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

Percentage Accurate: 95.2% → 98.5%

Time: 12.3s

Alternatives: 16

Speedup: 1.0×

• 27.6% 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: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.1× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* y 9.0) -1e+54)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* t (* -9.0 z)))))
   (fma x 2.0 (fma z (* y (* t -9.0)) (* b (* a 27.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y * 9.0) <= -1e+54) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (t * (-9.0 * z)))));
	} else {
		tmp = fma(x, 2.0, fma(z, (y * (t * -9.0)), (b * (a * 27.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(y * 9.0) <= -1e+54)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(-9.0 * z)))));
	else
		tmp = fma(x, 2.0, fma(z, Float64(y * Float64(t * -9.0)), Float64(b * Float64(a * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(y * 9.0), $MachinePrecision], -1e+54], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(t * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -1.0000000000000001e54

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-+r- 96.1%

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

      3. cancel-sign-sub-inv 96.1%

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

      4. *-commutative 96.1%

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

      5. distribute-rgt-neg-out 96.1%

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

      6. associate-*r* 93.9%

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

      7. *-commutative 93.9%

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

      8. distribute-rgt-neg-in 93.9%

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

      9. associate-+r+ 93.9%

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

      10. sub-neg 93.9%

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

      11. associate-*l* 93.9%

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

      12. fma-def 93.9%

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

      13. fma-neg 93.9%

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

      14. associate-*l* 93.9%

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

      15. *-commutative 93.9%

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

      16. associate-*r* 99.8%

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

      17. distribute-rgt-neg-in 99.8%

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

   3. Simplified 99.8%

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

   if -1.0000000000000001e54 < (*.f64 y 9)

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-+r- 96.1%

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

      3. cancel-sign-sub-inv 96.1%

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

      4. *-commutative 96.1%

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

      5. distribute-rgt-neg-out 96.1%

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

      6. associate-*r* 97.4%

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

      7. *-commutative 97.4%

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

      8. distribute-rgt-neg-in 97.4%

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

      9. associate-+r+ 97.4%

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

      10. sub-neg 97.4%

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

      11. +-commutative 97.4%

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

      12. associate-+l- 97.4%

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

      13. fma-neg 97.4%

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

      14. associate-*l* 93.9%

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

      15. fma-neg 94.4%

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

      16. *-commutative 94.4%

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

      17. fma-neg 93.9%

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

   3. Simplified 97.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -1 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(z, y \cdot \left(t \cdot -9\right), b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\right)\\ \end{array} \end{array} \]

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 (<= (* y 9.0) -5e+172)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* t (* -9.0 z)))))
   (+ (* b (* a 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 ((y * 9.0) <= -5e+172) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (t * (-9.0 * z)))));
	} else {
		tmp = (b * (a * 27.0)) + ((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 (Float64(y * 9.0) <= -5e+172)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(-9.0 * z)))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(Float64(y * 9.0) * z))));
	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[(y * 9.0), $MachinePrecision], -5e+172], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(t * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -5.0000000000000001e172

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-+r- 96.1%

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

      3. cancel-sign-sub-inv 96.1%

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

      4. *-commutative 96.1%

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

      5. distribute-rgt-neg-out 96.1%

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

      6. associate-*r* 91.9%

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

      7. *-commutative 91.9%

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

      8. distribute-rgt-neg-in 91.9%

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

      9. associate-+r+ 91.9%

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

      10. sub-neg 91.9%

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

      11. associate-*l* 92.0%

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

      12. fma-def 92.0%

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

      13. fma-neg 92.0%

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

      14. associate-*l* 92.0%

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

      15. *-commutative 92.0%

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

      16. associate-*r* 99.9%

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

      17. distribute-rgt-neg-in 99.9%

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

   3. Simplified 99.9%

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

   if -5.0000000000000001e172 < (*.f64 y 9)

   1. Initial program 96.1%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(\left(y \cdot 9\right) \cdot z\right)\right)\\ \end{array} \]

