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

Percentage Accurate: 95.8% → 98.8%

Time: 17.3s

Alternatives: 18

Speedup: 0.7×

• 28.0% 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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) 1e+136)
   (fma x 2.0 (fma t (* (* y z) -9.0) (* b (* a 27.0))))
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * 9.0) * z) <= 1e+136) {
		tmp = fma(x, 2.0, fma(t, ((y * z) * -9.0), (b * (a * 27.0))));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * 9.0) * z) <= 1e+136)
		tmp = fma(x, 2.0, fma(t, Float64(Float64(y * z) * -9.0), Float64(b * Float64(a * 27.0))));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision], 1e+136], N[(x * 2.0 + N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1.00000000000000006e136

   1. Initial program 96.8%

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

      1. associate-+l- 96.8%

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

      2. fma-neg 96.8%

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

      3. neg-sub0 96.8%

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

      4. associate-+l- 96.8%

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

      5. neg-sub0 96.8%

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

      6. *-commutative 96.8%

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

      7. distribute-rgt-neg-in 96.8%

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

      8. fma-def 96.8%

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

      9. *-commutative 96.8%

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

      10. associate-*r* 96.8%

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

      11. distribute-rgt-neg-in 96.8%

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

      12. *-commutative 96.8%

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

      13. metadata-eval 96.8%

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

   3. Simplified 96.8%

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

   if 1.00000000000000006e136 < (*.f64 (*.f64 y 9) z)

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-*l* 85.0%

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

      3. fma-def 88.2%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 10^{+136}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t_1 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 1e+136)
     (+ (* b (* a 27.0)) (- (* x 2.0) (* t_1 t)))
     (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 1e+136) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 1e+136)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t_1 * t)));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+136], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1.00000000000000006e136

   1. Initial program 96.8%

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

   if 1.00000000000000006e136 < (*.f64 (*.f64 y 9) z)

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-*l* 85.0%

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

      3. fma-def 88.2%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+136}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 3: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -6800000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2500000000000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))))
   (if (<= z -2.7e+59)
     (* -9.0 (* y (* z t)))
     (if (<= z -6800000000000.0)
       (* x 2.0)
       (if (<= z -6.8e-46)
         t_1
         (if (<= z -8.2e-75)
           (* 27.0 (* a b))
           (if (<= z -9e-148)
             t_1
             (if (<= z -2.5e-266)
               (* b (* a 27.0))
               (if (<= z 1.4e-287)
                 (* x 2.0)
                 (if (<= z 2500000000000.0) (* a (* 27.0 b)) t_1))))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -2.7e+59) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -6800000000000.0) {
		tmp = x * 2.0;
	} else if (z <= -6.8e-46) {
		tmp = t_1;
	} else if (z <= -8.2e-75) {
		tmp = 27.0 * (a * b);
	} else if (z <= -9e-148) {
		tmp = t_1;
	} else if (z <= -2.5e-266) {
		tmp = b * (a * 27.0);
	} else if (z <= 1.4e-287) {
		tmp = x * 2.0;
	} else if (z <= 2500000000000.0) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    if (z <= (-2.7d+59)) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= (-6800000000000.0d0)) then
        tmp = x * 2.0d0
    else if (z <= (-6.8d-46)) then
        tmp = t_1
    else if (z <= (-8.2d-75)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= (-9d-148)) then
        tmp = t_1
    else if (z <= (-2.5d-266)) then
        tmp = b * (a * 27.0d0)
    else if (z <= 1.4d-287) then
        tmp = x * 2.0d0
    else if (z <= 2500000000000.0d0) then
        tmp = a * (27.0d0 * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double tmp;
	if (z <= -2.7e+59) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= -6800000000000.0) {
		tmp = x * 2.0;
	} else if (z <= -6.8e-46) {
		tmp = t_1;
	} else if (z <= -8.2e-75) {
		tmp = 27.0 * (a * b);
	} else if (z <= -9e-148) {
		tmp = t_1;
	} else if (z <= -2.5e-266) {
		tmp = b * (a * 27.0);
	} else if (z <= 1.4e-287) {
		tmp = x * 2.0;
	} else if (z <= 2500000000000.0) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	tmp = 0
	if z <= -2.7e+59:
		tmp = -9.0 * (y * (z * t))
	elif z <= -6800000000000.0:
		tmp = x * 2.0
	elif z <= -6.8e-46:
		tmp = t_1
	elif z <= -8.2e-75:
		tmp = 27.0 * (a * b)
	elif z <= -9e-148:
		tmp = t_1
	elif z <= -2.5e-266:
		tmp = b * (a * 27.0)
	elif z <= 1.4e-287:
		tmp = x * 2.0
	elif z <= 2500000000000.0:
		tmp = a * (27.0 * b)
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (z <= -2.7e+59)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= -6800000000000.0)
		tmp = Float64(x * 2.0);
	elseif (z <= -6.8e-46)
		tmp = t_1;
	elseif (z <= -8.2e-75)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= -9e-148)
		tmp = t_1;
	elseif (z <= -2.5e-266)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 1.4e-287)
		tmp = Float64(x * 2.0);
	elseif (z <= 2500000000000.0)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (z <= -2.7e+59)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= -6800000000000.0)
		tmp = x * 2.0;
	elseif (z <= -6.8e-46)
		tmp = t_1;
	elseif (z <= -8.2e-75)
		tmp = 27.0 * (a * b);
	elseif (z <= -9e-148)
		tmp = t_1;
	elseif (z <= -2.5e-266)
		tmp = b * (a * 27.0);
	elseif (z <= 1.4e-287)
		tmp = x * 2.0;
	elseif (z <= 2500000000000.0)
		tmp = a * (27.0 * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+59], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6800000000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -6.8e-46], t$95$1, If[LessEqual[z, -8.2e-75], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-148], t$95$1, If[LessEqual[z, -2.5e-266], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-287], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2500000000000.0], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.7000000000000001e59

   1. Initial program 90.3%

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

   2. Taylor expanded in y around inf 48.6%

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

   if -2.7000000000000001e59 < z < -6.8e12 or -2.49999999999999996e-266 < z < 1.4000000000000001e-287

   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 49.3%

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

   if -6.8e12 < z < -6.79999999999999992e-46 or -8.20000000000000005e-75 < z < -9.00000000000000029e-148 or 2.5e12 < z

   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 y around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*l* 88.2%

