Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, A

Percentage Accurate: 95.5% → 98.8%

Time: 14.1s

Alternatives: 15

Speedup: 0.9×

• 27.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+246}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 5e+246)
   (fma x 2.0 (fma t (* (* y z) -9.0) (* (* a 27.0) b)))
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 5e+246) {
		tmp = fma(x, 2.0, fma(t, ((y * z) * -9.0), ((a * 27.0) * b)));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 5e+246)
		tmp = fma(x, 2.0, fma(t, Float64(Float64(y * z) * -9.0), Float64(Float64(a * 27.0) * b)));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 5e+246], N[(x * 2.0 + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 4.99999999999999976e246

   1. Initial program 95.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. fma-neg 95.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-sub0 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      6. *-commutative 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      7. distribute-rgt-neg-in 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(-\left(y \cdot 9\right) \cdot z\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      8. fma-def 97.2%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(t, -\left(y \cdot 9\right) \cdot z, \left(a \cdot 27\right) \cdot b\right)}\right) \]

      9. *-commutative 97.2%

         \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -\color{blue}{z \cdot \left(y \cdot 9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      10. associate-*r* 97.2%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -\color{blue}{\left(z \cdot y\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      11. distribute-rgt-neg-in 97.2%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \color{blue}{\left(z \cdot y\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      12. *-commutative 97.2%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot \left(-9\right), \left(a \cdot 27\right) \cdot b\right)\right) \]

      13. metadata-eval 97.2%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]

   if 4.99999999999999976e246 < (*.f64 (*.f64 y 9) z)

   1. Initial program 77.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 77.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 77.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      3. fma-def 77.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      5. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 99.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+246}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+246}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t_1 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 5e+246)
     (+ (* (* a 27.0) b) (- (* x 2.0) (* t_1 t)))
     (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 5e+246) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 5e+246)
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t_1 * t)));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+246], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 4.99999999999999976e246

   1. Initial program 95.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   if 4.99999999999999976e246 < (*.f64 (*.f64 y 9) z)

   1. Initial program 77.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 77.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 77.1%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      3. fma-def 77.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      5. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 99.9%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+246}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 8.5e+74)
   (fma x 2.0 (+ (* t (* y (* z -9.0))) (* a (* 27.0 b))))
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 8.5e+74) {
		tmp = fma(x, 2.0, ((t * (y * (z * -9.0))) + (a * (27.0 * b))));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 8.5e+74)
		tmp = fma(x, 2.0, Float64(Float64(t * Float64(y * Float64(z * -9.0))) + Float64(a * Float64(27.0 * b))));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 8.5e+74], N[(x * 2.0 + N[(N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 8.50000000000000028e74

   1. Initial program 95.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. fma-neg 95.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-sub0 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      6. *-commutative 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      7. distribute-rgt-neg-in 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(-\left(y \cdot 9\right) \cdot z\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      8. fma-def 96.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(t, -\left(y \cdot 9\right) \cdot z, \left(a \cdot 27\right) \cdot b\right)}\right) \]

      9. *-commutative 96.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -\color{blue}{z \cdot \left(y \cdot 9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      10. associate-*r* 96.8%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -\color{blue}{\left(z \cdot y\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      11. distribute-rgt-neg-in 96.8%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \color{blue}{\left(z \cdot y\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      12. *-commutative 96.8%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot \left(-9\right), \left(a \cdot 27\right) \cdot b\right)\right) \]

      13. metadata-eval 96.8%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. fma-udef 95.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(\left(y \cdot z\right) \cdot -9\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      2. associate-*l* 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, t \cdot \color{blue}{\left(y \cdot \left(z \cdot -9\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      3. associate-*r* 95.9%

         \[\leadsto \mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   5. Applied egg-rr 95.9%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)}\right) \]

   if 8.50000000000000028e74 < (*.f64 (*.f64 y 9) z)

   1. Initial program 86.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 86.0%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      3. fma-def 86.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-*l* 94.5%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      5. *-commutative 94.5%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 94.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + a \cdot \left(27 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 4: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 10^{+254}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t_1 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 1e+254)
     (+ (* (* a 27.0) b) (- (* x 2.0) (* t_1 t)))
     (- (* x 2.0) (* 9.0 (* y (* z t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 1e+254) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * 9.0d0) * z
    if (t_1 <= 1d+254) then
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (t_1 * t))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 1e+254) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 1e+254:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t))
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 1e+254)
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t_1 * t)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 1e+254)
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+254], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 9.9999999999999994e253

