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-6.5d-257)) then
        tmp = y * 4.0d0
    else if (z <= 3.1d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 3.8d-188) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if ((z <= 1.95d+174) .or. (.not. (z <= 1.22d+201)) .and. (z <= 6.6d+237)) 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 <= -4e+225) {
		tmp = t_0;
	} else if (z <= -4.2e+178) {
		tmp = t_1;
	} else if (z <= -1.95e+141) {
		tmp = t_0;
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -6.5e-257) {
		tmp = y * 4.0;
	} else if (z <= 3.1e-220) {
		tmp = x * -3.0;
	} else if (z <= 3.8e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if ((z <= 1.95e+174) || (!(z <= 1.22e+201) && (z <= 6.6e+237))) {
		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 <= -4e+225:
		tmp = t_0
	elif z <= -4.2e+178:
		tmp = t_1
	elif z <= -1.95e+141:
		tmp = t_0
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -6.5e-257:
		tmp = y * 4.0
	elif z <= 3.1e-220:
		tmp = x * -3.0
	elif z <= 3.8e-188:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif (z <= 1.95e+174) or (not (z <= 1.22e+201) and (z <= 6.6e+237)):
		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 <= -4e+225)
		tmp = t_0;
	elseif (z <= -4.2e+178)
		tmp = t_1;
	elseif (z <= -1.95e+141)
		tmp = t_0;
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -6.5e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.1e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.8e-188)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 1.95e+174) || (!(z <= 1.22e+201) && (z <= 6.6e+237)))
		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 <= -4e+225)
		tmp = t_0;
	elseif (z <= -4.2e+178)
		tmp = t_1;
	elseif (z <= -1.95e+141)
		tmp = t_0;
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -6.5e-257)
		tmp = y * 4.0;
	elseif (z <= 3.1e-220)
		tmp = x * -3.0;
	elseif (z <= 3.8e-188)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif ((z <= 1.95e+174) || (~((z <= 1.22e+201)) && (z <= 6.6e+237)))
		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, -4e+225], t$95$0, If[LessEqual[z, -4.2e+178], t$95$1, If[LessEqual[z, -1.95e+141], t$95$0, If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -6.5e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.1e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.8e-188], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 1.95e+174], And[N[Not[LessEqual[z, 1.22e+201]], $MachinePrecision], LessEqual[z, 6.6e+237]]], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999971e225 or -4.1999999999999997e178 < z < -1.94999999999999996e141 or 1.9499999999999999e174 < z < 1.22000000000000004e201 or 6.6000000000000001e237 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      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 78.0%

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

   5. Taylor expanded in z around inf 78.0%

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

   if -3.99999999999999971e225 < z < -4.1999999999999997e178 or -1.94999999999999996e141 < z < -7.7999999999999999e-10 or 1.1e-5 < z < 1.9499999999999999e174 or 1.22000000000000004e201 < z < 6.6000000000000001e237

   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 inf 71.1%

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

      1. sub-neg 71.1%

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

      2. distribute-rgt-in 71.1%

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

      3. metadata-eval 71.1%

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

      4. neg-mul-1 71.1%

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

      5. associate-*r* 71.1%

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

      6. *-commutative 71.1%

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

      7. associate-+r+ 71.1%

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

      8. metadata-eval 71.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 71.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 71.1%

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

      11. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in z around inf 68.2%

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

      1. *-commutative 68.2%

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

   9. Simplified 68.2%

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

   if -7.7999999999999999e-10 < z < -6.5000000000000002e-257 or 3.10000000000000011e-220 < z < 3.8e-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%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -6.5000000000000002e-257 < z < 3.10000000000000011e-220 or 3.8e-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 x around inf 64.1%