Alternative 3: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-113}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-190}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* t (* -9.0 (* y z)))))
   (if (<= z -6e-16)
     t_1
     (if (<= z -2.8e-61)
       (* a (* 27.0 b))
       (if (<= z -3.5e-113)
         (* x 2.0)
         (if (<= z -6.5e-190)
           (* 27.0 (* a b))
           (if (<= z -4.1e-288)
             (* x 2.0)
             (if (<= z 2.7e-82)
               (* b (* a 27.0))
               (if (<= z 1.2e-35) (* x 2.0) 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 = t * (-9.0 * (y * z));
	double tmp;
	if (z <= -6e-16) {
		tmp = t_1;
	} else if (z <= -2.8e-61) {
		tmp = a * (27.0 * b);
	} else if (z <= -3.5e-113) {
		tmp = x * 2.0;
	} else if (z <= -6.5e-190) {
		tmp = 27.0 * (a * b);
	} else if (z <= -4.1e-288) {
		tmp = x * 2.0;
	} else if (z <= 2.7e-82) {
		tmp = b * (a * 27.0);
	} else if (z <= 1.2e-35) {
		tmp = x * 2.0;
	} 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 = t * ((-9.0d0) * (y * z))
    if (z <= (-6d-16)) then
        tmp = t_1
    else if (z <= (-2.8d-61)) then
        tmp = a * (27.0d0 * b)
    else if (z <= (-3.5d-113)) then
        tmp = x * 2.0d0
    else if (z <= (-6.5d-190)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= (-4.1d-288)) then
        tmp = x * 2.0d0
    else if (z <= 2.7d-82) then
        tmp = b * (a * 27.0d0)
    else if (z <= 1.2d-35) then
        tmp = x * 2.0d0
    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 = t * (-9.0 * (y * z));
	double tmp;
	if (z <= -6e-16) {
		tmp = t_1;
	} else if (z <= -2.8e-61) {
		tmp = a * (27.0 * b);
	} else if (z <= -3.5e-113) {
		tmp = x * 2.0;
	} else if (z <= -6.5e-190) {
		tmp = 27.0 * (a * b);
	} else if (z <= -4.1e-288) {
		tmp = x * 2.0;
	} else if (z <= 2.7e-82) {
		tmp = b * (a * 27.0);
	} else if (z <= 1.2e-35) {
		tmp = x * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = t * (-9.0 * (y * z))
	tmp = 0
	if z <= -6e-16:
		tmp = t_1
	elif z <= -2.8e-61:
		tmp = a * (27.0 * b)
	elif z <= -3.5e-113:
		tmp = x * 2.0
	elif z <= -6.5e-190:
		tmp = 27.0 * (a * b)
	elif z <= -4.1e-288:
		tmp = x * 2.0
	elif z <= 2.7e-82:
		tmp = b * (a * 27.0)
	elif z <= 1.2e-35:
		tmp = x * 2.0
	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(t * Float64(-9.0 * Float64(y * z)))
	tmp = 0.0
	if (z <= -6e-16)
		tmp = t_1;
	elseif (z <= -2.8e-61)
		tmp = Float64(a * Float64(27.0 * b));
	elseif (z <= -3.5e-113)
		tmp = Float64(x * 2.0);
	elseif (z <= -6.5e-190)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= -4.1e-288)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.7e-82)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 1.2e-35)
		tmp = Float64(x * 2.0);
	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 = t * (-9.0 * (y * z));
	tmp = 0.0;
	if (z <= -6e-16)
		tmp = t_1;
	elseif (z <= -2.8e-61)
		tmp = a * (27.0 * b);
	elseif (z <= -3.5e-113)
		tmp = x * 2.0;
	elseif (z <= -6.5e-190)
		tmp = 27.0 * (a * b);
	elseif (z <= -4.1e-288)
		tmp = x * 2.0;
	elseif (z <= 2.7e-82)
		tmp = b * (a * 27.0);
	elseif (z <= 1.2e-35)
		tmp = x * 2.0;
	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[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-16], t$95$1, If[LessEqual[z, -2.8e-61], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-113], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -6.5e-190], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-288], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.7e-82], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-35], N[(x * 2.0), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.99999999999999987e-16 or 1.2000000000000001e-35 < z

   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. sub-neg 93.0%

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

      2. distribute-lft-neg-in 93.0%

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

      3. associate-*l* 93.0%

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

      4. *-commutative 93.0%

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

      5. *-commutative 93.0%

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

      6. cancel-sign-sub-inv 93.0%

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

      7. *-commutative 93.0%

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

      8. *-commutative 93.0%

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

      9. associate-*l* 93.0%

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

      10. associate-*l* 92.3%

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

      11. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. associate-*r* 50.7%

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

      2. *-commutative 50.7%

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

      3. associate-*l* 54.4%

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

      4. *-commutative 54.4%

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

      5. *-commutative 54.4%

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

   6. Simplified 54.4%

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

   7. Taylor expanded in z around 0 50.7%

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

      1. *-commutative 50.7%

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

      2. associate-*r* 50.4%

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

      3. *-commutative 50.4%

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

      4. associate-*r* 50.7%

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

      5. *-commutative 50.7%

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

      6. associate-*l* 50.7%

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

   9. Simplified 50.7%

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

   if -5.99999999999999987e-16 < z < -2.8000000000000001e-61

   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 0 99.9%

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

   3. Taylor expanded in a around inf 47.1%

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

      1. *-commutative 47.1%

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

      2. *-commutative 47.1%

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

      3. associate-*r* 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in b around 0 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-*l* 47.2%

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

   8. Simplified 47.2%

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

   if -2.8000000000000001e-61 < z < -3.50000000000000029e-113 or -6.4999999999999997e-190 < z < -4.10000000000000007e-288 or 2.7000000000000001e-82 < z < 1.2000000000000001e-35

   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. sub-neg 99.9%

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

      2. distribute-lft-neg-in 99.9%

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

      3. associate-*l* 99.9%

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

      4. *-commutative 99.9%

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

      5. *-commutative 99.9%

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

      6. cancel-sign-sub-inv 99.9%

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

      7. *-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 99.9%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 46.1%