   1. Initial program 95.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   if 9.9999999999999994e253 < (*.f64 (*.f64 y 9) z)

   1. Initial program 75.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around 0 89.1%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+254}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 5: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t_1 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 5e+290)
     (+ (* (* a 27.0) b) (- (* x 2.0) (* t_1 t)))
     (- (* x 2.0) (- (* (* y 9.0) (* z t)) (* a (* 27.0 b)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 5e+290) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * 9.0d0) * z
    if (t_1 <= 5d+290) then
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (t_1 * t))
    else
        tmp = (x * 2.0d0) - (((y * 9.0d0) * (z * t)) - (a * (27.0d0 * b)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 5e+290) {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 5e+290:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t))
	else:
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 5e+290)
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t_1 * t)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * Float64(z * t)) - Float64(a * Float64(27.0 * b))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 5e+290)
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t_1 * t));
	else
		tmp = (x * 2.0) - (((y * 9.0) * (z * t)) - (a * (27.0 * b)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+290], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 4.9999999999999998e290

   1. Initial program 96.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   if 4.9999999999999998e290 < (*.f64 (*.f64 y 9) z)

   1. Initial program 65.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 65.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 65.1%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 65.1%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 65.1%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 65.1%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 65.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 65.1%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 65.1%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 94.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)\\ \end{array} \]

Alternative 6: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-132}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* -9.0 (* y (* z t)))))
   (if (<= z -1.05e-77)
     t_2
     (if (<= z -1.25e-239)
       (* x 2.0)
       (if (<= z 9e-240)
         t_1
         (if (<= z 2.25e-132)
           (* x 2.0)
           (if (<= z 2.05e-107) t_1 (if (<= z 3.15e-90) (* x 2.0) t_2))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -1.05e-77) {
		tmp = t_2;
	} else if (z <= -1.25e-239) {
		tmp = x * 2.0;
	} else if (z <= 9e-240) {
		tmp = t_1;
	} else if (z <= 2.25e-132) {
		tmp = x * 2.0;
	} else if (z <= 2.05e-107) {
		tmp = t_1;
	} else if (z <= 3.15e-90) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (y * (z * t))
    if (z <= (-1.05d-77)) then
        tmp = t_2
    else if (z <= (-1.25d-239)) then
        tmp = x * 2.0d0
    else if (z <= 9d-240) then
        tmp = t_1
    else if (z <= 2.25d-132) then
        tmp = x * 2.0d0
    else if (z <= 2.05d-107) then
        tmp = t_1
    else if (z <= 3.15d-90) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -1.05e-77) {
		tmp = t_2;
	} else if (z <= -1.25e-239) {
		tmp = x * 2.0;
	} else if (z <= 9e-240) {
		tmp = t_1;
	} else if (z <= 2.25e-132) {
		tmp = x * 2.0;
	} else if (z <= 2.05e-107) {
		tmp = t_1;
	} else if (z <= 3.15e-90) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if z <= -1.05e-77:
		tmp = t_2
	elif z <= -1.25e-239:
		tmp = x * 2.0
	elif z <= 9e-240:
		tmp = t_1
	elif z <= 2.25e-132:
		tmp = x * 2.0
	elif z <= 2.05e-107:
		tmp = t_1
	elif z <= 3.15e-90:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (z <= -1.05e-77)
		tmp = t_2;
	elseif (z <= -1.25e-239)
		tmp = Float64(x * 2.0);
	elseif (z <= 9e-240)
		tmp = t_1;
	elseif (z <= 2.25e-132)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.05e-107)
		tmp = t_1;
	elseif (z <= 3.15e-90)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (z <= -1.05e-77)
		tmp = t_2;
	elseif (z <= -1.25e-239)
		tmp = x * 2.0;
	elseif (z <= 9e-240)
		tmp = t_1;
	elseif (z <= 2.25e-132)
		tmp = x * 2.0;
	elseif (z <= 2.05e-107)
		tmp = t_1;
	elseif (z <= 3.15e-90)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-77], t$95$2, If[LessEqual[z, -1.25e-239], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 9e-240], t$95$1, If[LessEqual[z, 2.25e-132], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.05e-107], t$95$1, If[LessEqual[z, 3.15e-90], N[(x * 2.0), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000008e-77 or 3.14999999999999989e-90 < z