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

      1. sub-neg 64.1%

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

      2. distribute-rgt-in 64.1%

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

      3. metadata-eval 64.1%

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

      4. neg-mul-1 64.1%

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

      5. associate-*r* 64.1%

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

      6. *-commutative 64.1%

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

      7. associate-+r+ 64.1%

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

      8. metadata-eval 64.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.1%

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

      11. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

   9. Simplified 64.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+225}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+178}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+141}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+174} \lor \neg \left(z \leq 1.22 \cdot 10^{+201}\right) \land z \leq 6.6 \cdot 10^{+237}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+228}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+173}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+199} \lor \neg \left(z \leq 1.35 \cdot 10^{+237}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -1.26e+228)
     t_0
     (if (<= z -7e+177)
       t_1
       (if (<= z -7.5e+141)
         t_0
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -3e-273)
             (* y 4.0)
             (if (<= z 3.7e-220)
               (* x -3.0)
               (if (<= z 3.8e-189)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (<= z 2.45e+173)
                     (* 6.0 (* x z))
                     (if (or (<= z 1.45e+199) (not (<= z 1.35e+237)))
                       t_0
                       t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.26e+228) {
		tmp = t_0;
	} else if (z <= -7e+177) {
		tmp = t_1;
	} else if (z <= -7.5e+141) {
		tmp = t_0;
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -3e-273) {
		tmp = y * 4.0;
	} else if (z <= 3.7e-220) {
		tmp = x * -3.0;
	} else if (z <= 3.8e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 2.45e+173) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 1.45e+199) || !(z <= 1.35e+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 = x * (z * 6.0d0)
    if (z <= (-1.26d+228)) then
        tmp = t_0
    else if (z <= (-7d+177)) then
        tmp = t_1
    else if (z <= (-7.5d+141)) then
        tmp = t_0
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-3d-273)) then
        tmp = y * 4.0d0
    else if (z <= 3.7d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 3.8d-189) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if (z <= 2.45d+173) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= 1.45d+199) .or. (.not. (z <= 1.35d+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 = x * (z * 6.0);
	double tmp;
	if (z <= -1.26e+228) {
		tmp = t_0;
	} else if (z <= -7e+177) {
		tmp = t_1;
	} else if (z <= -7.5e+141) {
		tmp = t_0;
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -3e-273) {
		tmp = y * 4.0;
	} else if (z <= 3.7e-220) {
		tmp = x * -3.0;
	} else if (z <= 3.8e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 2.45e+173) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 1.45e+199) || !(z <= 1.35e+237)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -1.26e+228:
		tmp = t_0
	elif z <= -7e+177:
		tmp = t_1
	elif z <= -7.5e+141:
		tmp = t_0
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -3e-273:
		tmp = y * 4.0
	elif z <= 3.7e-220:
		tmp = x * -3.0
	elif z <= 3.8e-189:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif z <= 2.45e+173:
		tmp = 6.0 * (x * z)
	elif (z <= 1.45e+199) or not (z <= 1.35e+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(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -1.26e+228)
		tmp = t_0;
	elseif (z <= -7e+177)
		tmp = t_1;
	elseif (z <= -7.5e+141)
		tmp = t_0;
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -3e-273)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.7e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.8e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.45e+173)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= 1.45e+199) || !(z <= 1.35e+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 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -1.26e+228)
		tmp = t_0;
	elseif (z <= -7e+177)
		tmp = t_1;
	elseif (z <= -7.5e+141)
		tmp = t_0;
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -3e-273)
		tmp = y * 4.0;
	elseif (z <= 3.7e-220)
		tmp = x * -3.0;
	elseif (z <= 3.8e-189)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif (z <= 2.45e+173)
		tmp = 6.0 * (x * z);
	elseif ((z <= 1.45e+199) || ~((z <= 1.35e+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[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+228], t$95$0, If[LessEqual[z, -7e+177], t$95$1, If[LessEqual[z, -7.5e+141], t$95$0, If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -3e-273], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.7e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.8e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.45e+173], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.45e+199], N[Not[LessEqual[z, 1.35e+237]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.26e228 or -6.99999999999999983e177 < z < -7.49999999999999937e141 or 2.45e173 < z < 1.4499999999999999e199 or 1.35e237 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      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 78.0%

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

   5. Taylor expanded in z around inf 78.0%

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

   if -1.26e228 < z < -6.99999999999999983e177 or -7.49999999999999937e141 < z < -7.7999999999999999e-10 or 1.4499999999999999e199 < z < 1.35e237

   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 inf 76.9%

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

      1. sub-neg 76.9%

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

      2. distribute-rgt-in 76.9%

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

      3. metadata-eval 76.9%

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

      4. neg-mul-1 76.9%

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

      5. associate-*r* 76.9%

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

      6. *-commutative 76.9%

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

      7. associate-+r+ 76.9%

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

      8. metadata-eval 76.9%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 76.9%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 76.9%

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

      11. *-commutative 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in z around inf 71.9%

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

   if -7.7999999999999999e-10 < z < -2.99999999999999987e-273 or 3.70000000000000015e-220 < z < 3.80000000000000022e-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%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -2.99999999999999987e-273 < z < 3.70000000000000015e-220 or 3.80000000000000022e-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 x around inf 64.1%

