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

Percentage Accurate: 95.3% → 98.7%

Time: 15.0s

Alternatives: 18

Speedup: 0.9×

• 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: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-224}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5e-224)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* z (* t -9.0)))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* -9.0 (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e-224) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (z * (t * -9.0)))));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (-9.0 * (z * y)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5e-224)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(z * Float64(t * -9.0)))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(-9.0 * Float64(z * y)))));
	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[z, -5e-224], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e-224

   1. Initial program 93.4%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around 0 96.2%

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

      1. associate-*r* 96.2%

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

      2. *-commutative 96.2%

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

      3. *-commutative 96.2%

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

   6. Simplified 96.2%

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

   if -4.9999999999999999e-224 < z

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-+r- 94.7%

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

      3. *-commutative 94.7%

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

      4. cancel-sign-sub-inv 94.7%

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

      5. associate-*r* 92.0%

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

      6. distribute-lft-neg-in 92.0%

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

      7. *-commutative 92.0%

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

      8. cancel-sign-sub-inv 92.0%

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

      9. associate-+r- 92.0%

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

      10. associate-*l* 92.1%

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

      11. fma-def 93.4%

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

      12. cancel-sign-sub-inv 93.4%

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

      13. fma-def 93.4%

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

      14. distribute-lft-neg-in 93.4%

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

      15. distribute-rgt-neg-in 93.4%

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

      16. *-commutative 93.4%

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

      17. associate-*r* 96.1%

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

      18. distribute-rgt-neg-out 96.1%

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

      19. *-commutative 96.1%

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

      20. associate-*r* 96.1%

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

   3. Simplified 96.1%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-224}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-63}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= t 5e-63)
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* z (* y (* t 9.0))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* -9.0 (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5e-63) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (z * (y * (t * 9.0)));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (-9.0 * (z * y)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 5e-63)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(z * Float64(y * Float64(t * 9.0))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(-9.0 * Float64(z * y)))));
	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[t, 5e-63], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.0000000000000002e-63

   1. Initial program 93.6%

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

      1. sub-neg 93.6%

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

      2. sub-neg 93.6%

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

      3. associate-*l* 93.5%

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

      4. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-+r- 93.5%

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

      3. associate-*l* 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in y around 0 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*r* 94.1%

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

      3. *-commutative 94.1%

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

      4. associate-*r* 94.1%

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

      5. *-commutative 94.1%

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

      6. metadata-eval 94.1%

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

      7. distribute-rgt-neg-in 94.1%

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

      8. associate-*r* 94.1%

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

      9. associate-*r* 94.1%

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

      10. distribute-rgt-neg-in 94.1%

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

      11. metadata-eval 94.1%

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

      12. associate-*l* 94.1%

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

      13. associate-*l* 94.6%

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

   8. Simplified 94.6%

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

   if 5.0000000000000002e-63 < t

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+r- 95.8%

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

      3. *-commutative 95.8%

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

      4. cancel-sign-sub-inv 95.8%

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

      5. associate-*r* 90.4%

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

      6. distribute-lft-neg-in 90.4%

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

      7. *-commutative 90.4%

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

      8. cancel-sign-sub-inv 90.4%

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

      9. associate-+r- 90.4%

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

      10. associate-*l* 91.7%

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

      11. fma-def 93.0%

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

      12. cancel-sign-sub-inv 93.0%

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

      13. fma-def 93.0%

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

      14. distribute-lft-neg-in 93.0%

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

      15. distribute-rgt-neg-in 93.0%

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

      16. *-commutative 93.0%

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

      17. associate-*r* 98.5%

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

      18. distribute-rgt-neg-out 98.5%

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

      19. *-commutative 98.5%

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

      20. associate-*r* 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-63}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-224}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5e-224)
   (fma a (* 27.0 b) (fma x 2.0 (* y (* t (* z -9.0)))))
   (fma a (* 27.0 b) (fma x 2.0 (* t (* -9.0 (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e-224) {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (y * (t * (z * -9.0)))));
	} else {
		tmp = fma(a, (27.0 * b), fma(x, 2.0, (t * (-9.0 * (z * y)))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5e-224)
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(y * Float64(t * Float64(z * -9.0)))));
	else
		tmp = fma(a, Float64(27.0 * b), fma(x, 2.0, Float64(t * Float64(-9.0 * Float64(z * y)))));
	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[z, -5e-224], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x * 2.0 + N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e-224