   1. Initial program 90.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 90.2%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.4%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.4%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.4%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 90.8%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 90.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 54.3%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -1.05000000000000008e-77 < z < -1.25e-239 or 9.0000000000000003e-240 < z < 2.25e-132 or 2.05e-107 < z < 3.14999999999999989e-90

   1. Initial program 99.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.5%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. fma-neg 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-sub0 99.5%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 99.5%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 99.5%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      7. associate-*l* 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      8. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      9. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b\right)}\right) \]

      10. *-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -\color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      11. distribute-rgt-neg-in 99.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \color{blue}{\left(z \cdot t\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]

   4. Taylor expanded in x around inf 52.9%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -1.25e-239 < z < 9.0000000000000003e-240 or 2.25e-132 < z < 2.05e-107

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 99.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 99.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 99.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around inf 60.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-77}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-240}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-132}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-107}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-90}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-81}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= z -4.8e-81)
     (* -9.0 (* y (* z t)))
     (if (<= z -2.4e-239)
       (* x 2.0)
       (if (<= z 6.5e-240)
         t_1
         (if (<= z 1.85e-131)
           (* x 2.0)
           (if (<= z 2.2e-111)
             t_1
             (if (<= z 9.5e-92) (* x 2.0) (* (* z -9.0) (* y t))))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -4.8e-81) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -2.4e-239) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-240) {
		tmp = t_1;
	} else if (z <= 1.85e-131) {
		tmp = x * 2.0;
	} else if (z <= 2.2e-111) {
		tmp = t_1;
	} else if (z <= 9.5e-92) {
		tmp = x * 2.0;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (z <= (-4.8d-81)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-2.4d-239)) then
        tmp = x * 2.0d0
    else if (z <= 6.5d-240) then
        tmp = t_1
    else if (z <= 1.85d-131) then
        tmp = x * 2.0d0
    else if (z <= 2.2d-111) then
        tmp = t_1
    else if (z <= 9.5d-92) then
        tmp = x * 2.0d0
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (z <= -4.8e-81) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -2.4e-239) {
		tmp = x * 2.0;
	} else if (z <= 6.5e-240) {
		tmp = t_1;
	} else if (z <= 1.85e-131) {
		tmp = x * 2.0;
	} else if (z <= 2.2e-111) {
		tmp = t_1;
	} else if (z <= 9.5e-92) {
		tmp = x * 2.0;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if z <= -4.8e-81:
		tmp = -9.0 * (y * (z * t))
	elif z <= -2.4e-239:
		tmp = x * 2.0
	elif z <= 6.5e-240:
		tmp = t_1
	elif z <= 1.85e-131:
		tmp = x * 2.0
	elif z <= 2.2e-111:
		tmp = t_1
	elif z <= 9.5e-92:
		tmp = x * 2.0
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -4.8e-81)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -2.4e-239)
		tmp = Float64(x * 2.0);
	elseif (z <= 6.5e-240)
		tmp = t_1;
	elseif (z <= 1.85e-131)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.2e-111)
		tmp = t_1;
	elseif (z <= 9.5e-92)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -4.8e-81)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -2.4e-239)
		tmp = x * 2.0;
	elseif (z <= 6.5e-240)
		tmp = t_1;
	elseif (z <= 1.85e-131)
		tmp = x * 2.0;
	elseif (z <= 2.2e-111)
		tmp = t_1;
	elseif (z <= 9.5e-92)
		tmp = x * 2.0;
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-81], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-239], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6.5e-240], t$95$1, If[LessEqual[z, 1.85e-131], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.2e-111], t$95$1, If[LessEqual[z, 9.5e-92], N[(x * 2.0), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.7999999999999998e-81

   1. Initial program 88.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 88.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 94.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 94.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 94.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 88.1%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 59.2%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -4.7999999999999998e-81 < z < -2.39999999999999993e-239 or 6.50000000000000007e-240 < z < 1.8500000000000001e-131 or 2.2e-111 < z < 9.49999999999999946e-92