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

      1. sub-neg 64.1%

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

      2. distribute-rgt-in 64.1%

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

      3. metadata-eval 64.1%

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

      4. neg-mul-1 64.1%

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

      5. associate-*r* 64.1%

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

      6. *-commutative 64.1%

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

      7. associate-+r+ 64.1%

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

      8. metadata-eval 64.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.1%

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

      11. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

   9. Simplified 64.1%

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

   if 1.1e-5 < z < 2.45e173

   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 inf 63.1%

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

      1. sub-neg 63.1%

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

      2. distribute-rgt-in 63.1%

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

      3. metadata-eval 63.1%

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

      4. neg-mul-1 63.1%

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

      5. associate-*r* 63.1%

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

      6. *-commutative 63.1%

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

      7. associate-+r+ 63.1%

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

      8. metadata-eval 63.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 63.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 63.1%

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

      11. *-commutative 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   9. Simplified 63.1%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+228}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+141}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+173}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+199} \lor \neg \left(z \leq 1.35 \cdot 10^{+237}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 5: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.9 \cdot 10^{-265}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+174}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+199} \lor \neg \left(z \leq 1.25 \cdot 10^{+236}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -1.2e+229)
     t_0
     (if (<= z -1.95e+178)
       t_1
       (if (<= z -1.25e+142)
         (* y (* z -6.0))
         (if (<= z -7.8e-10)
           t_1
           (if (<= z -8.9e-265)
             (* y 4.0)
             (if (<= z 5.3e-220)
               (* x -3.0)
               (if (<= z 1.45e-188)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (<= z 4e+174)
                     (* 6.0 (* x z))
                     (if (or (<= z 4.5e+199) (not (<= z 1.25e+236)))
                       t_0
                       t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -1.2e+229) {
		tmp = t_0;
	} else if (z <= -1.95e+178) {
		tmp = t_1;
	} else if (z <= -1.25e+142) {
		tmp = y * (z * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -8.9e-265) {
		tmp = y * 4.0;
	} else if (z <= 5.3e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.45e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 4e+174) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 4.5e+199) || !(z <= 1.25e+236)) {
		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 = x * (z * 6.0d0)
    if (z <= (-1.2d+229)) then
        tmp = t_0
    else if (z <= (-1.95d+178)) then
        tmp = t_1
    else if (z <= (-1.25d+142)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-7.8d-10)) then
        tmp = t_1
    else if (z <= (-8.9d-265)) then
        tmp = y * 4.0d0
    else if (z <= 5.3d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 1.45d-188) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if (z <= 4d+174) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= 4.5d+199) .or. (.not. (z <= 1.25d+236))) 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 = x * (z * 6.0);
	double tmp;
	if (z <= -1.2e+229) {
		tmp = t_0;
	} else if (z <= -1.95e+178) {
		tmp = t_1;
	} else if (z <= -1.25e+142) {
		tmp = y * (z * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = t_1;
	} else if (z <= -8.9e-265) {
		tmp = y * 4.0;
	} else if (z <= 5.3e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.45e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 4e+174) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 4.5e+199) || !(z <= 1.25e+236)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -1.2e+229:
		tmp = t_0
	elif z <= -1.95e+178:
		tmp = t_1
	elif z <= -1.25e+142:
		tmp = y * (z * -6.0)
	elif z <= -7.8e-10:
		tmp = t_1
	elif z <= -8.9e-265:
		tmp = y * 4.0
	elif z <= 5.3e-220:
		tmp = x * -3.0
	elif z <= 1.45e-188:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif z <= 4e+174:
		tmp = 6.0 * (x * z)
	elif (z <= 4.5e+199) or not (z <= 1.25e+236):
		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(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -1.2e+229)
		tmp = t_0;
	elseif (z <= -1.95e+178)
		tmp = t_1;
	elseif (z <= -1.25e+142)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -8.9e-265)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.3e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.45e-188)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif (z <= 4e+174)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= 4.5e+199) || !(z <= 1.25e+236))
		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 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -1.2e+229)
		tmp = t_0;
	elseif (z <= -1.95e+178)
		tmp = t_1;
	elseif (z <= -1.25e+142)
		tmp = y * (z * -6.0);
	elseif (z <= -7.8e-10)
		tmp = t_1;
	elseif (z <= -8.9e-265)
		tmp = y * 4.0;
	elseif (z <= 5.3e-220)
		tmp = x * -3.0;
	elseif (z <= 1.45e-188)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif (z <= 4e+174)
		tmp = 6.0 * (x * z);
	elseif ((z <= 4.5e+199) || ~((z <= 1.25e+236)))
		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[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+229], t$95$0, If[LessEqual[z, -1.95e+178], t$95$1, If[LessEqual[z, -1.25e+142], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-10], t$95$1, If[LessEqual[z, -8.9e-265], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.3e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.45e-188], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4e+174], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.5e+199], N[Not[LessEqual[z, 1.25e+236]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.2e229 or 4.00000000000000028e174 < z < 4.4999999999999997e199 or 1.24999999999999993e236 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      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 78.2%