   1. Initial program 93.4%

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

   3. Simplified 96.2%

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

   if -4.9999999999999999e-224 < z

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-+r- 94.7%

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

      3. *-commutative 94.7%

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

      4. cancel-sign-sub-inv 94.7%

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

      5. associate-*r* 92.0%

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

      6. distribute-lft-neg-in 92.0%

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

      7. *-commutative 92.0%

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

      8. cancel-sign-sub-inv 92.0%

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

      9. associate-+r- 92.0%

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

      10. associate-*l* 92.1%

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

      11. fma-def 93.4%

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

      12. cancel-sign-sub-inv 93.4%

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

      13. fma-def 93.4%

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

      14. distribute-lft-neg-in 93.4%

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

      15. distribute-rgt-neg-in 93.4%

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

      16. *-commutative 93.4%

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

      17. associate-*r* 96.1%

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

      18. distribute-rgt-neg-out 96.1%

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

      19. *-commutative 96.1%

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

      20. associate-*r* 96.1%

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

   3. Simplified 96.1%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-224}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, \mathsf{fma}\left(x, 2, t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\right)\right)\\ \end{array} \]

Alternative 4: 97.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -9 \cdot \left(y \cdot t\right), x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.4e+41)
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* 9.0 (* z t))))
   (fma z (* -9.0 (* y t)) (* 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 (z <= 1.4e+41) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	} else {
		tmp = fma(z, (-9.0 * (y * t)), (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 (z <= 1.4e+41)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(y * Float64(9.0 * Float64(z * t))));
	else
		tmp = fma(z, Float64(-9.0 * Float64(y * t)), Float64(x * 2.0));
	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[z, 1.4e+41], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(-9.0 * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4e41

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+r- 95.8%

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

      3. associate-*l* 96.3%

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

   5. Applied egg-rr 96.3%

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

   if 1.4e41 < z

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r- 90.9%

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

      3. *-commutative 90.9%

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

      4. cancel-sign-sub-inv 90.9%

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

      5. associate-*r* 95.2%

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

      6. distribute-lft-neg-in 95.2%

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

      7. *-commutative 95.2%

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

      8. cancel-sign-sub-inv 95.2%

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

      9. associate-+r- 95.2%

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

      10. associate-*l* 95.2%

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

      11. fma-def 98.3%

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

      12. cancel-sign-sub-inv 98.3%

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

      13. fma-def 98.3%

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

      14. distribute-lft-neg-in 98.3%

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

      15. distribute-rgt-neg-in 98.3%

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

      16. *-commutative 98.3%

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

      17. associate-*r* 94.0%

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

      18. distribute-rgt-neg-out 94.0%

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

      19. *-commutative 94.0%

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

      20. associate-*r* 94.0%

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

   3. Simplified 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l* 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*r* 89.4%

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

      5. *-commutative 89.4%

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

      6. add-cube-cbrt 89.1%

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

      7. pow3 89.1%

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

      8. *-commutative 89.1%

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

      9. associate-*r* 93.7%

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

      10. *-commutative 93.7%

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

      11. associate-*l* 93.7%

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

      12. *-commutative 93.7%

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

      13. *-commutative 93.7%

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

      14. associate-*r* 93.6%

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

   5. Applied egg-rr 93.6%

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

   6. Taylor expanded in a around 0 79.3%

      \[\leadsto \color{blue}{-9 \cdot \left({1}^{0.3333333333333333} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) + 2 \cdot x} \]
   7. Step-by-step derivation

      1. pow-base-1 79.3%

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

      2. associate-*r* 79.3%

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

      3. metadata-eval 79.3%

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

      4. associate-*r* 79.3%

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

      5. *-commutative 79.3%

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

      6. associate-*r* 83.7%

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

      7. associate-*r* 83.7%

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

      8. *-commutative 83.7%

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

      9. fma-def 83.7%

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

      10. associate-*r* 83.7%

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

      11. *-commutative 83.7%

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

      12. associate-*r* 83.7%

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

   8. Simplified 83.7%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -9 \cdot \left(y \cdot t\right), x \cdot 2\right)\\ \end{array} \]