   1. Initial program 99.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.5%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. fma-neg 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-sub0 99.5%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 99.5%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 99.5%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* 99.8%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      7. associate-*l* 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      8. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      9. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b\right)}\right) \]

      10. *-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -\color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      11. distribute-rgt-neg-in 99.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \color{blue}{\left(z \cdot t\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      12. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]

   4. Taylor expanded in x around inf 52.1%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2.39999999999999993e-239 < z < 6.50000000000000007e-240 or 1.8500000000000001e-131 < z < 2.2e-111

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 99.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 99.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 99.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around inf 60.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if 9.49999999999999946e-92 < z

   1. Initial program 92.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.1%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 93.3%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 49.5%

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

      1. *-commutative 49.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} \]

      2. associate-*r* 51.6%

         \[\leadsto \color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot -9 \]

      3. associate-*l* 51.5%

         \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} \]

   6. Simplified 51.5%

      \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-81}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-240}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-131}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-111}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 8: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+72}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.15e+72)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (+ (* (* a 27.0) b) (- (* x 2.0) (* t (* 9.0 (* y z)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.15e+72) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.15d+72)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = ((a * 27.0d0) * b) + ((x * 2.0d0) - (t * (9.0d0 * (y * z))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.15e+72) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.15e+72:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.15e+72)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(Float64(a * 27.0) * b) + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.15e+72)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = ((a * 27.0) * b) + ((x * 2.0) - (t * (9.0 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.15e+72], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000001e72

   1. Initial program 81.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around 0 78.9%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -2.1500000000000001e72 < z

   1. Initial program 96.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 96.5%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+72}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 9: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;z \leq -156000:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* a (* b -27.0)))))
   (if (<= z -156000.0)
     (* -9.0 (* y (* z t)))
     (if (<= z 2.8e-86)
       t_1
       (if (<= z 1.8e-21)
         (* y (* z (* t -9.0)))
         (if (<= z 2.9e+50) t_1 (* (* z -9.0) (* y t))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -156000.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.8e-86) {
		tmp = t_1;
	} else if (z <= 1.8e-21) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.9e+50) {
		tmp = t_1;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (a * (b * (-27.0d0)))
    if (z <= (-156000.0d0)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 2.8d-86) then
        tmp = t_1
    else if (z <= 1.8d-21) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 2.9d+50) then
        tmp = t_1
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -156000.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.8e-86) {
		tmp = t_1;
	} else if (z <= 1.8e-21) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.9e+50) {
		tmp = t_1;
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (a * (b * -27.0))
	tmp = 0
	if z <= -156000.0:
		tmp = -9.0 * (y * (z * t))
	elif z <= 2.8e-86:
		tmp = t_1
	elif z <= 1.8e-21:
		tmp = y * (z * (t * -9.0))
	elif z <= 2.9e+50:
		tmp = t_1
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)))
	tmp = 0.0
	if (z <= -156000.0)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 2.8e-86)
		tmp = t_1;
	elseif (z <= 1.8e-21)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 2.9e+50)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (a * (b * -27.0));
	tmp = 0.0;
	if (z <= -156000.0)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 2.8e-86)
		tmp = t_1;
	elseif (z <= 1.8e-21)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 2.9e+50)
		tmp = t_1;
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -156000.0], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-86], t$95$1, If[LessEqual[z, 1.8e-21], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+50], t$95$1, N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -156000

   1. Initial program 85.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 85.8%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 93.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 93.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 93.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 93.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 85.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 63.7%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -156000 < z < 2.80000000000000009e-86 or 1.79999999999999995e-21 < z < 2.9e50

   1. Initial program 99.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.7%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.7%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.7%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 86.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 86.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*l* 86.3%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 86.3%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   if 2.80000000000000009e-86 < z < 1.79999999999999995e-21

   1. Initial program 93.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 93.8%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 93.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} \]

      2. *-commutative 44.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 \]

      3. associate-*l* 44.7%

         \[\leadsto \color{blue}{y \cdot \left(\left(z \cdot t\right) \cdot -9\right)} \]

      4. associate-*r* 44.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

   if 2.9e50 < z

   1. Initial program 89.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 89.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 90.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 90.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 90.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 92.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 92.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 92.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 92.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 91.0%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 60.7%

