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

Percentage Accurate: 95.3% → 98.5%

Time: 16.1s

Alternatives: 15

Speedup: 1.0×

• 27.7% 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: 95.3% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -2e+76)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (fma x 2.0 (fma t (* (* y z) -9.0) (* b (* a 27.0))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -2e+76) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = fma(x, 2.0, fma(t, ((y * z) * -9.0), (b * (a * 27.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -2e+76)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = fma(x, 2.0, fma(t, Float64(Float64(y * z) * -9.0), Float64(b * Float64(a * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -2e+76], 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], N[(x * 2.0 + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -2.0000000000000001e76

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-*l* 88.4%

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

      3. fma-def 88.4%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      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%

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

   if -2.0000000000000001e76 < (*.f64 y 9)

   1. Initial program 96.1%

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

      1. associate-+l- 96.1%

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

      2. fma-neg 96.1%

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

      3. neg-sub0 96.1%

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

      4. associate-+l- 96.1%

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

      5. neg-sub0 96.1%

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

      6. *-commutative 96.1%

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

      7. distribute-rgt-neg-in 96.1%

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

      8. fma-def 96.1%

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

      9. *-commutative 96.1%

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

      10. associate-*r* 96.1%

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

      11. distribute-rgt-neg-in 96.1%

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

      12. *-commutative 96.1%

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

      13. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -2e+76)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (+ (- (* x 2.0) (* t (* 9.0 (* y z)))) (* b (* a 27.0)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -2e+76) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -2e+76)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(y * z)))) + Float64(b * Float64(a * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -2e+76], 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], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -2.0000000000000001e76

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-*l* 88.4%

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

      3. fma-def 88.4%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      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%

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

   if -2.0000000000000001e76 < (*.f64 y 9)

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 96.1%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(9 \cdot \left(y \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 3: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot t_1\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 2e+304)
     (+ (- (* x 2.0) (* t t_1)) (* b (* a 27.0)))
     (- (* x 2.0) (* z (* (* y 9.0) t))))))

C

assert(y < z && z < t);
assert(a < b);
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 <= 2e+304) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = (x * 2.0) - (z * ((y * 9.0) * t));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 <= 2d+304) then
        tmp = ((x * 2.0d0) - (t * t_1)) + (b * (a * 27.0d0))
    else
        tmp = (x * 2.0d0) - (z * ((y * 9.0d0) * t))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
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 <= 2e+304) {
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	} else {
		tmp = (x * 2.0) - (z * ((y * 9.0) * t));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 2e+304:
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0))
	else:
		tmp = (x * 2.0) - (z * ((y * 9.0) * t))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 2e+304)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t * t_1)) + Float64(b * Float64(a * 27.0)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(z * Float64(Float64(y * 9.0) * t)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 2e+304)
		tmp = ((x * 2.0) - (t * t_1)) + (b * (a * 27.0));
	else
		tmp = (x * 2.0) - (z * ((y * 9.0) * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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, 2e+304], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(N[(y * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1.9999999999999999e304

   1. Initial program 97.4%

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

   if 1.9999999999999999e304 < (*.f64 (*.f64 y 9) z)

   1. Initial program 57.5%

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

   2. Taylor expanded in y around 0 57.5%

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

      1. associate-+l- 57.5%

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

      2. associate-*r* 57.5%

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

      3. *-commutative 57.5%

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

      4. associate-*r* 57.5%

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

      5. associate-*l* 88.7%

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

      6. *-commutative 88.7%

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

      7. *-commutative 88.7%

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

      8. associate-*r* 88.7%

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

      9. associate-*r* 88.7%

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

   4. Applied egg-rr 88.7%

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

   5. Taylor expanded in y around inf 94.3%

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

      1. associate-*r* 94.3%

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

      2. associate-*r* 94.2%

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

      3. *-commutative 94.2%

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

      4. *-commutative 94.2%

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

      5. *-commutative 94.2%

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

      6. associate-*l* 94.2%

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

   7. Simplified 94.2%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\\ \end{array} \]

Alternative 4: 47.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 (<= x -1.45e+69)
     (* x 2.0)
     (if (<= x -3.4e-107)
       t_2
       (if (<= x -1.2e-289)
         t_1
         (if (<= x 2.8e-171)
           t_2
           (if (<= x 1.02e-104)
             (* b (* a 27.0))
             (if (<= x 4.4e+21) t_2 (if (<= x 3.5e+56) t_1 (* x 2.0))))))))))