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

      4. associate-*r* 88.1%

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

      5. associate-*l* 96.8%

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

      6. *-commutative 96.8%

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

   4. Simplified 96.8%

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

   5. Taylor expanded in z around inf 38.4%

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

      1. *-commutative 38.4%

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

      2. *-commutative 38.4%

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

      3. associate-*l* 38.5%

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

      4. *-commutative 38.5%

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

      5. associate-*r* 38.4%

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

   7. Simplified 38.4%

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

   8. Taylor expanded in y around 0 38.4%

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

      1. associate-*r* 45.5%

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

      2. *-commutative 45.5%

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

      3. associate-*l* 41.7%

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

   10. Simplified 41.7%

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

   if -6.79999999999999992e-46 < z < -8.20000000000000005e-75

   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 a around inf 40.6%

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

   if -9.00000000000000029e-148 < z < -2.49999999999999996e-266

   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 73.0%

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

      1. fma-neg 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-*l* 73.0%

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

      5. distribute-lft-neg-in 73.0%

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

      6. distribute-lft-neg-in 73.0%

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

      7. metadata-eval 73.0%

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

      8. *-commutative 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in a around inf 54.6%

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

      1. associate-*r* 54.7%

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

   7. Simplified 54.7%

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

   if 1.4000000000000001e-287 < z < 2.5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 59.5%

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

      1. fma-neg 59.5%

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

      2. *-commutative 59.5%

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

      3. *-commutative 59.5%

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

      4. associate-*l* 59.5%

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

      5. distribute-lft-neg-in 59.5%

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

      6. distribute-lft-neg-in 59.5%

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

      7. metadata-eval 59.5%

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

      8. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in a around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. associate-*l* 49.9%

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

   7. Simplified 49.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -6800000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-46}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-148}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2500000000000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6800000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-75}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-286}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2500000000000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))) (t_2 (* y (* -9.0 (* z t)))))
   (if (<= z -2.7e+59)
     t_2
     (if (<= z -6800000000000.0)
       (* x 2.0)
       (if (<= z -9.2e-49)
         t_2
         (if (<= z -7e-75)
           (* 27.0 (* a b))
           (if (<= z -2.4e-148)
             t_1
             (if (<= z -2.2e-266)
               (* b (* a 27.0))
               (if (<= z 7e-286)
                 (* x 2.0)
                 (if (<= z 2500000000000.0) (* a (* 27.0 b)) t_1))))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double t_2 = y * (-9.0 * (z * t));
	double tmp;
	if (z <= -2.7e+59) {
		tmp = t_2;
	} else if (z <= -6800000000000.0) {
		tmp = x * 2.0;
	} else if (z <= -9.2e-49) {
		tmp = t_2;
	} else if (z <= -7e-75) {
		tmp = 27.0 * (a * b);
	} else if (z <= -2.4e-148) {
		tmp = t_1;
	} else if (z <= -2.2e-266) {
		tmp = b * (a * 27.0);
	} else if (z <= 7e-286) {
		tmp = x * 2.0;
	} else if (z <= 2500000000000.0) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    t_2 = y * ((-9.0d0) * (z * t))
    if (z <= (-2.7d+59)) then
        tmp = t_2
    else if (z <= (-6800000000000.0d0)) then
        tmp = x * 2.0d0
    else if (z <= (-9.2d-49)) then
        tmp = t_2
    else if (z <= (-7d-75)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= (-2.4d-148)) then
        tmp = t_1
    else if (z <= (-2.2d-266)) then
        tmp = b * (a * 27.0d0)
    else if (z <= 7d-286) then
        tmp = x * 2.0d0
    else if (z <= 2500000000000.0d0) then
        tmp = a * (27.0d0 * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double t_2 = y * (-9.0 * (z * t));
	double tmp;
	if (z <= -2.7e+59) {
		tmp = t_2;
	} else if (z <= -6800000000000.0) {
		tmp = x * 2.0;
	} else if (z <= -9.2e-49) {
		tmp = t_2;
	} else if (z <= -7e-75) {
		tmp = 27.0 * (a * b);
	} else if (z <= -2.4e-148) {
		tmp = t_1;
	} else if (z <= -2.2e-266) {
		tmp = b * (a * 27.0);
	} else if (z <= 7e-286) {
		tmp = x * 2.0;
	} else if (z <= 2500000000000.0) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	t_2 = y * (-9.0 * (z * t))
	tmp = 0
	if z <= -2.7e+59:
		tmp = t_2
	elif z <= -6800000000000.0:
		tmp = x * 2.0
	elif z <= -9.2e-49:
		tmp = t_2
	elif z <= -7e-75:
		tmp = 27.0 * (a * b)
	elif z <= -2.4e-148:
		tmp = t_1
	elif z <= -2.2e-266:
		tmp = b * (a * 27.0)
	elif z <= 7e-286:
		tmp = x * 2.0
	elif z <= 2500000000000.0:
		tmp = a * (27.0 * b)
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(y * Float64(-9.0 * Float64(z * t)))
	tmp = 0.0
	if (z <= -2.7e+59)
		tmp = t_2;
	elseif (z <= -6800000000000.0)
		tmp = Float64(x * 2.0);
	elseif (z <= -9.2e-49)
		tmp = t_2;
	elseif (z <= -7e-75)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= -2.4e-148)
		tmp = t_1;
	elseif (z <= -2.2e-266)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 7e-286)
		tmp = Float64(x * 2.0);
	elseif (z <= 2500000000000.0)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (y * z));
	t_2 = y * (-9.0 * (z * t));
	tmp = 0.0;
	if (z <= -2.7e+59)
		tmp = t_2;
	elseif (z <= -6800000000000.0)
		tmp = x * 2.0;
	elseif (z <= -9.2e-49)
		tmp = t_2;
	elseif (z <= -7e-75)
		tmp = 27.0 * (a * b);
	elseif (z <= -2.4e-148)
		tmp = t_1;
	elseif (z <= -2.2e-266)
		tmp = b * (a * 27.0);
	elseif (z <= 7e-286)
		tmp = x * 2.0;
	elseif (z <= 2500000000000.0)
		tmp = a * (27.0 * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+59], t$95$2, If[LessEqual[z, -6800000000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -9.2e-49], t$95$2, If[LessEqual[z, -7e-75], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-148], t$95$1, If[LessEqual[z, -2.2e-266], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-286], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2500000000000.0], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.7000000000000001e59 or -6.8e12 < z < -9.1999999999999996e-49

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. *-commutative 44.0%

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

      3. associate-*l* 44.1%

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

      4. *-commutative 44.1%

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

      5. *-commutative 44.1%

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

   4. Simplified 44.1%

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

   if -2.7000000000000001e59 < z < -6.8e12 or -2.2e-266 < z < 6.99999999999999977e-286

   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 49.3%

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

   if -9.1999999999999996e-49 < z < -6.9999999999999997e-75

   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 a around inf 40.6%

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

   if -6.9999999999999997e-75 < z < -2.4000000000000001e-148 or 2.5e12 < z

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*l* 86.1%

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

      4. associate-*r* 86.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in z around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-commutative 40.2%