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

      1. *-commutative 60.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} \]

      2. associate-*r* 64.2%

         \[\leadsto \color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot -9 \]

      3. associate-*l* 64.2%

         \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -156000:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-86}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 10: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -850:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-86}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -850.0)
   (* -9.0 (* y (* z t)))
   (if (<= z 2.3e-86)
     (- (* x 2.0) (* b (* a -27.0)))
     (if (<= z 9.5e-22)
       (* y (* z (* t -9.0)))
       (if (<= z 2.6e+50)
         (- (* x 2.0) (* a (* b -27.0)))
         (* (* z -9.0) (* y t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -850.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.3e-86) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (z <= 9.5e-22) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.6e+50) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-850.0d0)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 2.3d-86) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else if (z <= 9.5d-22) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 2.6d+50) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (z * (-9.0d0)) * (y * t)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -850.0) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.3e-86) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (z <= 9.5e-22) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.6e+50) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (z * -9.0) * (y * t);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -850.0:
		tmp = -9.0 * (y * (z * t))
	elif z <= 2.3e-86:
		tmp = (x * 2.0) - (b * (a * -27.0))
	elif z <= 9.5e-22:
		tmp = y * (z * (t * -9.0))
	elif z <= 2.6e+50:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (z * -9.0) * (y * t)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -850.0)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 2.3e-86)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	elseif (z <= 9.5e-22)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 2.6e+50)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(z * -9.0) * Float64(y * t));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -850.0)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 2.3e-86)
		tmp = (x * 2.0) - (b * (a * -27.0));
	elseif (z <= 9.5e-22)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 2.6e+50)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (z * -9.0) * (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -850.0], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e-86], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-22], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+50], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * -9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -850

   1. Initial program 86.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 93.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 86.1%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 64.3%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -850 < z < 2.29999999999999996e-86

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 87.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 87.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*l* 87.6%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 87.6%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   7. Taylor expanded in a around 0 87.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 87.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(-27 \cdot a\right) \cdot b} \]

      2. *-commutative 87.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot -27\right)} \cdot b \]

      3. *-commutative 87.7%

         \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   9. Simplified 87.7%

      \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   if 2.29999999999999996e-86 < z < 9.4999999999999994e-22

   1. Initial program 93.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 93.8%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.8%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 93.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 93.7%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} \]

      2. *-commutative 44.7%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 \]

      3. associate-*l* 44.7%

         \[\leadsto \color{blue}{y \cdot \left(\left(z \cdot t\right) \cdot -9\right)} \]

      4. associate-*r* 44.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

   if 9.4999999999999994e-22 < z < 2.6000000000000002e50

   1. Initial program 99.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.7%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.7%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.7%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.7%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.7%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 82.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 82.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*l* 82.7%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 82.7%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   if 2.6000000000000002e50 < z

   1. Initial program 89.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 89.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 90.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 90.6%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 90.7%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 92.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 92.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 92.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 92.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 91.0%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in y around inf 60.7%

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

      1. *-commutative 60.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} \]

      2. associate-*r* 64.2%

         \[\leadsto \color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot -9 \]

      3. associate-*l* 64.2%

         \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -850:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-86}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -9\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 11: 79.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-109} \lor \neg \left(z \leq 1.15 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e-109) (not (<= z 1.15e-86)))
   (+ (* x 2.0) (* z (* y (* t -9.0))))
   (- (* x 2.0) (* b (* a -27.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-109) || !(z <= 1.15e-86)) {
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	} else {
		tmp = (x * 2.0) - (b * (a * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.4d-109)) .or. (.not. (z <= 1.15d-86))) then
        tmp = (x * 2.0d0) + (z * (y * (t * (-9.0d0))))
    else
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e-109) || !(z <= 1.15e-86)) {
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	} else {
		tmp = (x * 2.0) - (b * (a * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.4e-109) or not (z <= 1.15e-86):
		tmp = (x * 2.0) + (z * (y * (t * -9.0)))
	else:
		tmp = (x * 2.0) - (b * (a * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.4e-109) || !(z <= 1.15e-86))
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.4e-109) || ~((z <= 1.15e-86)))
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	else
		tmp = (x * 2.0) - (b * (a * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.4e-109], N[Not[LessEqual[z, 1.15e-86]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999999e-109 or 1.14999999999999998e-86 < z