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

   if -3.50000000000000029e-113 < z < -6.4999999999999997e-190

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 99.4%

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

   3. Taylor expanded in a around inf 40.9%

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

      1. *-commutative 40.9%

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

   5. Simplified 40.9%

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

   if -4.10000000000000007e-288 < z < 2.7000000000000001e-82

   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 y around 0 99.7%

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

   3. Taylor expanded in a around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. *-commutative 51.9%

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

      3. associate-*r* 51.8%

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

   5. Simplified 51.8%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-113}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-190}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-124}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 (* a (* 27.0 b))))
   (if (<= z -1.85e-13)
     (* z (* y (* t -9.0)))
     (if (<= z -2.55e-61)
       t_1
       (if (<= z -9.6e-124)
         (* x 2.0)
         (if (<= z -8e-191)
           t_1
           (if (<= z -3.4e-288)
             (* x 2.0)
             (if (<= z 4.2e-81)
               (* b (* a 27.0))
               (if (<= z 3.1e-33) (* x 2.0) (* t (* -9.0 (* y z))))))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.85e-13) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -2.55e-61) {
		tmp = t_1;
	} else if (z <= -9.6e-124) {
		tmp = x * 2.0;
	} else if (z <= -8e-191) {
		tmp = t_1;
	} else if (z <= -3.4e-288) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-81) {
		tmp = b * (a * 27.0);
	} else if (z <= 3.1e-33) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (y * z));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (27.0d0 * b)
    if (z <= (-1.85d-13)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= (-2.55d-61)) then
        tmp = t_1
    else if (z <= (-9.6d-124)) then
        tmp = x * 2.0d0
    else if (z <= (-8d-191)) then
        tmp = t_1
    else if (z <= (-3.4d-288)) then
        tmp = x * 2.0d0
    else if (z <= 4.2d-81) then
        tmp = b * (a * 27.0d0)
    else if (z <= 3.1d-33) then
        tmp = x * 2.0d0
    else
        tmp = t * ((-9.0d0) * (y * z))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (27.0 * b);
	double tmp;
	if (z <= -1.85e-13) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -2.55e-61) {
		tmp = t_1;
	} else if (z <= -9.6e-124) {
		tmp = x * 2.0;
	} else if (z <= -8e-191) {
		tmp = t_1;
	} else if (z <= -3.4e-288) {
		tmp = x * 2.0;
	} else if (z <= 4.2e-81) {
		tmp = b * (a * 27.0);
	} else if (z <= 3.1e-33) {
		tmp = x * 2.0;
	} else {
		tmp = t * (-9.0 * (y * z));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = a * (27.0 * b)
	tmp = 0
	if z <= -1.85e-13:
		tmp = z * (y * (t * -9.0))
	elif z <= -2.55e-61:
		tmp = t_1
	elif z <= -9.6e-124:
		tmp = x * 2.0
	elif z <= -8e-191:
		tmp = t_1
	elif z <= -3.4e-288:
		tmp = x * 2.0
	elif z <= 4.2e-81:
		tmp = b * (a * 27.0)
	elif z <= 3.1e-33:
		tmp = x * 2.0
	else:
		tmp = t * (-9.0 * (y * z))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1.85e-13)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= -2.55e-61)
		tmp = t_1;
	elseif (z <= -9.6e-124)
		tmp = Float64(x * 2.0);
	elseif (z <= -8e-191)
		tmp = t_1;
	elseif (z <= -3.4e-288)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.2e-81)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 3.1e-33)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(t * Float64(-9.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1.85e-13)
		tmp = z * (y * (t * -9.0));
	elseif (z <= -2.55e-61)
		tmp = t_1;
	elseif (z <= -9.6e-124)
		tmp = x * 2.0;
	elseif (z <= -8e-191)
		tmp = t_1;
	elseif (z <= -3.4e-288)
		tmp = x * 2.0;
	elseif (z <= 4.2e-81)
		tmp = b * (a * 27.0);
	elseif (z <= 3.1e-33)
		tmp = x * 2.0;
	else
		tmp = t * (-9.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-13], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.55e-61], t$95$1, If[LessEqual[z, -9.6e-124], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -8e-191], t$95$1, If[LessEqual[z, -3.4e-288], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.2e-81], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-33], N[(x * 2.0), $MachinePrecision], N[(t * N[(-9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.84999999999999994e-13

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. distribute-lft-neg-in 94.1%

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

      3. associate-*l* 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

      6. cancel-sign-sub-inv 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 94.1%

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

      10. associate-*l* 87.5%

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

      11. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 55.5%

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

      1. associate-*r* 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*l* 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

   6. Simplified 55.4%

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

   if -1.84999999999999994e-13 < z < -2.54999999999999984e-61 or -9.5999999999999997e-124 < z < -8.0000000000000002e-191

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in a around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. *-commutative 42.0%

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

      3. associate-*r* 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in b around 0 42.0%

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

      1. *-commutative 42.0%

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

      2. associate-*l* 42.1%

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

   8. Simplified 42.1%

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

   if -2.54999999999999984e-61 < z < -9.5999999999999997e-124 or -8.0000000000000002e-191 < z < -3.39999999999999972e-288 or 4.1999999999999998e-81 < z < 3.09999999999999997e-33

   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. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 44.1%

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

   if -3.39999999999999972e-288 < z < 4.1999999999999998e-81

   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 y around 0 99.7%

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

   3. Taylor expanded in a around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. *-commutative 51.9%

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

      3. associate-*r* 51.8%

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

   5. Simplified 51.8%

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

   if 3.09999999999999997e-33 < z

   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. sub-neg 91.9%

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

      2. distribute-lft-neg-in 91.9%

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

      3. associate-*l* 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

      6. cancel-sign-sub-inv 91.9%

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

      7. *-commutative 91.9%

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

      8. *-commutative 91.9%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 97.2%

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

      11. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 45.9%

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

      1. associate-*r* 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*l* 53.3%

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

      4. *-commutative 53.3%

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

      5. *-commutative 53.3%

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

   6. Simplified 53.3%

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

   7. Taylor expanded in z around 0 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*r* 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*r* 45.9%