Alternative 5: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-120}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 (+ (* b (* a 27.0)) (* (* z t) (* y -9.0)))))
   (if (<= z -3.5e-55)
     t_1
     (if (<= z 1.35e-120)
       (+ (* x 2.0) (* 27.0 (* a b)))
       (if (<= z 1.85e+40) t_1 (- (* x 2.0) (* 9.0 (* t (* z y)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	double tmp;
	if (z <= -3.5e-55) {
		tmp = t_1;
	} else if (z <= 1.35e-120) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (z <= 1.85e+40) {
		tmp = t_1;
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	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 = (b * (a * 27.0d0)) + ((z * t) * (y * (-9.0d0)))
    if (z <= (-3.5d-55)) then
        tmp = t_1
    else if (z <= 1.35d-120) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else if (z <= 1.85d+40) then
        tmp = t_1
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    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 = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	double tmp;
	if (z <= -3.5e-55) {
		tmp = t_1;
	} else if (z <= 1.35e-120) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else if (z <= 1.85e+40) {
		tmp = t_1;
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (b * (a * 27.0)) + ((z * t) * (y * -9.0))
	tmp = 0
	if z <= -3.5e-55:
		tmp = t_1
	elif z <= 1.35e-120:
		tmp = (x * 2.0) + (27.0 * (a * b))
	elif z <= 1.85e+40:
		tmp = t_1
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(z * t) * Float64(y * -9.0)))
	tmp = 0.0
	if (z <= -3.5e-55)
		tmp = t_1;
	elseif (z <= 1.35e-120)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	elseif (z <= 1.85e+40)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	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 = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	tmp = 0.0;
	if (z <= -3.5e-55)
		tmp = t_1;
	elseif (z <= 1.35e-120)
		tmp = (x * 2.0) + (27.0 * (a * b));
	elseif (z <= 1.85e+40)
		tmp = t_1;
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-55], t$95$1, If[LessEqual[z, 1.35e-120], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+40], t$95$1, N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000025e-55 or 1.3499999999999999e-120 < z < 1.85e40

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. sub-neg 92.6%

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

      3. associate-*l* 92.5%

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

      4. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around 0 68.0%

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

      1. cancel-sign-sub-inv 68.0%

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

      2. associate-*r* 68.0%

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

      3. metadata-eval 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-*r* 68.0%

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

      6. associate-*r* 68.1%

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

      7. *-commutative 68.1%

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

      8. *-commutative 68.1%

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

      9. *-commutative 68.1%

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

      10. associate-*r* 68.0%

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

      11. *-commutative 68.0%

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

   6. Applied egg-rr 68.0%

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

   if -3.50000000000000025e-55 < z < 1.3499999999999999e-120

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-*l* 98.7%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.3%

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

   if 1.85e40 < z

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 86.3%

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

      4. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around 0 79.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-120}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 6: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot 2 + t_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+39}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t_1\\ \end{array} \end{array} \]

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 (* 9.0 (* t (* z y)))) (t_2 (* 27.0 (* a b))))
   (if (<= z -8.5e-56)
     (+ (* b (* a 27.0)) (* (* z t) (* y -9.0)))
     (if (<= z 2e-121)
       (+ (* x 2.0) t_2)
       (if (<= z 5e+39) (- t_2 t_1) (- (* 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 = 9.0 * (t * (z * y));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (z <= -8.5e-56) {
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	} else if (z <= 2e-121) {
		tmp = (x * 2.0) + t_2;
	} else if (z <= 5e+39) {
		tmp = t_2 - t_1;
	} 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 = 9.0d0 * (t * (z * y))
    t_2 = 27.0d0 * (a * b)
    if (z <= (-8.5d-56)) then
        tmp = (b * (a * 27.0d0)) + ((z * t) * (y * (-9.0d0)))
    else if (z <= 2d-121) then
        tmp = (x * 2.0d0) + t_2
    else if (z <= 5d+39) then
        tmp = t_2 - t_1
    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 = 9.0 * (t * (z * y));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (z <= -8.5e-56) {
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	} else if (z <= 2e-121) {
		tmp = (x * 2.0) + t_2;
	} else if (z <= 5e+39) {
		tmp = t_2 - t_1;
	} 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 = 9.0 * (t * (z * y))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if z <= -8.5e-56:
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0))
	elif z <= 2e-121:
		tmp = (x * 2.0) + t_2
	elif z <= 5e+39:
		tmp = t_2 - t_1
	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(9.0 * Float64(t * Float64(z * y)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (z <= -8.5e-56)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(z * t) * Float64(y * -9.0)));
	elseif (z <= 2e-121)
		tmp = Float64(Float64(x * 2.0) + t_2);
	elseif (z <= 5e+39)
		tmp = Float64(t_2 - t_1);
	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 = 9.0 * (t * (z * y));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (z <= -8.5e-56)
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	elseif (z <= 2e-121)
		tmp = (x * 2.0) + t_2;
	elseif (z <= 5e+39)
		tmp = t_2 - t_1;
	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[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-56], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-121], N[(N[(x * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[z, 5e+39], N[(t$95$2 - t$95$1), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.49999999999999932e-56

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 90.4%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in x around 0 67.4%