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

   5. Taylor expanded in z around inf 78.3%

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

   if -1.2e229 < z < -1.9499999999999999e178 or -1.25e142 < z < -7.7999999999999999e-10 or 4.4999999999999997e199 < z < 1.24999999999999993e236

   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 inf 76.9%

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

      1. sub-neg 76.9%

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

      2. distribute-rgt-in 76.9%

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

      3. metadata-eval 76.9%

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

      4. neg-mul-1 76.9%

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

      5. associate-*r* 76.9%

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

      6. *-commutative 76.9%

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

      7. associate-+r+ 76.9%

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

      8. metadata-eval 76.9%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 76.9%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 76.9%

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

      11. *-commutative 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in z around inf 71.9%

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

   if -1.9499999999999999e178 < z < -1.25e142

   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%

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

   5. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -7.7999999999999999e-10 < z < -8.8999999999999999e-265 or 5.3e-220 < z < 1.4500000000000001e-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%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -8.8999999999999999e-265 < z < 5.3e-220 or 1.4500000000000001e-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 x around inf 64.1%

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

      1. sub-neg 64.1%

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

      2. distribute-rgt-in 64.1%

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

      3. metadata-eval 64.1%

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

      4. neg-mul-1 64.1%

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

      5. associate-*r* 64.1%

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

      6. *-commutative 64.1%

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

      7. associate-+r+ 64.1%

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

      8. metadata-eval 64.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.1%

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

      11. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

   9. Simplified 64.1%

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

   if 1.1e-5 < z < 4.00000000000000028e174

   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 inf 63.1%

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

      1. sub-neg 63.1%

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

      2. distribute-rgt-in 63.1%

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

      3. metadata-eval 63.1%

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

      4. neg-mul-1 63.1%

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

      5. associate-*r* 63.1%

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

      6. *-commutative 63.1%

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

      7. associate-+r+ 63.1%

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

      8. metadata-eval 63.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 63.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 63.1%

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

      11. *-commutative 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   9. Simplified 63.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+229}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -8.9 \cdot 10^{-265}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+174}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+199} \lor \neg \left(z \leq 1.25 \cdot 10^{+236}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 6: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-270}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+173}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+201} \lor \neg \left(z \leq 9.8 \cdot 10^{+235}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* x (* z 6.0))))
   (if (<= z -9.8e+225)
     t_0
     (if (<= z -5.8e+175)
       t_1
       (if (<= z -1.3e+141)
         (* y (* z -6.0))
         (if (<= z -7.8e-10)
           (* z (* x 6.0))
           (if (<= z -7.3e-270)
             (* y 4.0)
             (if (<= z 2.7e-219)
               (* x -3.0)
               (if (<= z 3.5e-189)
                 (* y 4.0)
                 (if (<= z 1.1e-5)
                   (* x -3.0)
                   (if (<= z 3.6e+173)
                     (* 6.0 (* x z))
                     (if (or (<= z 1.95e+201) (not (<= z 9.8e+235)))
                       t_0
                       t_1))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = x * (z * 6.0);
	double tmp;
	if (z <= -9.8e+225) {
		tmp = t_0;
	} else if (z <= -5.8e+175) {
		tmp = t_1;
	} else if (z <= -1.3e+141) {
		tmp = y * (z * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = z * (x * 6.0);
	} else if (z <= -7.3e-270) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-219) {
		tmp = x * -3.0;
	} else if (z <= 3.5e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 3.6e+173) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 1.95e+201) || !(z <= 9.8e+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 = x * (z * 6.0d0)
    if (z <= (-9.8d+225)) then
        tmp = t_0
    else if (z <= (-5.8d+175)) then
        tmp = t_1
    else if (z <= (-1.3d+141)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-7.8d-10)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-7.3d-270)) then
        tmp = y * 4.0d0
    else if (z <= 2.7d-219) then
        tmp = x * (-3.0d0)
    else if (z <= 3.5d-189) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-5) then
        tmp = x * (-3.0d0)
    else if (z <= 3.6d+173) then
        tmp = 6.0d0 * (x * z)
    else if ((z <= 1.95d+201) .or. (.not. (z <= 9.8d+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 = x * (z * 6.0);
	double tmp;
	if (z <= -9.8e+225) {
		tmp = t_0;
	} else if (z <= -5.8e+175) {
		tmp = t_1;
	} else if (z <= -1.3e+141) {
		tmp = y * (z * -6.0);
	} else if (z <= -7.8e-10) {
		tmp = z * (x * 6.0);
	} else if (z <= -7.3e-270) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-219) {
		tmp = x * -3.0;
	} else if (z <= 3.5e-189) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-5) {
		tmp = x * -3.0;
	} else if (z <= 3.6e+173) {
		tmp = 6.0 * (x * z);
	} else if ((z <= 1.95e+201) || !(z <= 9.8e+235)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = x * (z * 6.0)
	tmp = 0
	if z <= -9.8e+225:
		tmp = t_0
	elif z <= -5.8e+175:
		tmp = t_1
	elif z <= -1.3e+141:
		tmp = y * (z * -6.0)
	elif z <= -7.8e-10:
		tmp = z * (x * 6.0)
	elif z <= -7.3e-270:
		tmp = y * 4.0
	elif z <= 2.7e-219:
		tmp = x * -3.0
	elif z <= 3.5e-189:
		tmp = y * 4.0
	elif z <= 1.1e-5:
		tmp = x * -3.0
	elif z <= 3.6e+173:
		tmp = 6.0 * (x * z)
	elif (z <= 1.95e+201) or not (z <= 9.8e+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(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -9.8e+225)
		tmp = t_0;
	elseif (z <= -5.8e+175)
		tmp = t_1;
	elseif (z <= -1.3e+141)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -7.8e-10)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -7.3e-270)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.7e-219)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.5e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-5)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.6e+173)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((z <= 1.95e+201) || !(z <= 9.8e+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 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -9.8e+225)
		tmp = t_0;
	elseif (z <= -5.8e+175)
		tmp = t_1;
	elseif (z <= -1.3e+141)
		tmp = y * (z * -6.0);
	elseif (z <= -7.8e-10)
		tmp = z * (x * 6.0);
	elseif (z <= -7.3e-270)
		tmp = y * 4.0;
	elseif (z <= 2.7e-219)
		tmp = x * -3.0;
	elseif (z <= 3.5e-189)
		tmp = y * 4.0;
	elseif (z <= 1.1e-5)
		tmp = x * -3.0;
	elseif (z <= 3.6e+173)
		tmp = 6.0 * (x * z);
	elseif ((z <= 1.95e+201) || ~((z <= 9.8e+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[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+225], t$95$0, If[LessEqual[z, -5.8e+175], t$95$1, If[LessEqual[z, -1.3e+141], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-10], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.3e-270], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.7e-219], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.5e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.6e+173], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.95e+201], N[Not[LessEqual[z, 9.8e+235]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -9.80000000000000065e225 or 3.6000000000000002e173 < z < 1.95e201 or 9.7999999999999995e235 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      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 78.2%