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

      5. *-commutative 45.9%

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

      6. associate-*l* 45.9%

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

   9. Simplified 45.9%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-124}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-191}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 5: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-124}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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 (* a (* 27.0 b))))
   (if (<= z -1.7e-15)
     (* z (* y (* t -9.0)))
     (if (<= z -1.6e-61)
       t_1
       (if (<= z -7e-124)
         (* x 2.0)
         (if (<= z -3.4e-190)
           t_1
           (if (<= z -4.2e-288)
             (* x 2.0)
             (if (<= z 3.5e-81)
               (* b (* a 27.0))
               (if (<= z 6.5e-36) (* x 2.0) (* -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 = a * (27.0 * b);
	double tmp;
	if (z <= -1.7e-15) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -1.6e-61) {
		tmp = t_1;
	} else if (z <= -7e-124) {
		tmp = x * 2.0;
	} else if (z <= -3.4e-190) {
		tmp = t_1;
	} else if (z <= -4.2e-288) {
		tmp = x * 2.0;
	} else if (z <= 3.5e-81) {
		tmp = b * (a * 27.0);
	} else if (z <= 6.5e-36) {
		tmp = x * 2.0;
	} 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 = a * (27.0d0 * b)
    if (z <= (-1.7d-15)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= (-1.6d-61)) then
        tmp = t_1
    else if (z <= (-7d-124)) then
        tmp = x * 2.0d0
    else if (z <= (-3.4d-190)) then
        tmp = t_1
    else if (z <= (-4.2d-288)) then
        tmp = x * 2.0d0
    else if (z <= 3.5d-81) then
        tmp = b * (a * 27.0d0)
    else if (z <= 6.5d-36) then
        tmp = x * 2.0d0
    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 = a * (27.0 * b);
	double tmp;
	if (z <= -1.7e-15) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= -1.6e-61) {
		tmp = t_1;
	} else if (z <= -7e-124) {
		tmp = x * 2.0;
	} else if (z <= -3.4e-190) {
		tmp = t_1;
	} else if (z <= -4.2e-288) {
		tmp = x * 2.0;
	} else if (z <= 3.5e-81) {
		tmp = b * (a * 27.0);
	} else if (z <= 6.5e-36) {
		tmp = x * 2.0;
	} 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 = a * (27.0 * b)
	tmp = 0
	if z <= -1.7e-15:
		tmp = z * (y * (t * -9.0))
	elif z <= -1.6e-61:
		tmp = t_1
	elif z <= -7e-124:
		tmp = x * 2.0
	elif z <= -3.4e-190:
		tmp = t_1
	elif z <= -4.2e-288:
		tmp = x * 2.0
	elif z <= 3.5e-81:
		tmp = b * (a * 27.0)
	elif z <= 6.5e-36:
		tmp = x * 2.0
	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(a * Float64(27.0 * b))
	tmp = 0.0
	if (z <= -1.7e-15)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= -1.6e-61)
		tmp = t_1;
	elseif (z <= -7e-124)
		tmp = Float64(x * 2.0);
	elseif (z <= -3.4e-190)
		tmp = t_1;
	elseif (z <= -4.2e-288)
		tmp = Float64(x * 2.0);
	elseif (z <= 3.5e-81)
		tmp = Float64(b * Float64(a * 27.0));
	elseif (z <= 6.5e-36)
		tmp = Float64(x * 2.0);
	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 = a * (27.0 * b);
	tmp = 0.0;
	if (z <= -1.7e-15)
		tmp = z * (y * (t * -9.0));
	elseif (z <= -1.6e-61)
		tmp = t_1;
	elseif (z <= -7e-124)
		tmp = x * 2.0;
	elseif (z <= -3.4e-190)
		tmp = t_1;
	elseif (z <= -4.2e-288)
		tmp = x * 2.0;
	elseif (z <= 3.5e-81)
		tmp = b * (a * 27.0);
	elseif (z <= 6.5e-36)
		tmp = x * 2.0;
	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[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e-15], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-61], t$95$1, If[LessEqual[z, -7e-124], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, -3.4e-190], t$95$1, If[LessEqual[z, -4.2e-288], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 3.5e-81], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-36], N[(x * 2.0), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7e-15

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. distribute-lft-neg-in 94.1%

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

      3. associate-*l* 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

      6. cancel-sign-sub-inv 94.1%

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

      7. *-commutative 94.1%

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

      8. *-commutative 94.1%

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

      9. associate-*l* 94.1%

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

      10. associate-*l* 87.5%

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

      11. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in y around inf 55.5%

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

      1. associate-*r* 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*l* 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

   6. Simplified 55.4%

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

   if -1.7e-15 < z < -1.6000000000000001e-61 or -6.9999999999999997e-124 < z < -3.39999999999999981e-190

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in a around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. *-commutative 42.0%

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

      3. associate-*r* 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in b around 0 42.0%

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

      1. *-commutative 42.0%

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

      2. associate-*l* 42.1%

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

   8. Simplified 42.1%

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

   if -1.6000000000000001e-61 < z < -6.9999999999999997e-124 or -3.39999999999999981e-190 < z < -4.19999999999999991e-288 or 3.49999999999999986e-81 < z < 6.50000000000000012e-36

   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. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 99.8%

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

      11. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 44.1%

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

   if -4.19999999999999991e-288 < z < 3.49999999999999986e-81

   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 y around 0 99.7%

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

   3. Taylor expanded in a around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. *-commutative 51.9%

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

      3. associate-*r* 51.8%

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

   5. Simplified 51.8%

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

   if 6.50000000000000012e-36 < z

   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. sub-neg 91.9%

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

      2. distribute-lft-neg-in 91.9%

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

      3. associate-*l* 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

      6. cancel-sign-sub-inv 91.9%

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

      7. *-commutative 91.9%

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

      8. *-commutative 91.9%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 97.2%