   1. Initial program 90.5%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 90.5%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 94.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 94.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 94.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.6%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 91.1%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 91.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around 0 74.3%

      \[\leadsto \color{blue}{2 \cdot x + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 74.3%

         \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + 2 \cdot x} \]

      2. *-commutative 74.3%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} + 2 \cdot x \]

      3. *-commutative 74.3%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 + 2 \cdot x \]

      4. associate-*r* 70.9%

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot -9 + 2 \cdot x \]

      5. associate-*r* 70.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)} + 2 \cdot x \]

      6. *-commutative 70.9%

         \[\leadsto \left(y \cdot z\right) \cdot \left(t \cdot -9\right) + \color{blue}{x \cdot 2} \]

      7. fma-def 70.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, x \cdot 2\right)} \]

      8. *-commutative 70.9%

         \[\leadsto \mathsf{fma}\left(y \cdot z, t \cdot -9, \color{blue}{2 \cdot x}\right) \]

   6. Simplified 70.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 70.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right) + 2 \cdot x} \]

      2. *-commutative 70.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot \left(t \cdot -9\right) + 2 \cdot x \]

      3. associate-*l* 74.8%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right)} + 2 \cdot x \]

   8. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right) + 2 \cdot x} \]

   if -4.3999999999999999e-109 < z < 1.14999999999999998e-86

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*l* 89.3%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 89.3%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   7. Taylor expanded in a around 0 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(-27 \cdot a\right) \cdot b} \]

      2. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot -27\right)} \cdot b \]

      3. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   9. Simplified 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-109} \lor \neg \left(z \leq 1.15 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \]

Alternative 12: 79.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-110}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.8e-110)
   (+ (* x 2.0) (* z (* y (* t -9.0))))
   (if (<= z 1.15e-87)
     (- (* x 2.0) (* b (* a -27.0)))
     (+ (* x 2.0) (* (* y z) (* t -9.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e-110) {
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	} else if (z <= 1.15e-87) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.8d-110)) then
        tmp = (x * 2.0d0) + (z * (y * (t * (-9.0d0))))
    else if (z <= 1.15d-87) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e-110) {
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	} else if (z <= 1.15e-87) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.8e-110:
		tmp = (x * 2.0) + (z * (y * (t * -9.0)))
	elif z <= 1.15e-87:
		tmp = (x * 2.0) - (b * (a * -27.0))
	else:
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.8e-110)
		tmp = Float64(Float64(x * 2.0) + Float64(z * Float64(y * Float64(t * -9.0))));
	elseif (z <= 1.15e-87)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.8e-110)
		tmp = (x * 2.0) + (z * (y * (t * -9.0)));
	elseif (z <= 1.15e-87)
		tmp = (x * 2.0) - (b * (a * -27.0));
	else
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.8e-110], N[(N[(x * 2.0), $MachinePrecision] + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-87], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8000000000000005e-110

   1. Initial program 88.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 88.8%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 95.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 95.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 94.9%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 88.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around 0 76.6%

      \[\leadsto \color{blue}{2 \cdot x + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 76.6%

         \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + 2 \cdot x} \]

      2. *-commutative 76.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} + 2 \cdot x \]

      3. *-commutative 76.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 + 2 \cdot x \]

      4. associate-*r* 70.7%

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot -9 + 2 \cdot x \]

      5. associate-*r* 70.7%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)} + 2 \cdot x \]

      6. *-commutative 70.7%

         \[\leadsto \left(y \cdot z\right) \cdot \left(t \cdot -9\right) + \color{blue}{x \cdot 2} \]

      7. fma-def 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, x \cdot 2\right)} \]

      8. *-commutative 70.7%

         \[\leadsto \mathsf{fma}\left(y \cdot z, t \cdot -9, \color{blue}{2 \cdot x}\right) \]

   6. Simplified 70.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 70.7%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right) + 2 \cdot x} \]

      2. *-commutative 70.7%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot \left(t \cdot -9\right) + 2 \cdot x \]

      3. associate-*l* 75.4%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right)} + 2 \cdot x \]