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

      1. cancel-sign-sub-inv 67.4%

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

      2. associate-*r* 66.1%

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

      3. metadata-eval 66.1%

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

      4. *-commutative 66.1%

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

      5. associate-*r* 66.2%

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

      6. associate-*r* 66.2%

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

      7. *-commutative 66.2%

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

      8. *-commutative 66.2%

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

      9. *-commutative 66.2%

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

      10. associate-*r* 66.1%

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

      11. *-commutative 66.1%

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

   6. Applied egg-rr 66.1%

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

   if -8.49999999999999932e-56 < z < 2e-121

   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. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 90.4%

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

   if 2e-121 < z < 5.00000000000000015e39

   1. Initial program 94.4%

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

      1. sub-neg 94.4%

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

      2. sub-neg 94.4%

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

      3. associate-*l* 94.2%

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

      4. 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. Taylor expanded in x around 0 70.0%

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

   if 5.00000000000000015e39 < z

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 86.3%

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

      4. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around 0 79.3%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+39}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 7: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(z \cdot y\right) \cdot \left(t \cdot 9\right)\right)\\ \end{array} \end{array} \]

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 -1.42e+65)
   (+ (* b (* a 27.0)) (* (* z t) (* y -9.0)))
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* z y) (* t 9.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.42e+65) {
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	} else {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * y) * (t * 9.0)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.42d+65)) then
        tmp = (b * (a * 27.0d0)) + ((z * t) * (y * (-9.0d0)))
    else
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((z * y) * (t * 9.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.42e+65) {
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	} else {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * y) * (t * 9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.42e+65:
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0))
	else:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * y) * (t * 9.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.42e+65)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(z * t) * Float64(y * -9.0)));
	else
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(z * y) * Float64(t * 9.0))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.42e+65)
		tmp = (b * (a * 27.0)) + ((z * t) * (y * -9.0));
	else
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * y) * (t * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.42e+65], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.42000000000000012e65

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. sub-neg 88.0%

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

      3. associate-*l* 87.9%

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

      4. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around 0 64.3%

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

      1. cancel-sign-sub-inv 64.3%

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

      2. associate-*r* 64.3%

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

      3. metadata-eval 64.3%

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

      4. *-commutative 64.3%

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

      5. associate-*r* 64.4%

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

      6. associate-*r* 64.4%

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

      7. *-commutative 64.4%

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

      8. *-commutative 64.4%

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

      9. *-commutative 64.4%

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

      10. associate-*r* 64.2%

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

      11. *-commutative 64.2%

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

   6. Applied egg-rr 64.2%

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

   if -1.42000000000000012e65 < z

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. sub-neg 95.7%

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

      3. associate-*l* 94.2%

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

      4. 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 96.1%

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

      1. associate-*r* 96.1%

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

   6. Simplified 96.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(z \cdot y\right) \cdot \left(t \cdot 9\right)\right)\\ \end{array} \]

Alternative 8: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(z \cdot t\right) \cdot \left(y \cdot 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 1.4e+41)
   (+ (* a (* 27.0 b)) (- (* x 2.0) (* (* z t) (* y 9.0))))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.4e+41) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * t) * (y * 9.0)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.4d+41) then
        tmp = (a * (27.0d0 * b)) + ((x * 2.0d0) - ((z * t) * (y * 9.0d0)))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.4e+41) {
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * t) * (y * 9.0)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.4e+41:
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * t) * (y * 9.0)))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.4e+41)
		tmp = Float64(Float64(a * Float64(27.0 * b)) + Float64(Float64(x * 2.0) - Float64(Float64(z * t) * Float64(y * 9.0))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.4e+41)
		tmp = (a * (27.0 * b)) + ((x * 2.0) - ((z * t) * (y * 9.0)));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.4e+41], N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4e41

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   if 1.4e41 < z

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 86.3%

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

      4. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around 0 79.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 - \left(z \cdot t\right) \cdot \left(y \cdot 9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 9: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 1.4e+41)
   (- (+ (* a (* 27.0 b)) (* x 2.0)) (* y (* 9.0 (* z t))))
   (- (* x 2.0) (* 9.0 (* t (* z y))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.4e+41) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.4d+41) then
        tmp = ((a * (27.0d0 * b)) + (x * 2.0d0)) - (y * (9.0d0 * (z * t)))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.4e+41) {
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.4e+41:
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.4e+41)
		tmp = Float64(Float64(Float64(a * Float64(27.0 * b)) + Float64(x * 2.0)) - Float64(y * Float64(9.0 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.4e+41)
		tmp = ((a * (27.0 * b)) + (x * 2.0)) - (y * (9.0 * (z * t)));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.4e+41], N[(N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4e41