C

assert(y < z && z < t);
assert(a < b);
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 (x <= -1.45e+69) {
		tmp = x * 2.0;
	} else if (x <= -3.4e-107) {
		tmp = t_2;
	} else if (x <= -1.2e-289) {
		tmp = t_1;
	} else if (x <= 2.8e-171) {
		tmp = t_2;
	} else if (x <= 1.02e-104) {
		tmp = b * (a * 27.0);
	} else if (x <= 4.4e+21) {
		tmp = t_2;
	} else if (x <= 3.5e+56) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 (x <= (-1.45d+69)) then
        tmp = x * 2.0d0
    else if (x <= (-3.4d-107)) then
        tmp = t_2
    else if (x <= (-1.2d-289)) then
        tmp = t_1
    else if (x <= 2.8d-171) then
        tmp = t_2
    else if (x <= 1.02d-104) then
        tmp = b * (a * 27.0d0)
    else if (x <= 4.4d+21) then
        tmp = t_2
    else if (x <= 3.5d+56) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
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 (x <= -1.45e+69) {
		tmp = x * 2.0;
	} else if (x <= -3.4e-107) {
		tmp = t_2;
	} else if (x <= -1.2e-289) {
		tmp = t_1;
	} else if (x <= 2.8e-171) {
		tmp = t_2;
	} else if (x <= 1.02e-104) {
		tmp = b * (a * 27.0);
	} else if (x <= 4.4e+21) {
		tmp = t_2;
	} else if (x <= 3.5e+56) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if x <= -1.45e+69:
		tmp = x * 2.0
	elif x <= -3.4e-107:
		tmp = t_2
	elif x <= -1.2e-289:
		tmp = t_1
	elif x <= 2.8e-171:
		tmp = t_2
	elif x <= 1.02e-104:
		tmp = b * (a * 27.0)
	elif x <= 4.4e+21:
		tmp = t_2
	elif x <= 3.5e+56:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
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 (x <= -1.45e+69)
		tmp = Float64(x * 2.0);
	elseif (x <= -3.4e-107)
		tmp = t_2;
	elseif (x <= -1.2e-289)
		tmp = t_1;
	elseif (x <= 2.8e-171)
		tmp = t_2;
	elseif (x <= 1.02e-104)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= 4.4e+21)
		tmp = t_2;
	elseif (x <= 3.5e+56)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
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 (x <= -1.45e+69)
		tmp = x * 2.0;
	elseif (x <= -3.4e-107)
		tmp = t_2;
	elseif (x <= -1.2e-289)
		tmp = t_1;
	elseif (x <= 2.8e-171)
		tmp = t_2;
	elseif (x <= 1.02e-104)
		tmp = b * (a * 27.0);
	elseif (x <= 4.4e+21)
		tmp = t_2;
	elseif (x <= 3.5e+56)
		tmp = t_1;
	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.
NOTE: a and b 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[x, -1.45e+69], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -3.4e-107], t$95$2, If[LessEqual[x, -1.2e-289], t$95$1, If[LessEqual[x, 2.8e-171], t$95$2, If[LessEqual[x, 1.02e-104], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+21], t$95$2, If[LessEqual[x, 3.5e+56], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4499999999999999e69 or 3.49999999999999999e56 < x

   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. Taylor expanded in x around inf 61.8%

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

   if -1.4499999999999999e69 < x < -3.39999999999999994e-107 or -1.19999999999999997e-289 < x < 2.80000000000000023e-171 or 1.02000000000000001e-104 < x < 4.4e21

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 56.5%

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

   if -3.39999999999999994e-107 < x < -1.19999999999999997e-289 or 4.4e21 < x < 3.49999999999999999e56

   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. Taylor expanded in a around inf 67.8%

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

   if 2.80000000000000023e-171 < x < 1.02000000000000001e-104

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 80.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 80.0%

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

      2. associate-*r* 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 80.1%

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

      5. metadata-eval 80.1%

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

      6. associate-*r* 87.0%

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

   4. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + -9 \cdot \left(\left(y \cdot t\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 48.7%

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

      2. sqrt-unprod 79.3%

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

      3. swap-sqr 79.3%

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

      4. metadata-eval 79.3%

         \[\leadsto a \cdot \left(27 \cdot b\right) + \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      5. metadata-eval 79.3%

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

      6. swap-sqr 79.3%

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

      7. sqrt-unprod 41.0%

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

      8. add-sqr-sqrt 56.5%

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

      9. metadata-eval 56.5%

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

      10. cancel-sign-sub-inv 56.5%

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

      11. add-sqr-sqrt 25.8%

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

      12. sqrt-unprod 56.8%

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

      13. swap-sqr 56.8%

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

      14. metadata-eval 56.8%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      15. metadata-eval 56.8%