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

      11. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 45.9%

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

      1. *-commutative 45.9%

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

   6. Simplified 45.9%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-124}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-288}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-81}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 6: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;x \cdot 2 \leq -4 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 2 - t_2\\ \mathbf{elif}\;x \cdot 2 \leq 10000000000000:\\ \;\;\;\;t_1 - t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))) (t_2 (* 9.0 (* t (* y z)))))
   (if (<= (* x 2.0) -4e+92)
     (- (* x 2.0) t_2)
     (if (<= (* x 2.0) 10000000000000.0) (- t_1 t_2) (+ (* x 2.0) 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 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double tmp;
	if ((x * 2.0) <= -4e+92) {
		tmp = (x * 2.0) - t_2;
	} else if ((x * 2.0) <= 10000000000000.0) {
		tmp = t_1 - t_2;
	} else {
		tmp = (x * 2.0) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
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 ((x * 2.0d0) <= (-4d+92)) then
        tmp = (x * 2.0d0) - t_2
    else if ((x * 2.0d0) <= 10000000000000.0d0) then
        tmp = t_1 - t_2
    else
        tmp = (x * 2.0d0) + 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 = 27.0 * (a * b);
	double t_2 = 9.0 * (t * (y * z));
	double tmp;
	if ((x * 2.0) <= -4e+92) {
		tmp = (x * 2.0) - t_2;
	} else if ((x * 2.0) <= 10000000000000.0) {
		tmp = t_1 - t_2;
	} else {
		tmp = (x * 2.0) + t_1;
	}
	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 (x * 2.0) <= -4e+92:
		tmp = (x * 2.0) - t_2
	elif (x * 2.0) <= 10000000000000.0:
		tmp = t_1 - t_2
	else:
		tmp = (x * 2.0) + t_1
	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 (Float64(x * 2.0) <= -4e+92)
		tmp = Float64(Float64(x * 2.0) - t_2);
	elseif (Float64(x * 2.0) <= 10000000000000.0)
		tmp = Float64(t_1 - t_2);
	else
		tmp = Float64(Float64(x * 2.0) + 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 = 27.0 * (a * b);
	t_2 = 9.0 * (t * (y * z));
	tmp = 0.0;
	if ((x * 2.0) <= -4e+92)
		tmp = (x * 2.0) - t_2;
	elseif ((x * 2.0) <= 10000000000000.0)
		tmp = t_1 - t_2;
	else
		tmp = (x * 2.0) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
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[N[(x * 2.0), $MachinePrecision], -4e+92], N[(N[(x * 2.0), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 10000000000000.0], N[(t$95$1 - t$95$2), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 2) < -4.0000000000000002e92

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. distribute-lft-neg-in 96.1%

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

      3. associate-*l* 96.1%

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

      4. *-commutative 96.1%

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

      5. *-commutative 96.1%

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

      6. cancel-sign-sub-inv 96.1%

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

      7. *-commutative 96.1%

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

      8. *-commutative 96.1%

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

      9. associate-*l* 96.1%

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

      10. associate-*l* 97.9%

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

      11. associate-*l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in a around 0 83.0%

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

   if -4.0000000000000002e92 < (*.f64 x 2) < 1e13

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. distribute-lft-neg-in 96.1%

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

      3. associate-*l* 96.1%

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

      4. *-commutative 96.1%

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

      5. *-commutative 96.1%

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

      6. cancel-sign-sub-inv 96.1%

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

      7. *-commutative 96.1%

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

      8. *-commutative 96.1%

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

      9. associate-*l* 96.1%

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

      10. associate-*l* 93.7%

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

      11. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around 0 88.3%

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

   if 1e13 < (*.f64 x 2)

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. distribute-lft-neg-in 96.0%

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

      3. associate-*l* 96.0%

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

      4. *-commutative 96.0%

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

      5. *-commutative 96.0%

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

      6. cancel-sign-sub-inv 96.0%

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

      7. *-commutative 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-*l* 96.0%

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

      10. associate-*l* 96.3%

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

      11. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around 0 78.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4 \cdot 10^{+92}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \cdot 2 \leq 10000000000000:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 7: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+81} \lor \neg \left(a \cdot 27 \leq 2 \cdot 10^{-189}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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
 (if (or (<= (* a 27.0) -5e+81) (not (<= (* a 27.0) 2e-189)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* 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 tmp;
	if (((a * 27.0) <= -5e+81) || !((a * 27.0) <= 2e-189)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (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) :: tmp
    if (((a * 27.0d0) <= (-5d+81)) .or. (.not. ((a * 27.0d0) <= 2d-189))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (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 tmp;
	if (((a * 27.0) <= -5e+81) || !((a * 27.0) <= 2e-189)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * 27.0) <= -5e+81) or not ((a * 27.0) <= 2e-189):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * 27.0) <= -5e+81) || !(Float64(a * 27.0) <= 2e-189))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - 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)
	tmp = 0.0;
	if (((a * 27.0) <= -5e+81) || ~(((a * 27.0) <= 2e-189)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (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_] := If[Or[LessEqual[N[(a * 27.0), $MachinePrecision], -5e+81], N[Not[LessEqual[N[(a * 27.0), $MachinePrecision], 2e-189]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 27) < -4.9999999999999998e81 or 2.00000000000000014e-189 < (*.f64 a 27)

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. distribute-lft-neg-in 97.2%

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

      3. associate-*l* 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. cancel-sign-sub-inv 97.1%

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

      7. *-commutative 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-*l* 97.2%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 71.9%

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

   if -4.9999999999999998e81 < (*.f64 a 27) < 2.00000000000000014e-189

   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. Step-by-step derivation

      1. sub-neg 94.6%

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

      2. distribute-lft-neg-in 94.6%

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

      3. associate-*l* 94.6%

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

      4. *-commutative 94.6%

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

      5. *-commutative 94.6%

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

      6. cancel-sign-sub-inv 94.6%

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

      7. *-commutative 94.6%

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

      8. *-commutative 94.6%

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

      9. associate-*l* 94.6%

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

      10. associate-*l* 95.6%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around 0 81.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+81} \lor \neg \left(a \cdot 27 \leq 2 \cdot 10^{-189}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 8: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+81} \lor \neg \left(a \cdot 27 \leq 2 \cdot 10^{-189}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