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. sub-neg 95.3%

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

      3. associate-*l* 95.2%

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

      4. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+r- 95.8%

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

      3. associate-*l* 96.3%

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

   5. Applied egg-rr 96.3%

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

   if 1.4e41 < z

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. associate-*l* 86.3%

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

      4. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in a around 0 79.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+41}:\\ \;\;\;\;\left(a \cdot \left(27 \cdot b\right) + x \cdot 2\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 10: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+42}:\\ \;\;\;\;9 \cdot \left(z \cdot \left(y \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e+42)
   (* 9.0 (* z (* y (- t))))
   (if (<= z 9e+38)
     (+ (* x 2.0) (* 27.0 (* a b)))
     (- (* x 2.0) (* 9.0 (* t (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e+42) {
		tmp = 9.0 * (z * (y * -t));
	} else if (z <= 9e+38) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.05d+42)) then
        tmp = 9.0d0 * (z * (y * -t))
    else if (z <= 9d+38) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (t * (z * y)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e+42) {
		tmp = 9.0 * (z * (y * -t));
	} else if (z <= 9e+38) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.05e+42:
		tmp = 9.0 * (z * (y * -t))
	elif z <= 9e+38:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (t * (z * y)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.05e+42)
		tmp = Float64(9.0 * Float64(z * Float64(y * Float64(-t))));
	elseif (z <= 9e+38)
		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(z * y))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.05e+42)
		tmp = 9.0 * (z * (y * -t));
	elseif (z <= 9e+38)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (t * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.05e+42], N[(9.0 * N[(z * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+38], 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[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e42

   1. Initial program 88.9%

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

      1. sub-neg 88.9%

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

      2. sub-neg 88.9%

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

      3. associate-*l* 88.8%

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

      4. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in y around inf 44.6%

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

      1. associate-*r* 44.7%

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

      2. *-commutative 44.7%

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

      3. associate-*l* 44.6%

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

      4. associate-*r* 44.7%

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

      5. *-commutative 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in y around 0 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-*l* 44.6%

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

      3. metadata-eval 44.6%

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

      4. *-commutative 44.6%

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

      5. distribute-lft-neg-in 44.6%

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

      6. associate-*r* 48.2%

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

   9. Applied egg-rr 48.2%

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

   if -2.05e42 < z < 8.99999999999999961e38

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. sub-neg 97.7%

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

      3. associate-*l* 97.7%

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

      4. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 87.0%

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

   if 8.99999999999999961e38 < 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. sub-neg 91.0%

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

      3. associate-*l* 86.5%

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

      4. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in a around 0 79.1%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+42}:\\ \;\;\;\;9 \cdot \left(z \cdot \left(y \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 11: 48.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* z y)))))
   (if (<= z -8e-58)
     t_1
     (if (<= z -2.35e-296)
       (* x 2.0)
       (if (<= z 6.1e+38) (* 27.0 (* a b)) t_1)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (z <= -8e-58) {
		tmp = t_1;
	} else if (z <= -2.35e-296) {
		tmp = x * 2.0;
	} else if (z <= 6.1e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-9.0d0) * (t * (z * y))
    if (z <= (-8d-58)) then
        tmp = t_1
    else if (z <= (-2.35d-296)) then
        tmp = x * 2.0d0
    else if (z <= 6.1d+38) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (t * (z * y));
	double tmp;
	if (z <= -8e-58) {
		tmp = t_1;
	} else if (z <= -2.35e-296) {
		tmp = x * 2.0;
	} else if (z <= 6.1e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (z * y))
	tmp = 0
	if z <= -8e-58:
		tmp = t_1
	elif z <= -2.35e-296:
		tmp = x * 2.0
	elif z <= 6.1e+38:
		tmp = 27.0 * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(z * y)))
	tmp = 0.0
	if (z <= -8e-58)
		tmp = t_1;
	elseif (z <= -2.35e-296)
		tmp = Float64(x * 2.0);
	elseif (z <= 6.1e+38)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (t * (z * y));
	tmp = 0.0;
	if (z <= -8e-58)
		tmp = t_1;
	elseif (z <= -2.35e-296)
		tmp = x * 2.0;
	elseif (z <= 6.1e+38)
		tmp = 27.0 * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-58], t$95$1, If[LessEqual[z, -2.35e-296], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6.1e+38], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000002e-58 or 6.0999999999999999e38 < z