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

      16. swap-sqr 56.8%

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

      17. sqrt-unprod 48.7%

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

   6. Applied egg-rr 80.1%

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

   7. Taylor expanded in a around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*l* 64.7%

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

      4. *-commutative 64.7%

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

   9. Simplified 64.7%

      \[\leadsto \color{blue}{b \cdot \left(27 \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+69}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-107}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-289}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-171}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+56}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 5: 47.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 (* y (* -9.0 (* z t)))))
   (if (<= x -1.35e+69)
     (* x 2.0)
     (if (<= x -6.8e-108)
       t_2
       (if (<= x -2.4e-288)
         t_1
         (if (<= x 3.4e-181)
           t_2
           (if (<= x 2.5e-105)
             (* b (* a 27.0))
             (if (<= x 4.4e+21)
               (* -9.0 (* y (* z t)))
               (if (<= x 5.5e+55) t_1 (* x 2.0))))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = y * (-9.0 * (z * t));
	double tmp;
	if (x <= -1.35e+69) {
		tmp = x * 2.0;
	} else if (x <= -6.8e-108) {
		tmp = t_2;
	} else if (x <= -2.4e-288) {
		tmp = t_1;
	} else if (x <= 3.4e-181) {
		tmp = t_2;
	} else if (x <= 2.5e-105) {
		tmp = b * (a * 27.0);
	} else if (x <= 4.4e+21) {
		tmp = -9.0 * (y * (z * t));
	} else if (x <= 5.5e+55) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 = y * ((-9.0d0) * (z * t))
    if (x <= (-1.35d+69)) then
        tmp = x * 2.0d0
    else if (x <= (-6.8d-108)) then
        tmp = t_2
    else if (x <= (-2.4d-288)) then
        tmp = t_1
    else if (x <= 3.4d-181) then
        tmp = t_2
    else if (x <= 2.5d-105) then
        tmp = b * (a * 27.0d0)
    else if (x <= 4.4d+21) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (x <= 5.5d+55) then
        tmp = t_1
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
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 = y * (-9.0 * (z * t));
	double tmp;
	if (x <= -1.35e+69) {
		tmp = x * 2.0;
	} else if (x <= -6.8e-108) {
		tmp = t_2;
	} else if (x <= -2.4e-288) {
		tmp = t_1;
	} else if (x <= 3.4e-181) {
		tmp = t_2;
	} else if (x <= 2.5e-105) {
		tmp = b * (a * 27.0);
	} else if (x <= 4.4e+21) {
		tmp = -9.0 * (y * (z * t));
	} else if (x <= 5.5e+55) {
		tmp = t_1;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = y * (-9.0 * (z * t))
	tmp = 0
	if x <= -1.35e+69:
		tmp = x * 2.0
	elif x <= -6.8e-108:
		tmp = t_2
	elif x <= -2.4e-288:
		tmp = t_1
	elif x <= 3.4e-181:
		tmp = t_2
	elif x <= 2.5e-105:
		tmp = b * (a * 27.0)
	elif x <= 4.4e+21:
		tmp = -9.0 * (y * (z * t))
	elif x <= 5.5e+55:
		tmp = t_1
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(y * Float64(-9.0 * Float64(z * t)))
	tmp = 0.0
	if (x <= -1.35e+69)
		tmp = Float64(x * 2.0);
	elseif (x <= -6.8e-108)
		tmp = t_2;
	elseif (x <= -2.4e-288)
		tmp = t_1;
	elseif (x <= 3.4e-181)
		tmp = t_2;
	elseif (x <= 2.5e-105)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (x <= 4.4e+21)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (x <= 5.5e+55)
		tmp = t_1;
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = y * (-9.0 * (z * t));
	tmp = 0.0;
	if (x <= -1.35e+69)
		tmp = x * 2.0;
	elseif (x <= -6.8e-108)
		tmp = t_2;
	elseif (x <= -2.4e-288)
		tmp = t_1;
	elseif (x <= 3.4e-181)
		tmp = t_2;
	elseif (x <= 2.5e-105)
		tmp = b * (a * 27.0);
	elseif (x <= 4.4e+21)
		tmp = -9.0 * (y * (z * t));
	elseif (x <= 5.5e+55)
		tmp = t_1;
	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.
NOTE: a and b 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[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+69], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, -6.8e-108], t$95$2, If[LessEqual[x, -2.4e-288], t$95$1, If[LessEqual[x, 3.4e-181], t$95$2, If[LessEqual[x, 2.5e-105], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+21], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+55], t$95$1, N[(x * 2.0), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.3499999999999999e69 or 5.5000000000000004e55 < x

   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. Taylor expanded in x around inf 61.8%

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

   if -1.3499999999999999e69 < x < -6.80000000000000004e-108 or -2.3999999999999998e-288 < x < 3.4e-181

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 57.9%

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

      4. *-commutative 57.9%

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

      5. *-commutative 57.9%

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

   4. Simplified 57.9%

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

   if -6.80000000000000004e-108 < x < -2.3999999999999998e-288 or 4.4e21 < x < 5.5000000000000004e55

   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. Taylor expanded in a around inf 67.8%

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

   if 3.4e-181 < x < 2.49999999999999982e-105

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 80.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 80.0%

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

      2. associate-*r* 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 80.1%

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

      5. metadata-eval 80.1%

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

      6. associate-*r* 87.0%

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

   4. Applied egg-rr 87.0%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + -9 \cdot \left(\left(y \cdot t\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 48.7%

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

      2. sqrt-unprod 79.3%

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

      3. swap-sqr 79.3%

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

      4. metadata-eval 79.3%

         \[\leadsto a \cdot \left(27 \cdot b\right) + \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      5. metadata-eval 79.3%