   8. Applied egg-rr 75.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right) + 2 \cdot x} \]

   if -5.8000000000000005e-110 < z < 1.1500000000000001e-87

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*l* 89.3%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 89.3%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   7. Taylor expanded in a around 0 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(-27 \cdot a\right) \cdot b} \]

      2. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot -27\right)} \cdot b \]

      3. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   9. Simplified 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   if 1.1500000000000001e-87 < z

   1. Initial program 92.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.1%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 93.3%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around 0 72.1%

      \[\leadsto \color{blue}{2 \cdot x + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + 2 \cdot x} \]

      2. *-commutative 72.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} + 2 \cdot x \]

      3. *-commutative 72.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 + 2 \cdot x \]

      4. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot -9 + 2 \cdot x \]

      5. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)} + 2 \cdot x \]

      6. *-commutative 71.1%

         \[\leadsto \left(y \cdot z\right) \cdot \left(t \cdot -9\right) + \color{blue}{x \cdot 2} \]

      7. fma-def 71.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, x \cdot 2\right)} \]

      8. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(y \cdot z, t \cdot -9, \color{blue}{2 \cdot x}\right) \]

   6. Simplified 71.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 71.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right) + 2 \cdot x} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot \left(t \cdot -9\right) + 2 \cdot x \]

      3. associate-*l* 74.2%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right)} + 2 \cdot x \]

   8. Applied egg-rr 74.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right) + 2 \cdot x} \]

   9. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} + 2 \cdot x \]
   10. Step-by-step derivation

       1. *-commutative 72.1%

          \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} + 2 \cdot x \]

       2. associate-*r* 71.1%

          \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(z \cdot y\right)\right)} + 2 \cdot x \]

       3. associate-*r* 71.1%

          \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(z \cdot y\right)} + 2 \cdot x \]

       4. *-commutative 71.1%

          \[\leadsto \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)} + 2 \cdot x \]

   11. Simplified 71.1%

       \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} + 2 \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-110}:\\ \;\;\;\;x \cdot 2 + z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 13: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-110}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.85e-110)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= z 3.8e-87)
     (- (* x 2.0) (* b (* a -27.0)))
     (+ (* x 2.0) (* (* y z) (* t -9.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e-110) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 3.8e-87) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.85d-110)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (z <= 3.8d-87) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else
        tmp = (x * 2.0d0) + ((y * z) * (t * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e-110) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 3.8e-87) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else {
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.85e-110:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif z <= 3.8e-87:
		tmp = (x * 2.0) - (b * (a * -27.0))
	else:
		tmp = (x * 2.0) + ((y * z) * (t * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.85e-110)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 3.8e-87)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(y * z) * Float64(t * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.85e-110)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (z <= 3.8e-87)
		tmp = (x * 2.0) - (b * (a * -27.0));
	else
		tmp = (x * 2.0) + ((y * z) * (t * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.85e-110], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-87], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85000000000000008e-110

   1. Initial program 88.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around 0 76.6%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if -1.85000000000000008e-110 < z < 3.8e-87

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.6%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.6%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.6%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.6%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.8%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*l* 89.3%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 89.3%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   7. Taylor expanded in a around 0 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(-27 \cdot a\right) \cdot b} \]

      2. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot -27\right)} \cdot b \]

      3. *-commutative 89.4%

         \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   9. Simplified 89.4%

      \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   if 3.8e-87 < z

   1. Initial program 92.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 93.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 93.0%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 93.1%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.2%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 93.3%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around 0 72.1%

      \[\leadsto \color{blue}{2 \cdot x + -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + 2 \cdot x} \]

      2. *-commutative 72.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} + 2 \cdot x \]

      3. *-commutative 72.1%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 + 2 \cdot x \]

      4. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot -9 + 2 \cdot x \]

      5. associate-*r* 71.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right)} + 2 \cdot x \]

      6. *-commutative 71.1%

         \[\leadsto \left(y \cdot z\right) \cdot \left(t \cdot -9\right) + \color{blue}{x \cdot 2} \]

      7. fma-def 71.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, x \cdot 2\right)} \]

      8. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(y \cdot z, t \cdot -9, \color{blue}{2 \cdot x}\right) \]