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

      3. associate-*l* 40.3%

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

      4. *-commutative 40.3%

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

      5. associate-*r* 40.2%

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

   7. Simplified 40.2%

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

   8. Taylor expanded in y around 0 40.2%

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

      1. associate-*r* 47.5%

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

      2. *-commutative 47.5%

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

      3. associate-*l* 44.1%

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

   10. Simplified 44.1%

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

   if -2.4000000000000001e-148 < z < -2.2e-266

   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 73.0%

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

      1. fma-neg 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-*l* 73.0%

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

      5. distribute-lft-neg-in 73.0%

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

      6. distribute-lft-neg-in 73.0%

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

      7. metadata-eval 73.0%

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

      8. *-commutative 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in a around inf 54.6%

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

      1. associate-*r* 54.7%

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

   7. Simplified 54.7%

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

   if 6.99999999999999977e-286 < z < 2.5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 59.5%

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

      1. fma-neg 59.5%

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

      2. *-commutative 59.5%

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

      3. *-commutative 59.5%

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

      4. associate-*l* 59.5%

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

      5. distribute-lft-neg-in 59.5%

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

      6. distribute-lft-neg-in 59.5%

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

      7. metadata-eval 59.5%

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

      8. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in a around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. associate-*l* 49.9%

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

   7. Simplified 49.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -6800000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-75}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-148}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-286}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2500000000000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 5: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -230000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-76}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 25000000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))) (t_2 (* (* z t) (* y -9.0))))
   (if (<= z -2.7e+59)
     t_2
     (if (<= z -230000000000.0)
       (* x 2.0)
       (if (<= z -1.55e-48)
         t_2
         (if (<= z -6.6e-76)
           (* 27.0 (* a b))
           (if (<= z -3.5e-149)
             t_1
             (if (<= z -4.6e-267)
               (* b (* a 27.0))
               (if (<= z 9.5e-288)
                 (* x 2.0)
                 (if (<= z 25000000.0) (* a (* 27.0 b)) t_1))))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double t_2 = (z * t) * (y * -9.0);
	double tmp;
	if (z <= -2.7e+59) {
		tmp = t_2;
	} else if (z <= -230000000000.0) {
		tmp = x * 2.0;
	} else if (z <= -1.55e-48) {
		tmp = t_2;
	} else if (z <= -6.6e-76) {
		tmp = 27.0 * (a * b);
	} else if (z <= -3.5e-149) {
		tmp = t_1;
	} else if (z <= -4.6e-267) {
		tmp = b * (a * 27.0);
	} else if (z <= 9.5e-288) {
		tmp = x * 2.0;
	} else if (z <= 25000000.0) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (y * z))
    t_2 = (z * t) * (y * (-9.0d0))
    if (z <= (-2.7d+59)) then
        tmp = t_2
    else if (z <= (-230000000000.0d0)) then
        tmp = x * 2.0d0
    else if (z <= (-1.55d-48)) then
        tmp = t_2
    else if (z <= (-6.6d-76)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= (-3.5d-149)) then
        tmp = t_1
    else if (z <= (-4.6d-267)) then
        tmp = b * (a * 27.0d0)
    else if (z <= 9.5d-288) then
        tmp = x * 2.0d0
    else if (z <= 25000000.0d0) then
        tmp = a * (27.0d0 * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (y * z));
	double t_2 = (z * t) * (y * -9.0);
	double tmp;
	if (z <= -2.7e+59) {
		tmp = t_2;
	} else if (z <= -230000000000.0) {
		tmp = x * 2.0;
	} else if (z <= -1.55e-48) {
		tmp = t_2;
	} else if (z <= -6.6e-76) {
		tmp = 27.0 * (a * b);
	} else if (z <= -3.5e-149) {
		tmp = t_1;
	} else if (z <= -4.6e-267) {
		tmp = b * (a * 27.0);
	} else if (z <= 9.5e-288) {
		tmp = x * 2.0;
	} else if (z <= 25000000.0) {
		tmp = a * (27.0 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	t_2 = (z * t) * (y * -9.0)
	tmp = 0
	if z <= -2.7e+59:
		tmp = t_2
	elif z <= -230000000000.0:
		tmp = x * 2.0
	elif z <= -1.55e-48:
		tmp = t_2
	elif z <= -6.6e-76:
		tmp = 27.0 * (a * b)
	elif z <= -3.5e-149:
		tmp = t_1
	elif z <= -4.6e-267:
		tmp = b * (a * 27.0)
	elif z <= 9.5e-288:
		tmp = x * 2.0
	elif z <= 25000000.0:
		tmp = a * (27.0 * b)
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(Float64(z * t) * Float64(y * -9.0))
	tmp = 0.0
	if (z <= -2.7e+59)
		tmp = t_2;
	elseif (z <= -230000000000.0)
		tmp = Float64(x * 2.0);
	elseif (z <= -1.55e-48)
		tmp = t_2;
	elseif (z <= -6.6e-76)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= -3.5e-149)
		tmp = t_1;
	elseif (z <= -4.6e-267)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 9.5e-288)
		tmp = Float64(x * 2.0);
	elseif (z <= 25000000.0)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (y * z));
	t_2 = (z * t) * (y * -9.0);
	tmp = 0.0;
	if (z <= -2.7e+59)
		tmp = t_2;
	elseif (z <= -230000000000.0)
		tmp = x * 2.0;
	elseif (z <= -1.55e-48)
		tmp = t_2;
	elseif (z <= -6.6e-76)
		tmp = 27.0 * (a * b);
	elseif (z <= -3.5e-149)
		tmp = t_1;
	elseif (z <= -4.6e-267)
		tmp = b * (a * 27.0);
	elseif (z <= 9.5e-288)
		tmp = x * 2.0;
	elseif (z <= 25000000.0)
		tmp = a * (27.0 * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+59], t$95$2, If[LessEqual[z, -230000000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -1.55e-48], t$95$2, If[LessEqual[z, -6.6e-76], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-149], t$95$1, If[LessEqual[z, -4.6e-267], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-288], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 25000000.0], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.7000000000000001e59 or -2.3e11 < z < -1.55000000000000008e-48

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. *-commutative 44.0%

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

      3. associate-*l* 44.1%

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

      4. *-commutative 44.1%

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

      5. *-commutative 44.1%

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

   4. Simplified 44.1%

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

   5. Taylor expanded in y around 0 44.0%

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

      1. associate-*r* 44.1%

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

   7. Simplified 44.1%

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

   if -2.7000000000000001e59 < z < -2.3e11 or -4.6000000000000001e-267 < z < 9.49999999999999955e-288