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

      6. swap-sqr 79.3%

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

      7. sqrt-unprod 41.0%

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

      8. add-sqr-sqrt 56.5%

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

      9. metadata-eval 56.5%

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

      10. cancel-sign-sub-inv 56.5%

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

      11. add-sqr-sqrt 25.8%

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

      12. sqrt-unprod 56.8%

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

      13. swap-sqr 56.8%

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

      14. metadata-eval 56.8%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      15. metadata-eval 56.8%

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

      16. swap-sqr 56.8%

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

      17. sqrt-unprod 48.7%

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

   6. Applied egg-rr 80.1%

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

   7. Taylor expanded in a around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*l* 64.7%

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

      4. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if 2.49999999999999982e-105 < x < 4.4e21

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf 52.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+55}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 6: 46.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-216}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-208}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+60}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.5e-79)
   (* y (* -9.0 (* z t)))
   (if (<= z -5.6e-216)
     (* x 2.0)
     (if (<= z 3.5e-307)
       (* b (* a 27.0))
       (if (<= z 1.4e-208)
         (* x 2.0)
         (if (<= z 1.3e-140)
           (* y (* z (* t -9.0)))
           (if (<= z 1.85e+60) (* x 2.0) (* z (* t (* y -9.0))))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e-79) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= -5.6e-216) {
		tmp = x * 2.0;
	} else if (z <= 3.5e-307) {
		tmp = b * (a * 27.0);
	} else if (z <= 1.4e-208) {
		tmp = x * 2.0;
	} else if (z <= 1.3e-140) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 1.85e+60) {
		tmp = x * 2.0;
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 <= (-3.5d-79)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= (-5.6d-216)) then
        tmp = x * 2.0d0
    else if (z <= 3.5d-307) then
        tmp = b * (a * 27.0d0)
    else if (z <= 1.4d-208) then
        tmp = x * 2.0d0
    else if (z <= 1.3d-140) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 1.85d+60) then
        tmp = x * 2.0d0
    else
        tmp = z * (t * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e-79) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= -5.6e-216) {
		tmp = x * 2.0;
	} else if (z <= 3.5e-307) {
		tmp = b * (a * 27.0);
	} else if (z <= 1.4e-208) {
		tmp = x * 2.0;
	} else if (z <= 1.3e-140) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 1.85e+60) {
		tmp = x * 2.0;
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.5e-79:
		tmp = y * (-9.0 * (z * t))
	elif z <= -5.6e-216:
		tmp = x * 2.0
	elif z <= 3.5e-307:
		tmp = b * (a * 27.0)
	elif z <= 1.4e-208:
		tmp = x * 2.0
	elif z <= 1.3e-140:
		tmp = y * (z * (t * -9.0))
	elif z <= 1.85e+60:
		tmp = x * 2.0
	else:
		tmp = z * (t * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.5e-79)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= -5.6e-216)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.5e-307)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 1.4e-208)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.3e-140)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 1.85e+60)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(z * Float64(t * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.5e-79)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= -5.6e-216)
		tmp = x * 2.0;
	elseif (z <= 3.5e-307)
		tmp = b * (a * 27.0);
	elseif (z <= 1.4e-208)
		tmp = x * 2.0;
	elseif (z <= 1.3e-140)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 1.85e+60)
		tmp = x * 2.0;
	else
		tmp = z * (t * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.5e-79], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-216], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.5e-307], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-208], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.3e-140], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+60], N[(x * 2.0), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.5000000000000003e-79

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

      3. associate-*l* 45.4%

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

      4. *-commutative 45.4%

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

      5. *-commutative 45.4%

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

   4. Simplified 45.4%

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

   if -3.5000000000000003e-79 < z < -5.6e-216 or 3.5000000000000002e-307 < z < 1.40000000000000001e-208 or 1.2999999999999999e-140 < z < 1.84999999999999994e60

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 48.5%

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

   if -5.6e-216 < z < 3.5000000000000002e-307

   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. Taylor expanded in x around 0 53.5%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 53.5%

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

      2. associate-*r* 53.5%

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

      3. *-commutative 53.5%

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

      4. associate-*r* 53.4%

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

      5. metadata-eval 53.4%

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

      6. associate-*r* 49.0%

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

   4. Applied egg-rr 49.0%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + -9 \cdot \left(\left(y \cdot t\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 25.6%

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

      2. sqrt-unprod 48.7%

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

      3. swap-sqr 48.7%

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

      4. metadata-eval 48.7%

         \[\leadsto a \cdot \left(27 \cdot b\right) + \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      5. metadata-eval 48.7%

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

      6. swap-sqr 48.7%

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

      7. sqrt-unprod 43.4%

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

      8. add-sqr-sqrt 48.7%

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

      9. metadata-eval 48.7%

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

      10. cancel-sign-sub-inv 48.7%

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

      11. add-sqr-sqrt 25.6%

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

      12. sqrt-unprod 49.0%

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

      13. swap-sqr 49.0%

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

      14. metadata-eval 49.0%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      15. metadata-eval 49.0%