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 (<= (* a 27.0) -5e+81) (not (<= (* a 27.0) 2e-189)))
   (+ (* x 2.0) (* 27.0 (* a b)))
   (- (* x 2.0) (* (* y 9.0) (* t z)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a * 27.0) <= -5e+81) || !((a * 27.0) <= 2e-189)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - ((y * 9.0) * (t * 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 (((a * 27.0d0) <= (-5d+81)) .or. (.not. ((a * 27.0d0) <= 2d-189))) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - ((y * 9.0d0) * (t * 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 (((a * 27.0) <= -5e+81) || !((a * 27.0) <= 2e-189)) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - ((y * 9.0) * (t * z));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if ((a * 27.0) <= -5e+81) or not ((a * 27.0) <= 2e-189):
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - ((y * 9.0) * (t * z))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a * 27.0) <= -5e+81) || !(Float64(a * 27.0) <= 2e-189))
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(t * 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 (((a * 27.0) <= -5e+81) || ~(((a * 27.0) <= 2e-189)))
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - ((y * 9.0) * (t * 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[Or[LessEqual[N[(a * 27.0), $MachinePrecision], -5e+81], N[Not[LessEqual[N[(a * 27.0), $MachinePrecision], 2e-189]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 27) < -4.9999999999999998e81 or 2.00000000000000014e-189 < (*.f64 a 27)

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. distribute-lft-neg-in 97.2%

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

      3. associate-*l* 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. cancel-sign-sub-inv 97.1%

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

      7. *-commutative 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-*l* 97.2%

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

      10. associate-*l* 94.7%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 71.9%

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

   if -4.9999999999999998e81 < (*.f64 a 27) < 2.00000000000000014e-189

   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. Step-by-step derivation

      1. sub-neg 94.6%

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

      2. distribute-lft-neg-in 94.6%

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

      3. associate-*l* 94.6%

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

      4. *-commutative 94.6%

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

      5. *-commutative 94.6%

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

      6. cancel-sign-sub-inv 94.6%

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

      7. *-commutative 94.6%

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

      8. *-commutative 94.6%

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

      9. associate-*l* 94.6%

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

      10. associate-*l* 95.6%

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

      11. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

      1. associate-+l- 94.7%

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

      2. associate-*r* 93.7%

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

      3. associate-*r* 94.6%

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

      4. associate-*r* 95.6%

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

      5. associate-*l* 95.6%

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

      6. associate-*r* 94.7%

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

   5. Applied egg-rr 94.7%

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

      1. associate-*r* 95.6%

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

      2. add-cube-cbrt 95.4%

         \[\leadsto x \cdot 2 - \left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right) - \color{blue}{\left(\sqrt[3]{\left(a \cdot 27\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot 27\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot 27\right) \cdot b}}\right) \]

      3. pow3 95.4%

         \[\leadsto x \cdot 2 - \left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right) - \color{blue}{{\left(\sqrt[3]{\left(a \cdot 27\right) \cdot b}\right)}^{3}}\right) \]

      4. associate-*r* 94.5%

         \[\leadsto x \cdot 2 - \left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right) - {\left(\sqrt[3]{\color{blue}{a \cdot \left(27 \cdot b\right)}}\right)}^{3}\right) \]

   7. Applied egg-rr 94.5%

      \[\leadsto x \cdot 2 - \left(y \cdot \left(9 \cdot \left(z \cdot t\right)\right) - \color{blue}{{\left(\sqrt[3]{a \cdot \left(27 \cdot b\right)}\right)}^{3}}\right) \]

   8. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r* 81.5%

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

      3. associate-*r* 81.4%

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

      4. *-commutative 81.4%

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

   10. Simplified 81.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 27 \leq -5 \cdot 10^{+81} \lor \neg \left(a \cdot 27 \leq 2 \cdot 10^{-189}\right):\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 9: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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
 (if (<= z 3.8e+75)
   (+ (- (* x 2.0) (* (* y 9.0) (* t z))) (* a (* 27.0 b)))
   (- (* x 2.0) (* 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 tmp;
	if (z <= 3.8e+75) {
		tmp = ((x * 2.0) - ((y * 9.0) * (t * z))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (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) :: tmp
    if (z <= 3.8d+75) then
        tmp = ((x * 2.0d0) - ((y * 9.0d0) * (t * z))) + (a * (27.0d0 * b))
    else
        tmp = (x * 2.0d0) - (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 tmp;
	if (z <= 3.8e+75) {
		tmp = ((x * 2.0) - ((y * 9.0) * (t * z))) + (a * (27.0 * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 3.8e+75:
		tmp = ((x * 2.0) - ((y * 9.0) * (t * z))) + (a * (27.0 * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.8e+75)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(y * 9.0) * Float64(t * z))) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(x * 2.0) - 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)
	tmp = 0.0;
	if (z <= 3.8e+75)
		tmp = ((x * 2.0) - ((y * 9.0) * (t * z))) + (a * (27.0 * b));
	else
		tmp = (x * 2.0) - (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_] := If[LessEqual[z, 3.8e+75], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * 9.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.8000000000000002e75

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. distribute-lft-neg-in 98.0%

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

      3. associate-*l* 97.9%

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

      4. *-commutative 97.9%

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

      5. *-commutative 97.9%

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

      6. cancel-sign-sub-inv 97.9%

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

      7. *-commutative 97.9%

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

      8. *-commutative 97.9%

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

      9. associate-*l* 98.0%

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

      10. associate-*l* 95.0%

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

      11. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   if 3.8000000000000002e75 < z