   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 49.3%

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

   if -1.55000000000000008e-48 < z < -6.59999999999999967e-76

   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 a around inf 40.6%

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

   if -6.59999999999999967e-76 < z < -3.5e-149 or 2.5e7 < z

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*l* 86.1%

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

      4. associate-*r* 86.0%

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

      5. associate-*l* 96.2%

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

      6. *-commutative 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in z around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-commutative 40.2%

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

      3. associate-*l* 40.3%

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

      4. *-commutative 40.3%

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

      5. associate-*r* 40.2%

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

   7. Simplified 40.2%

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

   8. Taylor expanded in y around 0 40.2%

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

      1. associate-*r* 47.5%

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

      2. *-commutative 47.5%

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

      3. associate-*l* 44.1%

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

   10. Simplified 44.1%

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

   if -3.5e-149 < z < -4.6000000000000001e-267

   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 73.0%

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

      1. fma-neg 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-*l* 73.0%

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

      5. distribute-lft-neg-in 73.0%

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

      6. distribute-lft-neg-in 73.0%

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

      7. metadata-eval 73.0%

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

      8. *-commutative 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in a around inf 54.6%

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

      1. associate-*r* 54.7%

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

   7. Simplified 54.7%

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

   if 9.49999999999999955e-288 < z < 2.5e7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 59.5%

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

      1. fma-neg 59.5%

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

      2. *-commutative 59.5%

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

      3. *-commutative 59.5%

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

      4. associate-*l* 59.5%

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

      5. distribute-lft-neg-in 59.5%

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

      6. distribute-lft-neg-in 59.5%

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

      7. metadata-eval 59.5%

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

      8. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in a around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. associate-*l* 49.9%

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

   7. Simplified 49.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+59}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -230000000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-48}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-76}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-149}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 25000000:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 6: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t_1 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y 9.0) z)))
   (if (<= t_1 5e+302)
     (+ (* b (* a 27.0)) (- (* x 2.0) (* t_1 t)))
     (* y (* -9.0 (* z t))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 5e+302) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = y * (-9.0 * (z * t));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * 9.0d0) * z
    if (t_1 <= 5d+302) then
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t_1 * t))
    else
        tmp = y * ((-9.0d0) * (z * t))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 5e+302) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t_1 * t));
	} else {
		tmp = y * (-9.0 * (z * t));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 5e+302:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t_1 * t))
	else:
		tmp = y * (-9.0 * (z * t))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 5e+302)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t_1 * t)));
	else
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 5e+302)
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t_1 * t));
	else
		tmp = y * (-9.0 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+302], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 5e302

   1. Initial program 97.0%

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

   if 5e302 < (*.f64 (*.f64 y 9) z)

   1. Initial program 65.9%

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

   2. Taylor expanded in y around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*l* 92.9%

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

      4. *-commutative 92.9%

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

      5. *-commutative 92.9%

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

   4. Simplified 92.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+302}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 48.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-182}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* -9.0 (* t (* y z)))))
   (if (<= t -1.35e-125)
     t_2
     (if (<= t 1.7e-182)
       (* a (* 27.0 b))
       (if (<= t 1.5e-134)
         (* x 2.0)
         (if (<= t 2.5e-46)
           t_1
           (if (<= t 8e-18)
             (* x 2.0)
             (if (<= t 2.25e+44) t_1 (if (<= t 3e+92) (* x 2.0) t_2)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (t <= -1.35e-125) {
		tmp = t_2;
	} else if (t <= 1.7e-182) {
		tmp = a * (27.0 * b);
	} else if (t <= 1.5e-134) {
		tmp = x * 2.0;
	} else if (t <= 2.5e-46) {
		tmp = t_1;
	} else if (t <= 8e-18) {
		tmp = x * 2.0;
	} else if (t <= 2.25e+44) {
		tmp = t_1;
	} else if (t <= 3e+92) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    t_2 = (-9.0d0) * (t * (y * z))
    if (t <= (-1.35d-125)) then
        tmp = t_2
    else if (t <= 1.7d-182) then
        tmp = a * (27.0d0 * b)
    else if (t <= 1.5d-134) then
        tmp = x * 2.0d0
    else if (t <= 2.5d-46) then
        tmp = t_1
    else if (t <= 8d-18) then
        tmp = x * 2.0d0
    else if (t <= 2.25d+44) then
        tmp = t_1
    else if (t <= 3d+92) then
        tmp = x * 2.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double t_2 = -9.0 * (t * (y * z));
	double tmp;
	if (t <= -1.35e-125) {
		tmp = t_2;
	} else if (t <= 1.7e-182) {
		tmp = a * (27.0 * b);
	} else if (t <= 1.5e-134) {
		tmp = x * 2.0;
	} else if (t <= 2.5e-46) {
		tmp = t_1;
	} else if (t <= 8e-18) {
		tmp = x * 2.0;
	} else if (t <= 2.25e+44) {
		tmp = t_1;
	} else if (t <= 3e+92) {
		tmp = x * 2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	t_2 = -9.0 * (t * (y * z))
	tmp = 0
	if t <= -1.35e-125:
		tmp = t_2
	elif t <= 1.7e-182:
		tmp = a * (27.0 * b)
	elif t <= 1.5e-134:
		tmp = x * 2.0
	elif t <= 2.5e-46:
		tmp = t_1
	elif t <= 8e-18:
		tmp = x * 2.0
	elif t <= 2.25e+44:
		tmp = t_1
	elif t <= 3e+92:
		tmp = x * 2.0
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(-9.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (t <= -1.35e-125)
		tmp = t_2;
	elseif (t <= 1.7e-182)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (t <= 1.5e-134)
		tmp = Float64(x * 2.0);
	elseif (t <= 2.5e-46)
		tmp = t_1;
	elseif (t <= 8e-18)
		tmp = Float64(x * 2.0);
	elseif (t <= 2.25e+44)
		tmp = t_1;
	elseif (t <= 3e+92)
		tmp = Float64(x * 2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	t_2 = -9.0 * (t * (y * z));
	tmp = 0.0;
	if (t <= -1.35e-125)
		tmp = t_2;
	elseif (t <= 1.7e-182)
		tmp = a * (27.0 * b);
	elseif (t <= 1.5e-134)
		tmp = x * 2.0;
	elseif (t <= 2.5e-46)
		tmp = t_1;
	elseif (t <= 8e-18)
		tmp = x * 2.0;
	elseif (t <= 2.25e+44)
		tmp = t_1;
	elseif (t <= 3e+92)
		tmp = x * 2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-125], t$95$2, If[LessEqual[t, 1.7e-182], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-134], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 2.5e-46], t$95$1, If[LessEqual[t, 8e-18], N[(x * 2.0), $MachinePrecision], If[LessEqual[t, 2.25e+44], t$95$1, If[LessEqual[t, 3e+92], N[(x * 2.0), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3499999999999999e-125 or 3.00000000000000013e92 < t