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

      16. swap-sqr 49.0%

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

      17. sqrt-unprod 43.7%

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

   6. Applied egg-rr 53.4%

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

   7. Taylor expanded in a around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

      3. associate-*l* 53.1%

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

      4. *-commutative 53.1%

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

   9. Simplified 53.1%

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

   if 1.40000000000000001e-208 < z < 1.2999999999999999e-140

   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. Taylor expanded in y around inf 28.2%

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

      1. *-commutative 28.2%

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

      2. *-commutative 28.2%

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

      3. associate-*l* 28.2%

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

      4. *-commutative 28.2%

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

      5. *-commutative 28.2%

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

   4. Simplified 28.2%

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

      1. expm1-log1p-u 28.1%

         \[\leadsto y \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(t \cdot z\right)\right)\right)} \]

      2. expm1-udef 12.6%

         \[\leadsto y \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(t \cdot z\right)\right)} - 1\right)} \]

      3. *-commutative 12.6%

         \[\leadsto y \cdot \left(e^{\mathsf{log1p}\left(-9 \cdot \color{blue}{\left(z \cdot t\right)}\right)} - 1\right) \]

   6. Applied egg-rr 12.6%

      \[\leadsto y \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-9 \cdot \left(z \cdot t\right)\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 28.1%

         \[\leadsto y \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-9 \cdot \left(z \cdot t\right)\right)\right)} \]

      2. expm1-log1p 28.2%

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

      3. *-commutative 28.2%

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

      4. *-commutative 28.2%

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

      5. associate-*l* 28.4%

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

   8. Simplified 28.4%

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

   9. Taylor expanded in y around 0 28.2%

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

       1. associate-*r* 28.4%

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

       2. *-commutative 28.4%

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

   11. Simplified 28.4%

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

   12. Taylor expanded in y around 0 28.2%

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

       1. *-commutative 28.2%

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

       2. *-commutative 28.2%

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

       3. associate-*l* 28.2%

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

       4. associate-*l* 28.3%

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

   14. Simplified 28.3%

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

   if 1.84999999999999994e60 < z

   1. Initial program 84.3%

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

   2. Taylor expanded in y around 0 84.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. associate-*r* 48.8%

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

      2. associate-*r* 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-*r* 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-216}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-208}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+60}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 7: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{+54}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 -1.42e+54)
     (* -9.0 (* y (* z t)))
     (if (<= z -1e-38)
       t_1
       (if (<= z -8.5e-80)
         (* y (* -9.0 (* z t)))
         (if (<= z 4.5e+60) t_1 (* z (* t (* y -9.0)))))))))

C

assert(y < z && z < t);
assert(a < b);
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 <= -1.42e+54) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -1e-38) {
		tmp = t_1;
	} else if (z <= -8.5e-80) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 4.5e+60) {
		tmp = t_1;
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 <= (-1.42d+54)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-1d-38)) then
        tmp = t_1
    else if (z <= (-8.5d-80)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= 4.5d+60) then
        tmp = t_1
    else
        tmp = z * (t * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
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 <= -1.42e+54) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -1e-38) {
		tmp = t_1;
	} else if (z <= -8.5e-80) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 4.5e+60) {
		tmp = t_1;
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - ((a * b) * -27.0)
	tmp = 0
	if z <= -1.42e+54:
		tmp = -9.0 * (y * (z * t))
	elif z <= -1e-38:
		tmp = t_1
	elif z <= -8.5e-80:
		tmp = y * (-9.0 * (z * t))
	elif z <= 4.5e+60:
		tmp = t_1
	else:
		tmp = z * (t * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0))
	tmp = 0.0
	if (z <= -1.42e+54)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -1e-38)
		tmp = t_1;
	elseif (z <= -8.5e-80)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= 4.5e+60)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(t * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - ((a * b) * -27.0);
	tmp = 0.0;
	if (z <= -1.42e+54)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -1e-38)
		tmp = t_1;
	elseif (z <= -8.5e-80)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= 4.5e+60)
		tmp = t_1;
	else
		tmp = z * (t * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.42e+54], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e-38], t$95$1, If[LessEqual[z, -8.5e-80], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+60], t$95$1, N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.41999999999999995e54

   1. Initial program 92.0%

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

   2. Taylor expanded in y around inf 48.6%

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

   if -1.41999999999999995e54 < z < -9.9999999999999996e-39 or -8.49999999999999939e-80 < z < 4.50000000000000013e60

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 79.0%

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

      1. *-commutative 79.0%

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

   6. Simplified 79.0%

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

   if -9.9999999999999996e-39 < z < -8.49999999999999939e-80

   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. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-commutative 59.7%

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

      3. associate-*l* 59.8%

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

      4. *-commutative 59.8%

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

      5. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   if 4.50000000000000013e60 < z