   1. Initial program 90.7%

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

      1. sub-neg 90.7%

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

      2. sub-neg 90.7%

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

      3. associate-*l* 88.5%

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

      4. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around inf 51.6%

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

   if -8.0000000000000002e-58 < z < -2.35e-296

   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. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 54.0%

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

   if -2.35e-296 < z < 6.0999999999999999e38

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 97.0%

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

      4. 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 a around inf 51.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-58}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 12: 48.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-58}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -1.16e-58)
   (* -9.0 (* t (* z y)))
   (if (<= z -2.4e-296)
     (* x 2.0)
     (if (<= z 4.1e+38) (* 27.0 (* a b)) (* t (* -9.0 (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.16e-58) {
		tmp = -9.0 * (t * (z * y));
	} else if (z <= -2.4e-296) {
		tmp = x * 2.0;
	} else if (z <= 4.1e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.16d-58)) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (z <= (-2.4d-296)) then
        tmp = x * 2.0d0
    else if (z <= 4.1d+38) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.16e-58) {
		tmp = -9.0 * (t * (z * y));
	} else if (z <= -2.4e-296) {
		tmp = x * 2.0;
	} else if (z <= 4.1e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.16e-58:
		tmp = -9.0 * (t * (z * y))
	elif z <= -2.4e-296:
		tmp = x * 2.0
	elif z <= 4.1e+38:
		tmp = 27.0 * (a * b)
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.16e-58)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (z <= -2.4e-296)
		tmp = Float64(x * 2.0);
	elseif (z <= 4.1e+38)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.16e-58)
		tmp = -9.0 * (t * (z * y));
	elseif (z <= -2.4e-296)
		tmp = x * 2.0;
	elseif (z <= 4.1e+38)
		tmp = 27.0 * (a * b);
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.16e-58], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-296], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 4.1e+38], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.16000000000000007e-58

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 90.4%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around inf 38.8%

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

   if -1.16000000000000007e-58 < z < -2.39999999999999996e-296

   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. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 54.0%

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

   if -2.39999999999999996e-296 < z < 4.1000000000000003e38

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 97.0%

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

      4. 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 a around inf 51.9%

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

   if 4.1000000000000003e38 < 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. sub-neg 91.0%

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

      3. associate-*l* 86.5%

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

      4. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*l* 65.8%

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

      4. associate-*r* 65.8%

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

      5. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in y around 0 65.8%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-58}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 13: 48.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -6.6e-57)
   (* t (* z (* y -9.0)))
   (if (<= z -2.4e-296)
     (* x 2.0)
     (if (<= z 6e+38) (* 27.0 (* a b)) (* t (* -9.0 (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.6e-57) {
		tmp = t * (z * (y * -9.0));
	} else if (z <= -2.4e-296) {
		tmp = x * 2.0;
	} else if (z <= 6e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	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 <= (-6.6d-57)) then
        tmp = t * (z * (y * (-9.0d0)))
    else if (z <= (-2.4d-296)) then
        tmp = x * 2.0d0
    else if (z <= 6d+38) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t * ((-9.0d0) * (z * y))
    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 <= -6.6e-57) {
		tmp = t * (z * (y * -9.0));
	} else if (z <= -2.4e-296) {
		tmp = x * 2.0;
	} else if (z <= 6e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.6e-57:
		tmp = t * (z * (y * -9.0))
	elif z <= -2.4e-296:
		tmp = x * 2.0
	elif z <= 6e+38:
		tmp = 27.0 * (a * b)
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.6e-57)
		tmp = Float64(t * Float64(z * Float64(y * -9.0)));
	elseif (z <= -2.4e-296)
		tmp = Float64(x * 2.0);
	elseif (z <= 6e+38)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	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 <= -6.6e-57)
		tmp = t * (z * (y * -9.0));
	elseif (z <= -2.4e-296)
		tmp = x * 2.0;
	elseif (z <= 6e+38)
		tmp = 27.0 * (a * b);
	else
		tmp = t * (-9.0 * (z * y));
	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, -6.6e-57], N[(t * N[(z * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-296], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 6e+38], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5999999999999997e-57

   1. Initial program 90.5%

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

      1. sub-neg 90.5%

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

      2. sub-neg 90.5%

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

      3. associate-*l* 90.4%

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

      4. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around inf 38.8%

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

      1. associate-*r* 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-*l* 38.9%

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

      4. associate-*r* 38.9%

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

      5. *-commutative 38.9%

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

   6. Simplified 38.9%

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

   if -6.5999999999999997e-57 < z < -2.39999999999999996e-296

   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. sub-neg 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 54.0%