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 88.2%

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

      1. *-commutative 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*l* 88.2%

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

      4. associate-*r* 88.2%

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

      5. associate-*l* 93.8%

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

      6. *-commutative 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-*l* 41.8%

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

      4. *-commutative 41.8%

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

      5. associate-*r* 41.8%

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

   7. Simplified 41.8%

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

   8. Taylor expanded in y around 0 41.7%

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

      1. associate-*r* 49.3%

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

      2. *-commutative 49.3%

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

      3. associate-*l* 49.4%

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

   10. Simplified 49.4%

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

   if -1.3499999999999999e-125 < t < 1.69999999999999995e-182

   1. Initial program 90.9%

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

   2. Taylor expanded in x around 0 52.9%

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

      1. fma-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. *-commutative 53.0%

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

      4. associate-*l* 53.0%

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

      5. distribute-lft-neg-in 53.0%

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

      6. distribute-lft-neg-in 53.0%

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

      7. metadata-eval 53.0%

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

      8. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in a around inf 41.1%

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

      1. *-commutative 41.1%

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

      2. associate-*l* 41.1%

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

   7. Simplified 41.1%

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

   if 1.69999999999999995e-182 < t < 1.5e-134 or 2.49999999999999996e-46 < t < 8.0000000000000006e-18 or 2.25e44 < t < 3.00000000000000013e92

   1. Initial program 90.8%

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

   2. Taylor expanded in x around inf 45.3%

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

   if 1.5e-134 < t < 2.49999999999999996e-46 or 8.0000000000000006e-18 < t < 2.25e44

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 61.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-125}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-182}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-46}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+44}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 8: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-47}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a (* 27.0 b)) (* -9.0 (* z (* y t))))))
   (if (<= z -4.8e-47)
     (- (* x 2.0) (* y (* t (* 9.0 z))))
     (if (<= z -2.6e-75)
       t_1
       (if (<= z -7e-148)
         (- (* x 2.0) (* t (* y (* 9.0 z))))
         (if (<= z 1.3e-71) (- (* x 2.0) (* a (* b -27.0))) t_1))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	double tmp;
	if (z <= -4.8e-47) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else if (z <= -2.6e-75) {
		tmp = t_1;
	} else if (z <= -7e-148) {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	} else if (z <= 1.3e-71) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * (27.0d0 * b)) + ((-9.0d0) * (z * (y * t)))
    if (z <= (-4.8d-47)) then
        tmp = (x * 2.0d0) - (y * (t * (9.0d0 * z)))
    else if (z <= (-2.6d-75)) then
        tmp = t_1
    else if (z <= (-7d-148)) then
        tmp = (x * 2.0d0) - (t * (y * (9.0d0 * z)))
    else if (z <= 1.3d-71) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	double tmp;
	if (z <= -4.8e-47) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else if (z <= -2.6e-75) {
		tmp = t_1;
	} else if (z <= -7e-148) {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	} else if (z <= 1.3e-71) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	tmp = 0
	if z <= -4.8e-47:
		tmp = (x * 2.0) - (y * (t * (9.0 * z)))
	elif z <= -2.6e-75:
		tmp = t_1
	elif z <= -7e-148:
		tmp = (x * 2.0) - (t * (y * (9.0 * z)))
	elif z <= 1.3e-71:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))))
	tmp = 0.0
	if (z <= -4.8e-47)
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z))));
	elseif (z <= -2.6e-75)
		tmp = t_1;
	elseif (z <= -7e-148)
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z))));
	elseif (z <= 1.3e-71)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	tmp = 0.0;
	if (z <= -4.8e-47)
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	elseif (z <= -2.6e-75)
		tmp = t_1;
	elseif (z <= -7e-148)
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	elseif (z <= 1.3e-71)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-47], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-75], t$95$1, If[LessEqual[z, -7e-148], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-71], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.7999999999999999e-47

   1. Initial program 93.5%

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

      1. associate-+l- 93.5%

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

      2. sub-neg 93.5%

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

      3. neg-mul-1 93.5%

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

      4. metadata-eval 93.5%

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

      5. metadata-eval 93.5%

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

      6. cancel-sign-sub-inv 93.5%

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

      7. metadata-eval 93.5%

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

      8. *-lft-identity 93.5%

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

      9. associate-*l* 89.8%

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

      10. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. sub-neg 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*r* 89.7%

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

      4. associate-*r* 93.4%

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

      5. distribute-rgt-neg-in 93.4%

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

      6. *-commutative 93.4%

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

      7. distribute-rgt-neg-in 93.4%

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

      8. metadata-eval 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around inf 65.2%

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

      1. *-commutative 65.2%

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

      2. associate-*r* 73.7%

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

      3. associate-*r* 73.8%

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

      4. associate-*l* 65.3%

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

   8. Simplified 65.3%

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

   if -4.7999999999999999e-47 < z < -2.6e-75 or 1.2999999999999999e-71 < z

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0 62.4%

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

      1. cancel-sign-sub-inv 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 62.4%

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

      4. metadata-eval 62.4%

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

      5. associate-*r* 68.5%

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

   4. Applied egg-rr 68.5%

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

   if -2.6e-75 < z < -7.0000000000000001e-148

   1. Initial program 91.9%

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

      1. associate-+l- 91.9%

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

      2. sub-neg 91.9%

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

      3. neg-mul-1 91.9%

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

      4. metadata-eval 91.9%

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

      5. metadata-eval 91.9%

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

      6. cancel-sign-sub-inv 91.9%

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

      7. metadata-eval 91.9%

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

      8. *-lft-identity 91.9%

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

      9. associate-*l* 84.7%

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

      10. associate-*l* 84.7%

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

   3. Simplified 84.7%

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

      1. sub-neg 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r* 84.7%

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

      4. associate-*r* 92.2%

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

      5. distribute-rgt-neg-in 92.2%

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

      6. *-commutative 92.2%

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

      7. distribute-rgt-neg-in 92.2%

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

      8. metadata-eval 92.2%

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

   5. Applied egg-rr 92.2%

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

      1. flip-+ 62.6%

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

      2. div-inv 62.6%

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

   7. Applied egg-rr 61.7%

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

   8. Taylor expanded in y around inf 70.8%

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

      1. associate-*r* 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 66.6%

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

      4. *-commutative 66.6%

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

      5. associate-*l* 73.4%

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

   10. Simplified 73.4%

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

   if -7.0000000000000001e-148 < z < 1.2999999999999999e-71

   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. Step-by-step derivation

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      3. neg-mul-1 99.9%

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

      4. metadata-eval 99.9%

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

      5. metadata-eval 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. metadata-eval 99.9%