   1. Initial program 84.3%

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

   2. Taylor expanded in y around 0 84.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. associate-*r* 48.8%

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

      2. associate-*r* 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-*r* 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+54}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+60}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 8: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+60}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.6e+53)
   (* -9.0 (* y (* z t)))
   (if (<= z -1.08e-38)
     (- (* x 2.0) (* (* a b) -27.0))
     (if (<= z -2.3e-79)
       (* y (* -9.0 (* z t)))
       (if (<= z 1.85e+60)
         (+ (* x 2.0) (* a (* 27.0 b)))
         (* z (* t (* y -9.0))))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.6e+53) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -1.08e-38) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else if (z <= -2.3e-79) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1.85e+60) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 <= (-1.6d+53)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-1.08d-38)) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else if (z <= (-2.3d-79)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= 1.85d+60) then
        tmp = (x * 2.0d0) + (a * (27.0d0 * b))
    else
        tmp = z * (t * (y * (-9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.6e+53) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -1.08e-38) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else if (z <= -2.3e-79) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= 1.85e+60) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else {
		tmp = z * (t * (y * -9.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.6e+53:
		tmp = -9.0 * (y * (z * t))
	elif z <= -1.08e-38:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	elif z <= -2.3e-79:
		tmp = y * (-9.0 * (z * t))
	elif z <= 1.85e+60:
		tmp = (x * 2.0) + (a * (27.0 * b))
	else:
		tmp = z * (t * (y * -9.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.6e+53)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -1.08e-38)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	elseif (z <= -2.3e-79)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= 1.85e+60)
		tmp = Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(z * Float64(t * Float64(y * -9.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.6e+53)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -1.08e-38)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	elseif (z <= -2.3e-79)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= 1.85e+60)
		tmp = (x * 2.0) + (a * (27.0 * b));
	else
		tmp = z * (t * (y * -9.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.6e+53], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-38], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-79], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+60], N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.6e53

   1. Initial program 92.0%

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

   2. Taylor expanded in y around inf 48.6%

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

   if -1.6e53 < z < -1.08e-38

   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* 94.1%

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

      10. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   if -1.08e-38 < z < -2.30000000000000012e-79

   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. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-commutative 59.7%

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

      3. associate-*l* 59.8%

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

      4. *-commutative 59.8%

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

      5. *-commutative 59.8%

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

   4. Simplified 59.8%

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

   if -2.30000000000000012e-79 < z < 1.84999999999999994e60

   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. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. neg-mul-1 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-lft-identity 99.8%

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

      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 80.1%

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

      1. *-commutative 80.1%

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

   6. Simplified 80.1%

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

      1. associate-*l* 80.1%

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

      2. metadata-eval 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

      4. *-commutative 80.1%

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

      5. distribute-rgt-neg-in 80.1%

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

   8. Applied egg-rr 80.1%

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

   if 1.84999999999999994e60 < z

   1. Initial program 84.3%

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

   2. Taylor expanded in y around 0 84.4%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. associate-*r* 48.8%

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

      2. associate-*r* 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-*r* 48.7%

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

      5. *-commutative 48.7%

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

   5. Simplified 48.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+53}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+60}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \left(y \cdot -9\right)\right)\\ \end{array} \]

Alternative 9: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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) - (t * (9.0d0 * (y * z)))) + (b * (a * 27.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (t * (9.0 * (y * z)))) + (b * (a * 27.0));
end

Wolfram

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

Derivation

1. Initial program 94.6%

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

2. Taylor expanded in y around 0 94.6%

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

3. Final simplification 94.6%

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

Alternative 10: 78.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-82} \lor \neg \left(b \leq 6.6 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.5e-82) (not (<= b 6.6e+39)))
   (+ (* x 2.0) (* a (* 27.0 b)))
   (- (* x 2.0) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.5e-82) || !(b <= 6.6e+39)) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} 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.
NOTE: a and b 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 ((b <= (-9.5d-82)) .or. (.not. (b <= 6.6d+39))) then
        tmp = (x * 2.0d0) + (a * (27.0d0 * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.5e-82) || !(b <= 6.6e+39)) {
		tmp = (x * 2.0) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9.5e-82) or not (b <= 6.6e+39):
		tmp = (x * 2.0) + (a * (27.0 * b))
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.5e-82) || !(b <= 6.6e+39))
		tmp = Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b)));
	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])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9.5e-82) || ~((b <= 6.6e+39)))
		tmp = (x * 2.0) + (a * (27.0 * b));
	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.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.5e-82], N[Not[LessEqual[b, 6.6e+39]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $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 b < -9.4999999999999996e-82 or 6.60000000000000042e39 < b

   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. sub-neg 95.9%

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

      3. neg-mul-1 95.9%

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

      4. metadata-eval 95.9%

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

      5. metadata-eval 95.9%

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

      6. cancel-sign-sub-inv 95.9%

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

      7. metadata-eval 95.9%

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

      8. *-lft-identity 95.9%

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

      9. associate-*l* 94.3%

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

      10. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. *-commutative 71.2%

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

   6. Simplified 71.2%

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

      1. associate-*l* 71.2%

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

      2. metadata-eval 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. *-commutative 71.2%