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

   5. Taylor expanded in z around inf 78.3%

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

   if -9.80000000000000065e225 < z < -5.8e175 or 1.95e201 < z < 9.7999999999999995e235

   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 inf 85.9%

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

      1. sub-neg 85.9%

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

      2. distribute-rgt-in 85.9%

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

      3. metadata-eval 85.9%

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

      4. neg-mul-1 85.9%

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

      5. associate-*r* 85.9%

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

      6. *-commutative 85.9%

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

      7. associate-+r+ 85.9%

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

      8. metadata-eval 85.9%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 85.9%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 85.9%

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

      11. *-commutative 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in z around inf 85.9%

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

   if -5.8e175 < z < -1.3e141

   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%

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

   5. Taylor expanded in z around inf 76.9%

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

      1. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   if -1.3e141 < z < -7.7999999999999999e-10

   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 99.7%

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

   5. Taylor expanded in z around inf 91.6%

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

   6. Taylor expanded in y around 0 62.9%

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

   if -7.7999999999999999e-10 < z < -7.29999999999999993e-270 or 2.7e-219 < z < 3.5000000000000001e-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%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -7.29999999999999993e-270 < z < 2.7e-219 or 3.5000000000000001e-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 x around inf 64.1%

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

      1. sub-neg 64.1%

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

      2. distribute-rgt-in 64.1%

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

      3. metadata-eval 64.1%

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

      4. neg-mul-1 64.1%

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

      5. associate-*r* 64.1%

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

      6. *-commutative 64.1%

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

      7. associate-+r+ 64.1%

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

      8. metadata-eval 64.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.1%

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

      11. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

   9. Simplified 64.1%

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

   if 1.1e-5 < z < 3.6000000000000002e173

   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 inf 63.1%

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

      1. sub-neg 63.1%

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

      2. distribute-rgt-in 63.1%

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

      3. metadata-eval 63.1%

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

      4. neg-mul-1 63.1%

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

      5. associate-*r* 63.1%

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

      6. *-commutative 63.1%

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

      7. associate-+r+ 63.1%

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

      8. metadata-eval 63.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 63.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 63.1%