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

      8. *-lft-identity 99.9%

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

      9. associate-*l* 99.9%

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

      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 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r* 91.8%

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

   6. Simplified 91.8%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-47}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-71}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-79}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 10^{-63}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3e-45)
   (- (* x 2.0) (* y (* t (* 9.0 z))))
   (if (<= z -1.65e-79)
     (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))
     (if (<= z -8.6e-148)
       (- (* x 2.0) (* t (* y (* 9.0 z))))
       (if (<= z 1e-63)
         (- (* x 2.0) (* a (* b -27.0)))
         (+ (* a (* 27.0 b)) (* -9.0 (* z (* y t)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-45) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else if (z <= -1.65e-79) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else if (z <= -8.6e-148) {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	} else if (z <= 1e-63) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3d-45)) then
        tmp = (x * 2.0d0) - (y * (t * (9.0d0 * z)))
    else if (z <= (-1.65d-79)) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    else if (z <= (-8.6d-148)) then
        tmp = (x * 2.0d0) - (t * (y * (9.0d0 * z)))
    else if (z <= 1d-63) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (a * (27.0d0 * b)) + ((-9.0d0) * (z * (y * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e-45) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else if (z <= -1.65e-79) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else if (z <= -8.6e-148) {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	} else if (z <= 1e-63) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3e-45:
		tmp = (x * 2.0) - (y * (t * (9.0 * z)))
	elif z <= -1.65e-79:
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	elif z <= -8.6e-148:
		tmp = (x * 2.0) - (t * (y * (9.0 * z)))
	elif z <= 1e-63:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3e-45)
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z))));
	elseif (z <= -1.65e-79)
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= -8.6e-148)
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z))));
	elseif (z <= 1e-63)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(-9.0 * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3e-45)
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	elseif (z <= -1.65e-79)
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	elseif (z <= -8.6e-148)
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	elseif (z <= 1e-63)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (a * (27.0 * b)) + (-9.0 * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3e-45], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-79], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-148], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-63], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.00000000000000011e-45

   1. Initial program 93.5%

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

      1. associate-+l- 93.5%

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

      2. sub-neg 93.5%

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

      3. neg-mul-1 93.5%

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

      4. metadata-eval 93.5%

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

      5. metadata-eval 93.5%

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

      6. cancel-sign-sub-inv 93.5%

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

      7. metadata-eval 93.5%

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

      8. *-lft-identity 93.5%

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

      9. associate-*l* 89.8%

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

      10. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. sub-neg 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*r* 89.7%

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

      4. associate-*r* 93.4%

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

      5. distribute-rgt-neg-in 93.4%

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

      6. *-commutative 93.4%

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

      7. distribute-rgt-neg-in 93.4%

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

      8. metadata-eval 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around inf 65.2%

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

      1. *-commutative 65.2%

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

      2. associate-*r* 73.7%

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

      3. associate-*r* 73.8%

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

      4. associate-*l* 65.3%

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

   8. Simplified 65.3%

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

   if -3.00000000000000011e-45 < z < -1.6499999999999999e-79

   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 x around 0 82.8%

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

   if -1.6499999999999999e-79 < z < -8.5999999999999997e-148

   1. Initial program 91.3%

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

      1. associate-+l- 91.3%

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

      2. sub-neg 91.3%

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

      3. neg-mul-1 91.3%

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

      4. metadata-eval 91.3%

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

      5. metadata-eval 91.3%

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

      6. cancel-sign-sub-inv 91.3%

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

      7. metadata-eval 91.3%

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

      8. *-lft-identity 91.3%

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

      9. associate-*l* 83.4%

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

      10. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

      1. sub-neg 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*r* 83.4%

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

      4. associate-*r* 91.5%

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

      5. distribute-rgt-neg-in 91.5%

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

      6. *-commutative 91.5%

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

      7. distribute-rgt-neg-in 91.5%

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

      8. metadata-eval 91.5%

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

   5. Applied egg-rr 91.5%

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

      1. flip-+ 59.5%

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

      2. div-inv 59.5%

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

   7. Applied egg-rr 58.5%

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

   8. Taylor expanded in y around inf 68.3%

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

      1. associate-*r* 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-*r* 63.9%

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

      4. *-commutative 63.9%

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

      5. associate-*l* 71.3%

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

   10. Simplified 71.3%

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

   if -8.5999999999999997e-148 < z < 1.00000000000000007e-63

   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. Step-by-step derivation

      1. associate-+l- 99.9%

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

      2. sub-neg 99.9%

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

      3. neg-mul-1 99.9%

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

      4. metadata-eval 99.9%

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

      5. metadata-eval 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. metadata-eval 99.9%

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

      8. *-lft-identity 99.9%

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

      9. associate-*l* 99.9%

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

      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 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r* 91.8%