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

   if -2.39999999999999996e-296 < z < 6.0000000000000002e38

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 97.0%

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

      4. 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 a around inf 51.9%

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

   if 6.0000000000000002e38 < 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. sub-neg 91.0%

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

      3. associate-*l* 86.5%

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

      4. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*l* 65.8%

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

      4. associate-*r* 65.8%

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

      5. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in y around 0 65.8%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 14: 50.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;9 \cdot \left(z \cdot \left(y \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -1.65e-51)
   (* 9.0 (* z (* y (- t))))
   (if (<= z -2.35e-296)
     (* x 2.0)
     (if (<= z 9.5e+38) (* 27.0 (* a b)) (* t (* -9.0 (* z y)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e-51) {
		tmp = 9.0 * (z * (y * -t));
	} else if (z <= -2.35e-296) {
		tmp = x * 2.0;
	} else if (z <= 9.5e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.65d-51)) then
        tmp = 9.0d0 * (z * (y * -t))
    else if (z <= (-2.35d-296)) then
        tmp = x * 2.0d0
    else if (z <= 9.5d+38) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e-51) {
		tmp = 9.0 * (z * (y * -t));
	} else if (z <= -2.35e-296) {
		tmp = x * 2.0;
	} else if (z <= 9.5e+38) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.65e-51:
		tmp = 9.0 * (z * (y * -t))
	elif z <= -2.35e-296:
		tmp = x * 2.0
	elif z <= 9.5e+38:
		tmp = 27.0 * (a * b)
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e-51)
		tmp = Float64(9.0 * Float64(z * Float64(y * Float64(-t))));
	elseif (z <= -2.35e-296)
		tmp = Float64(x * 2.0);
	elseif (z <= 9.5e+38)
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.65e-51)
		tmp = 9.0 * (z * (y * -t));
	elseif (z <= -2.35e-296)
		tmp = x * 2.0;
	elseif (z <= 9.5e+38)
		tmp = 27.0 * (a * b);
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e-51], N[(9.0 * N[(z * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-296], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 9.5e+38], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.64999999999999986e-51

   1. Initial program 91.7%

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

      1. sub-neg 91.7%

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

      2. sub-neg 91.7%

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

      3. associate-*l* 91.6%

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

      4. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around inf 38.0%

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

      1. associate-*r* 38.0%

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

      2. *-commutative 38.0%

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

      3. associate-*l* 38.0%

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

      4. associate-*r* 38.0%

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

      5. *-commutative 38.0%

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

   6. Simplified 38.0%

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

   7. Taylor expanded in y around 0 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-*l* 38.0%

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

      3. metadata-eval 38.0%

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

      4. *-commutative 38.0%

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

      5. distribute-lft-neg-in 38.0%

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

      6. associate-*r* 40.6%

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

   9. Applied egg-rr 40.6%

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

   if -1.64999999999999986e-51 < z < -2.35e-296

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. sub-neg 97.8%

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

      3. associate-*l* 97.8%

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

      4. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 52.9%

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

   if -2.35e-296 < z < 9.4999999999999995e38

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. sub-neg 97.1%

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

      3. associate-*l* 97.0%

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

      4. 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 a around inf 51.9%

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

   if 9.4999999999999995e38 < 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. sub-neg 91.0%

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

      3. associate-*l* 86.5%

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

      4. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in y around inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*l* 65.8%

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

      4. associate-*r* 65.8%

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

      5. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in y around 0 65.8%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;9 \cdot \left(z \cdot \left(y \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-296}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 15: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+42}:\\ \;\;\;\;9 \cdot \left(z \cdot \left(y \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+85}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

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 -1.85e+42)
   (* 9.0 (* z (* y (- t))))
   (if (<= z 3e+85) (+ (* x 2.0) (* 27.0 (* a b))) (* t (* -9.0 (* z y))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+42) {
		tmp = 9.0 * (z * (y * -t));
	} else if (z <= 3e+85) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.85d+42)) then
        tmp = 9.0d0 * (z * (y * -t))
    else if (z <= 3d+85) then
        tmp = (x * 2.0d0) + (27.0d0 * (a * b))
    else
        tmp = t * ((-9.0d0) * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+42) {
		tmp = 9.0 * (z * (y * -t));
	} else if (z <= 3e+85) {
		tmp = (x * 2.0) + (27.0 * (a * b));
	} else {
		tmp = t * (-9.0 * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.85e+42:
		tmp = 9.0 * (z * (y * -t))
	elif z <= 3e+85:
		tmp = (x * 2.0) + (27.0 * (a * b))
	else:
		tmp = t * (-9.0 * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.85e+42)
		tmp = Float64(9.0 * Float64(z * Float64(y * Float64(-t))));
	elseif (z <= 3e+85)
		tmp = Float64(Float64(x * 2.0) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(t * Float64(-9.0 * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.85e+42)
		tmp = 9.0 * (z * (y * -t));
	elseif (z <= 3e+85)
		tmp = (x * 2.0) + (27.0 * (a * b));
	else
		tmp = t * (-9.0 * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.85e+42], N[(9.0 * N[(z * N[(y * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+85], N[(N[(x * 2.0), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999998e42