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

      11. *-commutative 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   9. Simplified 63.1%

      \[\leadsto \color{blue}{6 \cdot \left(z \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+225}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-270}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+173}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+201} \lor \neg \left(z \leq 9.8 \cdot 10^{+235}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-269}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -7.8e-10)
     t_0
     (if (<= z -1.95e-269)
       (* y 4.0)
       (if (<= z 1.6e-219)
         (* x -3.0)
         (if (<= z 2.4e-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 <= -1.95e-269) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-219) {
		tmp = x * -3.0;
	} else if (z <= 2.4e-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 <= (-1.95d-269)) then
        tmp = y * 4.0d0
    else if (z <= 1.6d-219) then
        tmp = x * (-3.0d0)
    else if (z <= 2.4d-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 <= -1.95e-269) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-219) {
		tmp = x * -3.0;
	} else if (z <= 2.4e-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 <= -1.95e-269:
		tmp = y * 4.0
	elif z <= 1.6e-219:
		tmp = x * -3.0
	elif z <= 2.4e-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 <= -1.95e-269)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.6e-219)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.4e-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 <= -1.95e-269)
		tmp = y * 4.0;
	elseif (z <= 1.6e-219)
		tmp = x * -3.0;
	elseif (z <= 2.4e-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, -1.95e-269], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.6e-219], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.4e-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 z around inf 97.6%

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

   5. Taylor expanded in z around inf 97.8%

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

   if -7.7999999999999999e-10 < z < -1.95e-269 or 1.59999999999999999e-219 < z < 2.4e-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%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -1.95e-269 < z < 1.59999999999999999e-219 or 2.4e-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 x around inf 60.3%

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

      1. sub-neg 60.3%

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

      2. distribute-rgt-in 60.3%

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

      3. metadata-eval 60.3%

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

      4. neg-mul-1 60.3%

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

      5. associate-*r* 60.3%

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

      6. *-commutative 60.3%

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

      7. associate-+r+ 60.3%

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

      8. metadata-eval 60.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 60.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 60.3%

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

      11. *-commutative 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-269}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-219}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -7.8e-10)
     t_0
     (if (<= z -6.8e-271)
       (* y 4.0)
       (if (<= z 5.3e-220)
         (* x -3.0)
         (if (<= z 1.05e-188)
           (* y 4.0)
           (if (<= z 1.25e+14) (* x (+ -3.0 (* z 6.0))) 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 <= -6.8e-271) {
		tmp = y * 4.0;
	} else if (z <= 5.3e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.25e+14) {
		tmp = x * (-3.0 + (z * 6.0));
	} 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 <= (-6.8d-271)) then
        tmp = y * 4.0d0
    else if (z <= 5.3d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d-188) then
        tmp = y * 4.0d0
    else if (z <= 1.25d+14) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    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 <= -6.8e-271) {
		tmp = y * 4.0;
	} else if (z <= 5.3e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-188) {
		tmp = y * 4.0;
	} else if (z <= 1.25e+14) {
		tmp = x * (-3.0 + (z * 6.0));
	} 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 <= -6.8e-271:
		tmp = y * 4.0
	elif z <= 5.3e-220:
		tmp = x * -3.0
	elif z <= 1.05e-188:
		tmp = y * 4.0
	elif z <= 1.25e+14:
		tmp = x * (-3.0 + (z * 6.0))
	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 <= -6.8e-271)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.3e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05e-188)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.25e+14)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	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 <= -6.8e-271)
		tmp = y * 4.0;
	elseif (z <= 5.3e-220)
		tmp = x * -3.0;
	elseif (z <= 1.05e-188)
		tmp = y * 4.0;
	elseif (z <= 1.25e+14)
		tmp = x * (-3.0 + (z * 6.0));
	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, -6.8e-271], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.3e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05e-188], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.25e+14], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.7999999999999999e-10 or 1.25e14 < 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 z around inf 97.8%

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

   5. Taylor expanded in z around inf 97.9%

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

   if -7.7999999999999999e-10 < z < -6.8000000000000001e-271 or 5.3e-220 < z < 1.05e-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%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -6.8000000000000001e-271 < z < 5.3e-220

   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 inf 71.8%

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

      1. sub-neg 71.8%

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

      2. distribute-rgt-in 71.8%

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

      3. metadata-eval 71.8%

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

      4. neg-mul-1 71.8%

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

      5. associate-*r* 71.8%

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

      6. *-commutative 71.8%

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

      7. associate-+r+ 71.8%

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

      8. metadata-eval 71.8%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 71.8%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 71.8%

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

      11. *-commutative 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in z around 0 71.8%