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

   6. Simplified 91.8%

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

   if 1.00000000000000007e-63 < z

   1. Initial program 93.1%

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

   2. Taylor expanded in x around 0 61.2%

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

      1. cancel-sign-sub-inv 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

      4. metadata-eval 61.2%

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

      5. associate-*r* 67.7%

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

   4. Applied egg-rr 67.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot 27\right) + -9 \cdot \left(\left(y \cdot t\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-79}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 10^{-63}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 10: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1950:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 700000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* a (* b -27.0)))))
   (if (<= z -4.1e+114)
     (* y (* -9.0 (* z t)))
     (if (<= z -1950.0)
       t_1
       (if (<= z -9.2e-39)
         (* (* z t) (* y -9.0))
         (if (<= z 700000000000.0) t_1 (* -9.0 (* t (* y z)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -4.1e+114) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= -1950.0) {
		tmp = t_1;
	} else if (z <= -9.2e-39) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= 700000000000.0) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (a * (b * (-27.0d0)))
    if (z <= (-4.1d+114)) then
        tmp = y * ((-9.0d0) * (z * t))
    else if (z <= (-1950.0d0)) then
        tmp = t_1
    else if (z <= (-9.2d-39)) then
        tmp = (z * t) * (y * (-9.0d0))
    else if (z <= 700000000000.0d0) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (t * (y * z))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -4.1e+114) {
		tmp = y * (-9.0 * (z * t));
	} else if (z <= -1950.0) {
		tmp = t_1;
	} else if (z <= -9.2e-39) {
		tmp = (z * t) * (y * -9.0);
	} else if (z <= 700000000000.0) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (y * z));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (a * (b * -27.0))
	tmp = 0
	if z <= -4.1e+114:
		tmp = y * (-9.0 * (z * t))
	elif z <= -1950.0:
		tmp = t_1
	elif z <= -9.2e-39:
		tmp = (z * t) * (y * -9.0)
	elif z <= 700000000000.0:
		tmp = t_1
	else:
		tmp = -9.0 * (t * (y * z))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)))
	tmp = 0.0
	if (z <= -4.1e+114)
		tmp = Float64(y * Float64(-9.0 * Float64(z * t)));
	elseif (z <= -1950.0)
		tmp = t_1;
	elseif (z <= -9.2e-39)
		tmp = Float64(Float64(z * t) * Float64(y * -9.0));
	elseif (z <= 700000000000.0)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(t * Float64(y * z)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (a * (b * -27.0));
	tmp = 0.0;
	if (z <= -4.1e+114)
		tmp = y * (-9.0 * (z * t));
	elseif (z <= -1950.0)
		tmp = t_1;
	elseif (z <= -9.2e-39)
		tmp = (z * t) * (y * -9.0);
	elseif (z <= 700000000000.0)
		tmp = t_1;
	else
		tmp = -9.0 * (t * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+114], N[(y * N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1950.0], t$95$1, If[LessEqual[z, -9.2e-39], N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 700000000000.0], t$95$1, N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1000000000000001e114

   1. Initial program 87.2%

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

   2. Taylor expanded in y around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*l* 53.9%

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

      4. *-commutative 53.9%

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

      5. *-commutative 53.9%

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

   4. Simplified 53.9%

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

   if -4.1000000000000001e114 < z < -1950 or -9.20000000000000033e-39 < z < 7e11

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. sub-neg 99.1%

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

      3. neg-mul-1 99.1%

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

      4. metadata-eval 99.1%

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

      5. metadata-eval 99.1%

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

      6. cancel-sign-sub-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. *-lft-identity 99.1%

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

      9. associate-*l* 98.5%

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

      10. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*r* 81.9%

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

   6. Simplified 81.9%

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

   if -1950 < z < -9.20000000000000033e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l* 60.5%

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

      4. *-commutative 60.5%

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

      5. *-commutative 60.5%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. associate-*r* 60.2%

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

   7. Simplified 60.2%

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

   if 7e11 < z

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. *-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l* 86.3%

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

      4. associate-*r* 86.3%

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

      5. associate-*l* 98.3%

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

      6. *-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in z around inf 40.2%

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

      1. *-commutative 40.2%

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

      2. *-commutative 40.2%

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

      3. associate-*l* 40.3%

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

      4. *-commutative 40.3%

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

      5. associate-*r* 40.2%

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

   7. Simplified 40.2%

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

   8. Taylor expanded in y around 0 40.2%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

      3. associate-*l* 44.3%

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

   10. Simplified 44.3%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1950:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 700000000000:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 11: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

2. Taylor expanded in y around 0 92.4%

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

   1. *-commutative 92.4%

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

   2. *-commutative 92.4%

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

   3. associate-*l* 92.4%

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

   4. associate-*r* 92.4%

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

   5. associate-*l* 96.4%

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

   6. *-commutative 96.4%

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

4. Simplified 96.4%

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

5. Final simplification 96.4%

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

Alternative 12: 76.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-148} \lor \neg \left(t \leq 1.3 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e-148) (not (<= t 1.3e+56)))
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (- (* x 2.0) (* a (* b -27.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e-148) || !(t <= 1.3e+56)) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.05d-148)) .or. (.not. (t <= 1.3d+56))) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e-148) || !(t <= 1.3e+56)) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (a * (b * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e-148) or not (t <= 1.3e+56):
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) - (a * (b * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e-148) || !(t <= 1.3e+56))
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.05e-148) || ~((t <= 1.3e+56)))
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) - (a * (b * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e-148], N[Not[LessEqual[t, 1.3e+56]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e-148 or 1.30000000000000005e56 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in a around 0 65.1%

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

   if -1.05e-148 < t < 1.30000000000000005e56

   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. Step-by-step derivation

      1. associate-+l- 93.0%

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

      2. sub-neg 93.0%

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

      3. neg-mul-1 93.0%

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

      4. metadata-eval 93.0%

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

      5. metadata-eval 93.0%

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

      6. cancel-sign-sub-inv 93.0%

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

      7. metadata-eval 93.0%

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

      8. *-lft-identity 93.0%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*r* 83.6%

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

   6. Simplified 83.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-148} \lor \neg \left(t \leq 1.3 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \end{array} \]

Alternative 13: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e-148)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= t 3.4e+67)
     (- (* x 2.0) (* a (* b -27.0)))
     (- (* x 2.0) (* t (* y (* 9.0 z)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e-148) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (t <= 3.4e+67) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.05d-148)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (t <= 3.4d+67) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (x * 2.0d0) - (t * (y * (9.0d0 * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e-148) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (t <= 3.4e+67) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e-148:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif t <= 3.4e+67:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (x * 2.0) - (t * (y * (9.0 * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e-148)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (t <= 3.4e+67)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.05e-148)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (t <= 3.4e+67)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e-148], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+67], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-148

   1. Initial program 95.3%

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

   2. Taylor expanded in a around 0 64.0%

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

   if -1.05e-148 < t < 3.4000000000000002e67

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. sub-neg 93.1%

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

      3. neg-mul-1 93.1%

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

      4. metadata-eval 93.1%

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

      5. metadata-eval 93.1%

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

      6. cancel-sign-sub-inv 93.1%

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

      7. metadata-eval 93.1%

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

      8. *-lft-identity 93.1%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r* 83.8%

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

   6. Simplified 83.8%

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

   if 3.4000000000000002e67 < t

   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* 80.7%

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

      10. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

      1. sub-neg 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*r* 80.8%

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

      4. associate-*r* 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. flip-+ 30.4%

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

      2. div-inv 30.3%

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

   7. Applied egg-rr 32.4%

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

   8. Taylor expanded in y around inf 66.9%

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

      1. associate-*r* 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-*l* 84.2%

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

   10. Simplified 84.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \]

Alternative 14: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+66}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e-148)
   (- (* x 2.0) (* y (* t (* 9.0 z))))
   (if (<= t 2e+66)
     (- (* x 2.0) (* a (* b -27.0)))
     (- (* x 2.0) (* t (* y (* 9.0 z)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e-148) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else if (t <= 2e+66) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.05d-148)) then
        tmp = (x * 2.0d0) - (y * (t * (9.0d0 * z)))
    else if (t <= 2d+66) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (x * 2.0d0) - (t * (y * (9.0d0 * z)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e-148) {
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	} else if (t <= 2e+66) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e-148:
		tmp = (x * 2.0) - (y * (t * (9.0 * z)))
	elif t <= 2e+66:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = (x * 2.0) - (t * (y * (9.0 * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e-148)
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(9.0 * z))));
	elseif (t <= 2e+66)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(9.0 * z))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.05e-148)
		tmp = (x * 2.0) - (y * (t * (9.0 * z)));
	elseif (t <= 2e+66)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = (x * 2.0) - (t * (y * (9.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e-148], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+66], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-148