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

      5. distribute-rgt-neg-in 71.2%

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

   8. Applied egg-rr 71.2%

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

   if -9.4999999999999996e-82 < b < 6.60000000000000042e39

   1. Initial program 93.4%

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

   2. Taylor expanded in a around 0 80.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-82} \lor \neg \left(b \leq 6.6 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 78.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;t_1 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* 27.0 b))))
   (if (<= b -7.5e-62)
     (+ t_1 (* -9.0 (* z (* y t))))
     (if (<= b 1.75e+39)
       (- (* x 2.0) (* 9.0 (* y (* z t))))
       (+ (* x 2.0) t_1)))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (b <= -7.5e-62) {
		tmp = t_1 + (-9.0 * (z * (y * t)));
	} else if (b <= 1.75e+39) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 = a * (27.0d0 * b)
    if (b <= (-7.5d-62)) then
        tmp = t_1 + ((-9.0d0) * (z * (y * t)))
    else if (b <= 1.75d+39) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = (x * 2.0d0) + t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (b <= -7.5e-62) {
		tmp = t_1 + (-9.0 * (z * (y * t)));
	} else if (b <= 1.75e+39) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) + t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if b <= -7.5e-62:
		tmp = t_1 + (-9.0 * (z * (y * t)))
	elif b <= 1.75e+39:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) + t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (b <= -7.5e-62)
		tmp = Float64(t_1 + Float64(-9.0 * Float64(z * Float64(y * t))));
	elseif (b <= 1.75e+39)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) + t_1);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (b <= -7.5e-62)
		tmp = t_1 + (-9.0 * (z * (y * t)));
	elseif (b <= 1.75e+39)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e-62], N[(t$95$1 + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e+39], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5000000000000003e-62

   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. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 68.7%

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

      2. associate-*r* 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*r* 68.6%

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

      5. metadata-eval 68.6%

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

      6. associate-*r* 67.3%

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

   4. Applied egg-rr 67.3%

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

   if -7.5000000000000003e-62 < b < 1.7500000000000001e39

   1. Initial program 92.9%

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

   2. Taylor expanded in a around 0 79.2%

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

   if 1.7500000000000001e39 < b

   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. associate-+l- 92.1%

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

      2. sub-neg 92.1%

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

      3. neg-mul-1 92.1%

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

      4. metadata-eval 92.1%

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

      5. metadata-eval 92.1%

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

      6. cancel-sign-sub-inv 92.1%

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

      7. metadata-eval 92.1%

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

      8. *-lft-identity 92.1%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 80.3%

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

      1. *-commutative 80.3%

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

   6. Simplified 80.3%

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

      1. associate-*l* 80.5%

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

      2. metadata-eval 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

      4. *-commutative 80.5%

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

      5. distribute-rgt-neg-in 80.5%

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

   8. Applied egg-rr 80.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 12: 78.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{-56}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2 - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y (* z t)))))
   (if (<= b -1.7e-56)
     (- (* 27.0 (* a b)) t_1)
     (if (<= b 4.3e+39) (- (* x 2.0) t_1) (+ (* x 2.0) (* a (* 27.0 b)))))))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (z * t));
	double tmp;
	if (b <= -1.7e-56) {
		tmp = (27.0 * (a * b)) - t_1;
	} else if (b <= 4.3e+39) {
		tmp = (x * 2.0) - t_1;
	} else {
		tmp = (x * 2.0) + (a * (27.0 * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 = 9.0d0 * (y * (z * t))
    if (b <= (-1.7d-56)) then
        tmp = (27.0d0 * (a * b)) - t_1
    else if (b <= 4.3d+39) then
        tmp = (x * 2.0d0) - t_1
    else
        tmp = (x * 2.0d0) + (a * (27.0d0 * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 9.0 * (y * (z * t));
	double tmp;
	if (b <= -1.7e-56) {
		tmp = (27.0 * (a * b)) - t_1;
	} else if (b <= 4.3e+39) {
		tmp = (x * 2.0) - t_1;
	} else {
		tmp = (x * 2.0) + (a * (27.0 * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	t_1 = 9.0 * (y * (z * t))
	tmp = 0
	if b <= -1.7e-56:
		tmp = (27.0 * (a * b)) - t_1
	elif b <= 4.3e+39:
		tmp = (x * 2.0) - t_1
	else:
		tmp = (x * 2.0) + (a * (27.0 * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (b <= -1.7e-56)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - t_1);
	elseif (b <= 4.3e+39)
		tmp = Float64(Float64(x * 2.0) - t_1);
	else
		tmp = Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 9.0 * (y * (z * t));
	tmp = 0.0;
	if (b <= -1.7e-56)
		tmp = (27.0 * (a * b)) - t_1;
	elseif (b <= 4.3e+39)
		tmp = (x * 2.0) - t_1;
	else
		tmp = (x * 2.0) + (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.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e-56], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, 4.3e+39], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.69999999999999991e-56

   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. Taylor expanded in x around 0 68.2%