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

      1. *-commutative 71.8%

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

   9. Simplified 71.8%

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

   if 1.05e-188 < z < 1.25e14

   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 inf 56.8%

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

      1. sub-neg 56.8%

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

      2. distribute-rgt-in 56.8%

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

      3. metadata-eval 56.8%

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

      4. neg-mul-1 56.8%

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

      5. associate-*r* 56.8%

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

      6. *-commutative 56.8%

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

      7. associate-+r+ 56.8%

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

      8. metadata-eval 56.8%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 56.8%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 56.8%

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

      11. *-commutative 56.8%

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

   6. Simplified 56.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 9: 49.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3.15e+15)
     t_0
     (if (<= z -1.35e-271)
       (* y 4.0)
       (if (<= z 5.5e-220)
         (* x -3.0)
         (if (<= z 1.52e-189) (* y 4.0) (if (<= z 0.62) (* 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 <= -1.35e-271) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.52e-189) {
		tmp = y * 4.0;
	} else if (z <= 0.62) {
		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 <= (-1.35d-271)) then
        tmp = y * 4.0d0
    else if (z <= 5.5d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 1.52d-189) then
        tmp = y * 4.0d0
    else if (z <= 0.62d0) 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 <= -1.35e-271) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-220) {
		tmp = x * -3.0;
	} else if (z <= 1.52e-189) {
		tmp = y * 4.0;
	} else if (z <= 0.62) {
		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 <= -1.35e-271:
		tmp = y * 4.0
	elif z <= 5.5e-220:
		tmp = x * -3.0
	elif z <= 1.52e-189:
		tmp = y * 4.0
	elif z <= 0.62:
		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 <= -1.35e-271)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.5e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.52e-189)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.62)
		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 <= -1.35e-271)
		tmp = y * 4.0;
	elseif (z <= 5.5e-220)
		tmp = x * -3.0;
	elseif (z <= 1.52e-189)
		tmp = y * 4.0;
	elseif (z <= 0.62)
		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, -1.35e-271], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.5e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.52e-189], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.15e15 or 0.619999999999999996 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      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 52.8%

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

   5. Taylor expanded in z around inf 52.8%

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

   if -3.15e15 < z < -1.3499999999999999e-271 or 5.4999999999999999e-220 < z < 1.5199999999999999e-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%

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

   5. Taylor expanded in z around 0 59.7%

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

      1. *-commutative 59.7%

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

   7. Simplified 59.7%

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

   if -1.3499999999999999e-271 < z < 5.4999999999999999e-220 or 1.5199999999999999e-189 < z < 0.619999999999999996

   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 x around inf 60.3%

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

      1. sub-neg 60.3%

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

      2. distribute-rgt-in 60.3%

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

      3. metadata-eval 60.3%

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

      4. neg-mul-1 60.3%

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

      5. associate-*r* 60.3%

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

      6. *-commutative 60.3%

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

      7. associate-+r+ 60.3%

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

      8. metadata-eval 60.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 60.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 60.3%

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

      11. *-commutative 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   9. Simplified 60.3%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+15}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-189}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* y (+ 4.0 (* z -6.0)))))
   (if (<= y -1.28e-64)
     t_1
     (if (<= y 7.6e-104)
       t_0
       (if (<= y 1.8e-30)
         (* -6.0 (* (- y x) z))
         (if (<= y 3.1e+87) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -1.28e-64) {
		tmp = t_1;
	} else if (y <= 7.6e-104) {
		tmp = t_0;
	} else if (y <= 1.8e-30) {
		tmp = -6.0 * ((y - x) * z);
	} else if (y <= 3.1e+87) {
		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 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = y * (4.0d0 + (z * (-6.0d0)))
    if (y <= (-1.28d-64)) then
        tmp = t_1
    else if (y <= 7.6d-104) then
        tmp = t_0
    else if (y <= 1.8d-30) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (y <= 3.1d+87) 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 = x * (-3.0 + (z * 6.0));
	double t_1 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -1.28e-64) {
		tmp = t_1;
	} else if (y <= 7.6e-104) {
		tmp = t_0;
	} else if (y <= 1.8e-30) {
		tmp = -6.0 * ((y - x) * z);
	} else if (y <= 3.1e+87) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = y * (4.0 + (z * -6.0))
	tmp = 0
	if y <= -1.28e-64:
		tmp = t_1
	elif y <= 7.6e-104:
		tmp = t_0
	elif y <= 1.8e-30:
		tmp = -6.0 * ((y - x) * z)
	elif y <= 3.1e+87:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -1.28e-64)
		tmp = t_1;
	elseif (y <= 7.6e-104)
		tmp = t_0;
	elseif (y <= 1.8e-30)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (y <= 3.1e+87)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -1.28e-64)
		tmp = t_1;
	elseif (y <= 7.6e-104)
		tmp = t_0;
	elseif (y <= 1.8e-30)
		tmp = -6.0 * ((y - x) * z);
	elseif (y <= 3.1e+87)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.28e-64], t$95$1, If[LessEqual[y, 7.6e-104], t$95$0, If[LessEqual[y, 1.8e-30], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+87], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.28e-64 or 3.1e87 < y