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. sub-neg 95.3%

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

      3. neg-mul-1 95.3%

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

      4. metadata-eval 95.3%

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

      5. metadata-eval 95.3%

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

      6. cancel-sign-sub-inv 95.3%

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

      7. metadata-eval 95.3%

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

      8. *-lft-identity 95.3%

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

      9. associate-*l* 91.8%

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

      10. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. sub-neg 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

      4. associate-*r* 94.4%

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

      5. distribute-rgt-neg-in 94.4%

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

      6. *-commutative 94.4%

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

      7. distribute-rgt-neg-in 94.4%

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

      8. metadata-eval 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in y around inf 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-*r* 65.7%

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

      3. associate-*r* 65.8%

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

      4. associate-*l* 64.0%

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

   8. Simplified 64.0%

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

   if -1.05e-148 < t < 1.99999999999999989e66

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. sub-neg 93.1%

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

      3. neg-mul-1 93.1%

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

      4. metadata-eval 93.1%

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

      5. metadata-eval 93.1%

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

      6. cancel-sign-sub-inv 93.1%

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

      7. metadata-eval 93.1%

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

      8. *-lft-identity 93.1%

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

      9. associate-*l* 98.9%

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

      10. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r* 83.8%

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

   6. Simplified 83.8%

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

   if 1.99999999999999989e66 < t

   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* 80.7%

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

      10. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

      1. sub-neg 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*r* 80.8%

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

      4. associate-*r* 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. flip-+ 30.4%

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

      2. div-inv 30.3%

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

   7. Applied egg-rr 32.4%

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

   8. Taylor expanded in y around inf 66.9%

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

      1. associate-*r* 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-*l* 84.2%

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

   10. Simplified 84.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+66}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\\ \end{array} \]

Alternative 15: 46.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+18} \lor \neg \left(a \leq 1.2 \cdot 10^{-79}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.2e+18) (not (<= a 1.2e-79))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+18) || !(a <= 1.2e-79)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-7.2d+18)) .or. (.not. (a <= 1.2d-79))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+18) || !(a <= 1.2e-79)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.2e+18) or not (a <= 1.2e-79):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.2e+18) || !(a <= 1.2e-79))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7.2e+18) || ~((a <= 1.2e-79)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.2e+18], N[Not[LessEqual[a, 1.2e-79]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.2e18 or 1.20000000000000003e-79 < a

   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 a around inf 52.8%

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

   if -7.2e18 < a < 1.20000000000000003e-79

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 45.6%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+18} \lor \neg \left(a \leq 1.2 \cdot 10^{-79}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 16: 46.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.8e+19)
   (* 27.0 (* a b))
   (if (<= a 1.9e-82) (* x 2.0) (* a (* 27.0 b)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.8e+19) {
		tmp = 27.0 * (a * b);
	} else if (a <= 1.9e-82) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.8d+19)) then
        tmp = 27.0d0 * (a * b)
    else if (a <= 1.9d-82) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.8e+19) {
		tmp = 27.0 * (a * b);
	} else if (a <= 1.9e-82) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.8e+19:
		tmp = 27.0 * (a * b)
	elif a <= 1.9e-82:
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.8e+19)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (a <= 1.9e-82)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.8e+19)
		tmp = 27.0 * (a * b);
	elseif (a <= 1.9e-82)
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.8e+19], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-82], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8e19

   1. Initial program 95.6%

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

   2. Taylor expanded in a around inf 52.0%

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

   if -5.8e19 < a < 1.9000000000000001e-82

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 45.1%

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

   if 1.9000000000000001e-82 < a

   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 x around 0 68.6%

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

      1. fma-neg 68.6%

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

      2. *-commutative 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*l* 68.6%

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

      5. distribute-lft-neg-in 68.6%

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

      6. distribute-lft-neg-in 68.6%

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

      7. metadata-eval 68.6%

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

      8. *-commutative 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in a around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-*l* 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-82}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 17: 46.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-83}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.4e+20)
   (* b (* a 27.0))
   (if (<= a 9.8e-83) (* x 2.0) (* a (* 27.0 b)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.4e+20) {
		tmp = b * (a * 27.0);
	} else if (a <= 9.8e-83) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.4d+20)) then
        tmp = b * (a * 27.0d0)
    else if (a <= 9.8d-83) then
        tmp = x * 2.0d0
    else
        tmp = a * (27.0d0 * b)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.4e+20) {
		tmp = b * (a * 27.0);
	} else if (a <= 9.8e-83) {
		tmp = x * 2.0;
	} else {
		tmp = a * (27.0 * b);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.4e+20:
		tmp = b * (a * 27.0)
	elif a <= 9.8e-83:
		tmp = x * 2.0
	else:
		tmp = a * (27.0 * b)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.4e+20)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (a <= 9.8e-83)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(a * Float64(27.0 * b));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.4e+20)
		tmp = b * (a * 27.0);
	elseif (a <= 9.8e-83)
		tmp = x * 2.0;
	else
		tmp = a * (27.0 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.4e+20], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e-83], N[(x * 2.0), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.4e20

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 74.3%

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

      1. fma-neg 74.3%

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

      2. *-commutative 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*l* 74.4%

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

      5. distribute-lft-neg-in 74.4%

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

      6. distribute-lft-neg-in 74.4%

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

      7. metadata-eval 74.4%

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

      8. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in a around inf 52.0%

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

      1. associate-*r* 52.1%

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

   7. Simplified 52.1%

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

   if -5.4e20 < a < 9.8e-83

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 45.1%

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

   if 9.8e-83 < a

   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 x around 0 68.6%

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

      1. fma-neg 68.6%

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

      2. *-commutative 68.6%

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

      3. *-commutative 68.6%

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

      4. associate-*l* 68.6%

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

      5. distribute-lft-neg-in 68.6%

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

      6. distribute-lft-neg-in 68.6%

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

      7. metadata-eval 68.6%

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

      8. *-commutative 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in a around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-*l* 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-83}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 18: 30.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

2. Taylor expanded in x around inf 31.9%

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

3. Final simplification 31.9%

   \[\leadsto x \cdot 2 \]

Developer target: 95.4% 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 2023199 
(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)))