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

   if -1.69999999999999991e-56 < b < 4.3e39

   1. Initial program 92.9%

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

   2. Taylor expanded in a around 0 79.3%

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

   if 4.3e39 < b

   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. associate-+l- 92.1%

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

      2. sub-neg 92.1%

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

      3. neg-mul-1 92.1%

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

      4. metadata-eval 92.1%

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

      5. metadata-eval 92.1%

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

      6. cancel-sign-sub-inv 92.1%

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

      7. metadata-eval 92.1%

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

      8. *-lft-identity 92.1%

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

      9. associate-*l* 94.0%

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

      10. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 80.3%

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

      1. *-commutative 80.3%

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

   6. Simplified 80.3%

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

      1. associate-*l* 80.5%

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

      2. metadata-eval 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

      4. *-commutative 80.5%

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

      5. distribute-rgt-neg-in 80.5%

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

   8. Applied egg-rr 80.5%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-56}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 13: 47.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+62} \lor \neg \left(a \leq 5.5 \cdot 10^{-73}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.9e+62) (not (<= a 5.5e-73))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.9e+62) || !(a <= 5.5e-73)) {
		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.
NOTE: a and b 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 ((a <= (-3.9d+62)) .or. (.not. (a <= 5.5d-73))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.9e+62) || !(a <= 5.5e-73)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.9e+62) or not (a <= 5.5e-73):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.9e+62) || !(a <= 5.5e-73))
		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])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.9e+62) || ~((a <= 5.5e-73)))
		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.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.9e+62], N[Not[LessEqual[a, 5.5e-73]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9e62 or 5.50000000000000006e-73 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 52.8%

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

   if -3.9e62 < a < 5.50000000000000006e-73

   1. Initial program 93.0%

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

   2. Taylor expanded in x around inf 44.2%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+62} \lor \neg \left(a \leq 5.5 \cdot 10^{-73}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14: 47.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ [a, b] = \mathsf{sort}([a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+62} \lor \neg \left(a \leq 6.6 \cdot 10^{-81}\right):\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.1e+62) (not (<= a 6.6e-81))) (* b (* a 27.0)) (* x 2.0)))

C

assert(y < z && z < t);
assert(a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.1e+62) || !(a <= 6.6e-81)) {
		tmp = b * (a * 27.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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 ((a <= (-3.1d+62)) .or. (.not. (a <= 6.6d-81))) then
        tmp = b * (a * 27.0d0)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
assert a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.1e+62) || !(a <= 6.6e-81)) {
		tmp = b * (a * 27.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.1e+62) or not (a <= 6.6e-81):
		tmp = b * (a * 27.0)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
a, b = sort([a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.1e+62) || !(a <= 6.6e-81))
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.1e+62) || ~((a <= 6.6e-81)))
		tmp = b * (a * 27.0);
	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.
NOTE: a and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.1e+62], N[Not[LessEqual[a, 6.6e-81]], $MachinePrecision]], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.10000000000000014e62 or 6.59999999999999975e-81 < a

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 72.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 72.0%

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

      2. associate-*r* 72.0%

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

      3. *-commutative 72.0%

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

      4. associate-*r* 72.0%

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

      5. metadata-eval 72.0%

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

      6. associate-*r* 75.1%

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

   4. Applied egg-rr 75.1%

      \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right) + -9 \cdot \left(\left(y \cdot t\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 40.1%

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

      2. sqrt-unprod 54.4%

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

      3. swap-sqr 54.4%

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

      4. metadata-eval 54.4%

         \[\leadsto a \cdot \left(27 \cdot b\right) + \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      5. metadata-eval 54.4%

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

      6. swap-sqr 54.4%

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

      7. sqrt-unprod 34.5%

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

      8. add-sqr-sqrt 50.3%

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

      9. metadata-eval 50.3%

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

      10. cancel-sign-sub-inv 50.3%

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

      11. add-sqr-sqrt 32.7%

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

      12. sqrt-unprod 59.2%

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

      13. swap-sqr 59.2%

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

      14. metadata-eval 59.2%

          \[\leadsto a \cdot \left(27 \cdot b\right) - \sqrt{\color{blue}{81} \cdot \left(\left(\left(y \cdot t\right) \cdot z\right) \cdot \left(\left(y \cdot t\right) \cdot z\right)\right)} \]

      15. metadata-eval 59.2%

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

      16. swap-sqr 59.2%

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

      17. sqrt-unprod 51.9%

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

   6. Applied egg-rr 72.0%

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

   7. Taylor expanded in a around inf 52.4%

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

      1. *-commutative 52.4%

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

      2. *-commutative 52.4%

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

      3. associate-*l* 52.4%

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

      4. *-commutative 52.4%

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

   9. Simplified 52.4%

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

   if -3.10000000000000014e62 < a < 6.59999999999999975e-81

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 43.8%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+62} \lor \neg \left(a \leq 6.6 \cdot 10^{-81}\right):\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 15: 31.3% accurate, 5.7× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
NOTE: a and b 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);
assert(a < b);
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.
NOTE: a and b 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;
assert a < b;
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])
[a, b] = sort([a, b])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

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

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
a, b = num2cell(sort([a, b])){:}
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.
NOTE: a and b 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 94.6%

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

2. Taylor expanded in x around inf 34.5%

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

3. Final simplification 34.5%

   \[\leadsto x \cdot 2 \]

Developer target: 94.9% 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 2023230 
(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)))