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      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 87.3%

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

   if -1.28e-64 < y < 7.6000000000000001e-104 or 1.8000000000000002e-30 < y < 3.1e87

   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 inf 82.8%

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

      1. sub-neg 82.8%

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

      2. distribute-rgt-in 82.8%

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

      3. metadata-eval 82.8%

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

      4. neg-mul-1 82.8%

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

      5. associate-*r* 82.8%

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

      6. *-commutative 82.8%

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

      7. associate-+r+ 82.8%

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

      8. metadata-eval 82.8%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 82.8%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 82.8%

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

      11. *-commutative 82.8%

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

   6. Simplified 82.8%

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

   if 7.6000000000000001e-104 < y < 1.8000000000000002e-30

   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 z around inf 73.7%

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

   5. Taylor expanded in z around inf 74.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-30}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 11: 97.8% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* z (* (- y x) -6.0))
   (if (<= z 0.64) (+ x (* (- y x) 4.0)) (* -6.0 (* (- y x) z)))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.6d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.64d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.64) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.64:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.64)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.64)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.64], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 z around inf 98.6%

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

   5. Taylor expanded in z around inf 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l* 98.6%

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

   7. Simplified 98.6%

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

   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 z around 0 96.3%

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

   if 0.640000000000000013 < 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 z around inf 99.4%

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

   5. Taylor expanded in z around inf 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%

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

Alternative 12: 97.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} 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 * ((y - x) * (-6.0d0))
    else if (z <= 0.55d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    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 * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.55:
		tmp = (y * 4.0) + (x * -3.0)
	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(y - x) * -6.0));
	elseif (z <= 0.55)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	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 * ((y - x) * -6.0);
	elseif (z <= 0.55)
		tmp = (y * 4.0) + (x * -3.0);
	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[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $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 z around inf 98.6%

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

   5. Taylor expanded in z around inf 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l* 98.6%

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

   7. Simplified 98.6%

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

   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%

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

   5. 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 z around inf 99.4%

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

   5. Taylor expanded in z around inf 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%

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

Alternative 13: 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 14: 38.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5e-36) (* x -3.0) (if (<= x 1.35e-31) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5e-36) {
		tmp = x * -3.0;
	} else if (x <= 1.35e-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 <= (-5d-36)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.35d-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 <= -5e-36) {
		tmp = x * -3.0;
	} else if (x <= 1.35e-31) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5e-36:
		tmp = x * -3.0
	elif x <= 1.35e-31:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5e-36)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.35e-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 <= -5e-36)
		tmp = x * -3.0;
	elseif (x <= 1.35e-31)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5e-36], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.35e-31], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000004e-36 or 1.35000000000000007e-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 x around inf 81.1%

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

      1. sub-neg 81.1%

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

      2. distribute-rgt-in 81.1%

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

      3. metadata-eval 81.1%

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

      4. neg-mul-1 81.1%

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

      5. associate-*r* 81.1%

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

      6. *-commutative 81.1%

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

      7. associate-+r+ 81.1%

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

      8. metadata-eval 81.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 81.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 81.1%

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

      11. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in z around 0 32.4%

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

      1. *-commutative 32.4%

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

   9. Simplified 32.4%

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

   if -5.00000000000000004e-36 < x < 1.35000000000000007e-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%

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

   5. Taylor expanded in z around 0 40.3%

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

      1. *-commutative 40.3%

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

   7. Simplified 40.3%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 15: 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 x around inf 53.4%

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

   1. sub-neg 53.4%

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

   2. distribute-rgt-in 53.4%

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

   3. metadata-eval 53.4%

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

   4. neg-mul-1 53.4%

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

   5. associate-*r* 53.4%

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

   6. *-commutative 53.4%

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

   7. associate-+r+ 53.4%

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

   8. metadata-eval 53.4%

      \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   9. associate-*r* 53.4%

      \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

   10. metadata-eval 53.4%

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

   11. *-commutative 53.4%

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

6. Simplified 53.4%

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

7. Taylor expanded in z around 0 21.1%

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

   1. *-commutative 21.1%

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

9. Simplified 21.1%

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

10. Final simplification 21.1%

    \[\leadsto x \cdot -3 \]

Alternative 16: 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))))