   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. Step-by-step derivation

      1. sub-neg 87.2%

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

      2. distribute-lft-neg-in 87.2%

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

      3. associate-*l* 87.1%

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

      4. *-commutative 87.1%

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

      5. *-commutative 87.1%

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

      6. cancel-sign-sub-inv 87.1%

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

      7. *-commutative 87.1%

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

      8. *-commutative 87.1%

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

      9. associate-*l* 87.2%

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

      10. associate-*l* 95.6%

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

      11. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around 0 69.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+75}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 10: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - y \cdot \left(9 \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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
 (if (<= z 8.5e+63)
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* y (* 9.0 (* t z)))))
   (- (* x 2.0) (* 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 tmp;
	if (z <= 8.5e+63) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (y * (9.0 * (t * z))));
	} else {
		tmp = (x * 2.0) - (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) :: tmp
    if (z <= 8.5d+63) then
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - (y * (9.0d0 * (t * z))))
    else
        tmp = (x * 2.0d0) - (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 tmp;
	if (z <= 8.5e+63) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (y * (9.0 * (t * z))));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (y * z)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 8.5e+63:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (y * (9.0 * (t * z))))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (y * z)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 8.5e+63)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(y * Float64(9.0 * Float64(t * z)))));
	else
		tmp = Float64(Float64(x * 2.0) - 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)
	tmp = 0.0;
	if (z <= 8.5e+63)
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (y * (9.0 * (t * z))));
	else
		tmp = (x * 2.0) - (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_] := If[LessEqual[z, 8.5e+63], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.5000000000000004e63

   1. Initial program 97.9%

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

      1. sub-neg 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*l* 97.9%

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

      4. *-commutative 97.9%

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

      5. *-commutative 97.9%

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

      6. cancel-sign-sub-inv 97.9%

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

      7. *-commutative 97.9%

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

      8. *-commutative 97.9%

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

      9. associate-*l* 97.9%

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

      10. associate-*l* 94.9%

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

      11. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

      1. associate-+l- 94.4%

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

      2. associate-*r* 97.5%

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

      3. associate-*r* 97.9%

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

      4. associate-*r* 94.9%

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

      5. associate-*l* 94.9%

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

      6. associate-*r* 94.5%

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

   5. Applied egg-rr 94.5%

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

   if 8.5000000000000004e63 < z

   1. Initial program 87.7%

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

      1. sub-neg 87.7%

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

      2. distribute-lft-neg-in 87.7%

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

      3. associate-*l* 87.6%

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

      4. *-commutative 87.6%

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

      5. *-commutative 87.6%

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

      6. cancel-sign-sub-inv 87.6%

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

      7. *-commutative 87.6%

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

      8. *-commutative 87.6%

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

      9. associate-*l* 87.7%

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

      10. associate-*l* 95.8%

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

      11. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 68.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - y \cdot \left(9 \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 11: 95.3% accurate, 1.0× speedup

Math

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

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) (* t (* 9.0 (* y z))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a * 27.0)) + ((x * 2.0) - (t * (9.0 * (y * 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) - (t * (9.0d0 * (y * 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) - (t * (9.0 * (y * 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) - (t * (9.0 * (y * 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(t * Float64(9.0 * Float64(y * 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) - (t * (9.0 * (y * 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[(t * N[(9.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

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

2. Taylor expanded in y around 0 96.1%

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

3. Final simplification 96.1%

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

Alternative 12: 76.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

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
 (if (<= z -4.5e+64)
   (* z (* y (* t -9.0)))
   (if (<= z 1.55e-10) (+ (* x 2.0) (* 27.0 (* a b))) (* -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 tmp;
	if (z <= -4.5e+64) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= 1.55e-10) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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) :: tmp
    if (z <= (-4.5d+64)) then
        tmp = z * (y * (t * (-9.0d0)))
    else if (z <= 1.55d-10) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    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 tmp;
	if (z <= -4.5e+64) {
		tmp = z * (y * (t * -9.0));
	} else if (z <= 1.55e-10) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} 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):
	tmp = 0
	if z <= -4.5e+64:
		tmp = z * (y * (t * -9.0))
	elif z <= 1.55e-10:
		tmp = (x * 2.0) + (27.0 * (a * b))
	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)
	tmp = 0.0
	if (z <= -4.5e+64)
		tmp = Float64(z * Float64(y * Float64(t * -9.0)));
	elseif (z <= 1.55e-10)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	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)
	tmp = 0.0;
	if (z <= -4.5e+64)
		tmp = z * (y * (t * -9.0));
	elseif (z <= 1.55e-10)
		tmp = (x * 2.0) + (27.0 * (a * b));
	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_] := If[LessEqual[z, -4.5e+64], N[(z * N[(y * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-10], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999973e64

   1. Initial program 92.7%

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

      1. sub-neg 92.7%

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

      2. distribute-lft-neg-in 92.7%

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

      3. associate-*l* 92.6%

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

      4. *-commutative 92.6%

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

      5. *-commutative 92.6%

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

      6. cancel-sign-sub-inv 92.6%

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

      7. *-commutative 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-*l* 92.7%

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

      10. associate-*l* 84.3%

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

      11. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. associate-*r* 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-*l* 61.7%

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

      4. *-commutative 61.7%

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

      5. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if -4.49999999999999973e64 < z < 1.55000000000000008e-10

   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. sub-neg 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. cancel-sign-sub-inv 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-*l* 99.8%

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

      10. associate-*l* 98.5%

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

      11. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around 0 79.5%

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

   if 1.55000000000000008e-10 < z

   1. Initial program 91.0%

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

      1. sub-neg 91.0%

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

      2. distribute-lft-neg-in 91.0%

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

      3. associate-*l* 91.0%

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

      4. *-commutative 91.0%

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

      5. *-commutative 91.0%

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

      6. cancel-sign-sub-inv 91.0%

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

      7. *-commutative 91.0%

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

      8. *-commutative 91.0%

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

      9. associate-*l* 91.0%

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

      10. associate-*l* 96.8%

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

      11. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 47.7%

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

      1. *-commutative 47.7%

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

   6. Simplified 47.7%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(y \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \end{array} \]