   1. Initial program 88.9%

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

      1. sub-neg 88.9%

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

      2. sub-neg 88.9%

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

      3. associate-*l* 88.8%

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

      4. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in y around inf 44.6%

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

      1. associate-*r* 44.7%

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

      2. *-commutative 44.7%

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

      3. associate-*l* 44.6%

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

      4. associate-*r* 44.7%

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

      5. *-commutative 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in y around 0 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-*l* 44.6%

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

      3. metadata-eval 44.6%

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

      4. *-commutative 44.6%

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

      5. distribute-lft-neg-in 44.6%

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

      6. associate-*r* 48.2%

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

   9. Applied egg-rr 48.2%

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

   if -1.84999999999999998e42 < z < 3e85

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. sub-neg 97.8%

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

      3. associate-*l* 96.4%

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

      4. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around 0 85.6%

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

   if 3e85 < z

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. sub-neg 90.1%

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

      3. associate-*l* 88.4%

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

      4. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*l* 67.9%

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

      4. associate-*r* 67.9%

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

      5. *-commutative 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in y around 0 67.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+42}:\\ \;\;\;\;9 \cdot \left(z \cdot \left(y \cdot \left(-t\right)\right)\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+85}:\\ \;\;\;\;x \cdot 2 + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 16: 45.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+129} \lor \neg \left(a \leq 4.95 \cdot 10^{-57}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3e+129) (not (<= a 4.95e-57))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3e+129) || !(a <= 4.95e-57)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3d+129)) .or. (.not. (a <= 4.95d-57))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3e+129) || !(a <= 4.95e-57)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3e+129) or not (a <= 4.95e-57):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3e+129) || !(a <= 4.95e-57))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3e+129) || ~((a <= 4.95e-57)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3e+129], N[Not[LessEqual[a, 4.95e-57]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0000000000000003e129 or 4.9499999999999998e-57 < a

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. sub-neg 92.2%

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

      3. associate-*l* 91.3%

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

      4. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 52.6%

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

   if -3.0000000000000003e129 < a < 4.9499999999999998e-57

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. sub-neg 96.2%

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

      3. associate-*l* 94.6%

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

      4. 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 41.9%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+129} \lor \neg \left(a \leq 4.95 \cdot 10^{-57}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 17: 45.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+129} \lor \neg \left(a \leq 4.4 \cdot 10^{-57}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 (or (<= a -3e+129) (not (<= a 4.4e-57))) (* 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 ((a <= -3e+129) || !(a <= 4.4e-57)) {
		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 ((a <= (-3d+129)) .or. (.not. (a <= 4.4d-57))) 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 ((a <= -3e+129) || !(a <= 4.4e-57)) {
		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 (a <= -3e+129) or not (a <= 4.4e-57):
		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 ((a <= -3e+129) || !(a <= 4.4e-57))
		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 ((a <= -3e+129) || ~((a <= 4.4e-57)))
		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[Or[LessEqual[a, -3e+129], N[Not[LessEqual[a, 4.4e-57]], $MachinePrecision]], N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0000000000000003e129 or 4.39999999999999997e-57 < a

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. sub-neg 92.2%

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

      3. associate-*l* 91.3%

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

      4. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 52.6%

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

      1. associate-*r* 52.6%

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

      2. *-commutative 52.6%

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

      3. associate-*r* 52.6%

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

   6. Simplified 52.6%

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

   if -3.0000000000000003e129 < a < 4.39999999999999997e-57

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. sub-neg 96.2%

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

      3. associate-*l* 94.6%

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

      4. 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 41.9%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+129} \lor \neg \left(a \leq 4.4 \cdot 10^{-57}\right):\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 18: 30.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

   1. sub-neg 94.2%

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

   2. sub-neg 94.2%

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

   3. associate-*l* 93.0%

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

   4. associate-*l* 93.4%

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

3. Simplified 93.4%

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

4. Taylor expanded in x around inf 32.3%

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

5. Final simplification 32.3%

   \[\leadsto x \cdot 2 \]

Developer target: 94.7% 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 2023306 
(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)))