   6. Simplified 71.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, t \cdot -9, 2 \cdot x\right)} \]
   7. Step-by-step derivation

      1. fma-udef 71.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(t \cdot -9\right) + 2 \cdot x} \]

      2. *-commutative 71.1%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot \left(t \cdot -9\right) + 2 \cdot x \]

      3. associate-*l* 74.2%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right)} + 2 \cdot x \]

   8. Applied egg-rr 74.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(t \cdot -9\right)\right) + 2 \cdot x} \]

   9. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} + 2 \cdot x \]
   10. Step-by-step derivation

       1. *-commutative 72.1%

          \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} + 2 \cdot x \]

       2. associate-*r* 71.1%

          \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(z \cdot y\right)\right)} + 2 \cdot x \]

       3. associate-*r* 71.1%

          \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(z \cdot y\right)} + 2 \cdot x \]

       4. *-commutative 71.1%

          \[\leadsto \left(-9 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)} + 2 \cdot x \]

   11. Simplified 71.1%

       \[\leadsto \color{blue}{\left(-9 \cdot t\right) \cdot \left(y \cdot z\right)} + 2 \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-110}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(y \cdot z\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 14: 47.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+106)
   (* x 2.0)
   (if (<= x 1.8e+19) (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+106) {
		tmp = x * 2.0;
	} else if (x <= 1.8e+19) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.5d+106)) then
        tmp = x * 2.0d0
    else if (x <= 1.8d+19) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+106) {
		tmp = x * 2.0;
	} else if (x <= 1.8e+19) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.5e+106:
		tmp = x * 2.0
	elif x <= 1.8e+19:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+106)
		tmp = Float64(x * 2.0);
	elseif (x <= 1.8e+19)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.5e+106)
		tmp = x * 2.0;
	elseif (x <= 1.8e+19)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+106], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 1.8e+19], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e106 or 1.8e19 < x

   1. Initial program 94.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.1%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. fma-neg 94.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-sub0 94.1%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 94.1%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 94.1%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      6. associate-*l* 97.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      7. associate-*l* 97.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      8. distribute-rgt-neg-in 97.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      9. fma-def 97.9%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b\right)}\right) \]

      10. *-commutative 97.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -\color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      11. distribute-rgt-neg-in 97.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \color{blue}{\left(z \cdot t\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      12. metadata-eval 97.9%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   3. Simplified 97.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]

   4. Taylor expanded in x around inf 60.6%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -2.4999999999999999e106 < x < 1.8e19

   1. Initial program 93.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 93.6%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*r* 94.9%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      3. *-commutative 94.9%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      4. associate-*r* 94.9%

         \[\leadsto \left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      5. fma-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

      6. cancel-sign-sub-inv 94.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{x \cdot 2 + \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

      7. fma-def 94.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \color{blue}{\mathsf{fma}\left(x, 2, \left(-9\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)}\right) \]

      8. metadata-eval 94.9%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, \color{blue}{-9} \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\right) \]

      9. associate-*r* 93.5%

         \[\leadsto \mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}\right)\right) \]

   3. Applied egg-rr 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, \mathsf{fma}\left(x, 2, -9 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)\right)} \]

   4. Taylor expanded in a around inf 44.8%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 15: 30.6% accurate, 5.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * 2.0d0
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. associate-+l- 93.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

   2. fma-neg 93.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

   3. neg-sub0 93.8%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

   4. associate-+l- 93.8%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

   5. neg-sub0 93.8%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

   6. associate-*l* 96.1%

      \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

   7. associate-*l* 96.1%

      \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

   8. distribute-rgt-neg-in 96.1%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]

   9. fma-def 96.4%

      \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(y, -9 \cdot \left(z \cdot t\right), \left(a \cdot 27\right) \cdot b\right)}\right) \]

   10. *-commutative 96.4%

       \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, -\color{blue}{\left(z \cdot t\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   11. distribute-rgt-neg-in 96.4%

       \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \color{blue}{\left(z \cdot t\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   12. metadata-eval 96.4%

       \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \left(z \cdot t\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]

4. Taylor expanded in x around inf 31.7%

   \[\leadsto \color{blue}{2 \cdot x} \]

5. Final simplification 31.7%

   \[\leadsto x \cdot 2 \]

Developer target: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))