Alternative 13: 48.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+87}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 10^{+14}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.1e+87) (* x 2.0) (if (<= x 1e+14) (* a (* 27.0 b)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.1e+87) {
		tmp = x * 2.0;
	} else if (x <= 1e+14) {
		tmp = a * (27.0 * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.1d+87)) then
        tmp = x * 2.0d0
    else if (x <= 1d+14) then
        tmp = a * (27.0d0 * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.1e+87) {
		tmp = x * 2.0;
	} else if (x <= 1e+14) {
		tmp = a * (27.0 * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.1e+87:
		tmp = x * 2.0
	elif x <= 1e+14:
		tmp = a * (27.0 * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.1e+87)
		tmp = Float64(x * 2.0);
	elseif (x <= 1e+14)
		tmp = Float64(a * Float64(27.0 * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.1e+87)
		tmp = x * 2.0;
	elseif (x <= 1e+14)
		tmp = a * (27.0 * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.1e+87], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 1e+14], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e87 or 1e14 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. distribute-lft-neg-in 96.1%

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

      3. associate-*l* 96.0%

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

      4. *-commutative 96.0%

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

      5. *-commutative 96.0%

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

      6. cancel-sign-sub-inv 96.0%

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

      7. *-commutative 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-*l* 96.1%

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

      10. associate-*l* 97.1%

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

      11. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 59.9%

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

   if -3.1e87 < x < 1e14

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 96.1%

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

   3. Taylor expanded in a around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. *-commutative 43.8%

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

      3. associate-*r* 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in b around 0 43.8%

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

      1. *-commutative 43.8%

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

      2. associate-*l* 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+87}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 10^{+14}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14: 48.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+88}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.42e+88)
   (* x 2.0)
   (if (<= x 3.2e+15) (* b (* a 27.0)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.42e+88) {
		tmp = x * 2.0;
	} else if (x <= 3.2e+15) {
		tmp = b * (a * 27.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.42d+88)) then
        tmp = x * 2.0d0
    else if (x <= 3.2d+15) then
        tmp = b * (a * 27.0d0)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.42e+88) {
		tmp = x * 2.0;
	} else if (x <= 3.2e+15) {
		tmp = b * (a * 27.0);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.42e+88:
		tmp = x * 2.0
	elif x <= 3.2e+15:
		tmp = b * (a * 27.0)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.42e+88)
		tmp = Float64(x * 2.0);
	elseif (x <= 3.2e+15)
		tmp = Float64(b * Float64(a * 27.0));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.42e+88)
		tmp = x * 2.0;
	elseif (x <= 3.2e+15)
		tmp = b * (a * 27.0);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.42e+88], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 3.2e+15], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.41999999999999996e88 or 3.2e15 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. distribute-lft-neg-in 96.1%

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

      3. associate-*l* 96.0%

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

      4. *-commutative 96.0%

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

      5. *-commutative 96.0%

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

      6. cancel-sign-sub-inv 96.0%

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

      7. *-commutative 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-*l* 96.1%

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

      10. associate-*l* 97.1%

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

      11. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 59.9%

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

   if -1.41999999999999996e88 < x < 3.2e15

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 96.1%

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

   3. Taylor expanded in a around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. *-commutative 43.8%

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

      3. associate-*r* 43.7%

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

   5. Simplified 43.7%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+88}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+15}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 15: 48.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.8e+85) (* x 2.0) (if (<= x 3.6e+15) (* 27.0 (* a b)) (* x 2.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+85) {
		tmp = x * 2.0;
	} else if (x <= 3.6e+15) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.8d+85)) then
        tmp = x * 2.0d0
    else if (x <= 3.6d+15) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+85) {
		tmp = x * 2.0;
	} else if (x <= 3.6e+15) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.8e+85:
		tmp = x * 2.0
	elif x <= 3.6e+15:
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.8e+85)
		tmp = Float64(x * 2.0);
	elseif (x <= 3.6e+15)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.8e+85)
		tmp = x * 2.0;
	elseif (x <= 3.6e+15)
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.8e+85], N[(x * 2.0), $MachinePrecision], If[LessEqual[x, 3.6e+15], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e85 or 3.6e15 < x

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. distribute-lft-neg-in 96.1%

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

      3. associate-*l* 96.0%

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

      4. *-commutative 96.0%

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

      5. *-commutative 96.0%

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

      6. cancel-sign-sub-inv 96.0%

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

      7. *-commutative 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-*l* 96.1%

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

      10. associate-*l* 97.1%

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

      11. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 59.9%

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

   if -1.7999999999999999e85 < x < 3.6e15

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 96.1%

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

   3. Taylor expanded in a around inf 43.8%

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

      1. *-commutative 43.8%

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

   5. Simplified 43.8%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 16: 31.5% 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 96.1%

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

   1. sub-neg 96.1%

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

   2. distribute-lft-neg-in 96.1%

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

   3. associate-*l* 96.1%

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

   4. *-commutative 96.1%

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

   5. *-commutative 96.1%

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

   6. cancel-sign-sub-inv 96.1%

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

   7. *-commutative 96.1%

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

   8. *-commutative 96.1%

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

   9. associate-*l* 96.1%

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

   10. associate-*l* 95.1%

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

   11. associate-*l* 94.7%

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

3. Simplified 94.7%

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

4. Taylor expanded in x around inf 29.9%

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

5. Final simplification 29.9%

   \[\leadsto x \cdot 2 \]

Developer target: 94.9% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023293 
(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)))