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

Percentage Accurate: 95.2% → 98.8%

Time: 15.6s

Alternatives: 18

Speedup: 0.9×

• 27.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

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

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3e-85)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (fma x 2.0 (fma t (* (* z y) -9.0) (* b (* a 27.0))))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000022e-85

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-*l* 84.5%

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

      3. fma-def 87.0%

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

      4. associate-*l* 97.4%

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

      5. *-commutative 97.4%

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

      6. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   if -3.00000000000000022e-85 < z

   1. Initial program 96.0%

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

      1. associate-+l- 96.0%

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

      2. fma-neg 96.0%

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

      3. neg-sub0 96.0%

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

      4. associate-+l- 96.0%

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

      5. neg-sub0 96.0%

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

      6. *-commutative 96.0%

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

      7. distribute-rgt-neg-in 96.0%

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

      8. fma-def 96.6%

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

      9. *-commutative 96.6%

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

      10. associate-*r* 96.6%

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

      11. distribute-rgt-neg-in 96.6%

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

      12. *-commutative 96.6%

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

      13. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

4. Final simplification 96.8%

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

Alternative 2: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

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 2e-139)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* t (* y (* z 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 <= 2e-139) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (t * (y * (z * 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 <= 2e-139)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(t * Float64(y * Float64(z * 9.0)))));
	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, 2e-139], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.00000000000000006e-139

   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. +-commutative 91.0%

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

      2. associate-*l* 90.6%

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

      3. fma-def 91.7%

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

      4. associate-*l* 98.1%

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

      5. *-commutative 98.1%

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

      6. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   if 2.00000000000000006e-139 < z

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-*l* 95.1%

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

      3. fma-def 95.1%

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

      4. associate-*l* 93.9%

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

      5. *-commutative 93.9%

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

      6. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

      1. associate-*r* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*r* 95.1%

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

      4. cancel-sign-sub-inv 95.1%

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

      5. associate-*l* 95.1%

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

   5. Applied egg-rr 95.1%

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

      1. fma-udef 95.1%

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

      2. associate-*l* 95.1%

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

      3. *-commutative 95.1%

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

      4. associate-*l* 95.1%

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

      5. cancel-sign-sub-inv 95.1%

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

      6. +-commutative 95.1%

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

      7. associate-+l- 95.1%

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

      8. associate-*l* 95.1%

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

      9. *-commutative 95.1%

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

      10. associate-*l* 95.1%

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

   7. Applied egg-rr 95.1%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

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 2e-139)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (fma a (* 27.0 b) (- (* x 2.0) (* t (* y (* z 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 <= 2e-139) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (t * (y * (z * 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 <= 2e-139)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))));
	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, 2e-139], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.00000000000000006e-139

   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. +-commutative 91.0%

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

      2. associate-*l* 90.6%

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

      3. fma-def 91.7%

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

      4. associate-*l* 98.1%

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

      5. *-commutative 98.1%

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

      6. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   if 2.00000000000000006e-139 < z

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-*l* 95.1%

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

      3. fma-def 95.1%

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

      4. associate-*l* 93.9%

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

      5. *-commutative 93.9%

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

      6. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

      1. associate-*r* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*r* 95.1%

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

      4. cancel-sign-sub-inv 95.1%

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

      5. associate-*l* 95.1%

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

   5. Applied egg-rr 95.1%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 4: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;9 \cdot y \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - z \cdot \left(t \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= (* 9.0 y) -2e+33)
     (+ t_1 (- (* x 2.0) (* y (* 9.0 (* z t)))))
     (+ t_1 (- (* x 2.0) (* z (* t (* 9.0 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);
	double tmp;
	if ((9.0 * y) <= -2e+33) {
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = t_1 + ((x * 2.0) - (z * (t * (9.0 * 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)
    if ((9.0d0 * y) <= (-2d+33)) then
        tmp = t_1 + ((x * 2.0d0) - (y * (9.0d0 * (z * t))))
    else
        tmp = t_1 + ((x * 2.0d0) - (z * (t * (9.0d0 * 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);
	double tmp;
	if ((9.0 * y) <= -2e+33) {
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = t_1 + ((x * 2.0) - (z * (t * (9.0 * 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)
	tmp = 0
	if (9.0 * y) <= -2e+33:
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))))
	else:
		tmp = t_1 + ((x * 2.0) - (z * (t * (9.0 * y))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (Float64(9.0 * y) <= -2e+33)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(z * Float64(t * Float64(9.0 * 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);
	tmp = 0.0;
	if ((9.0 * y) <= -2e+33)
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))));
	else
		tmp = t_1 + ((x * 2.0) - (z * (t * (9.0 * 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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(9.0 * y), $MachinePrecision], -2e+33], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(z * N[(t * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y 9) < -1.9999999999999999e33

   1. Initial program 86.6%

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

   2. Taylor expanded in y around 0 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*r* 97.4%

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

   4. Simplified 97.4%

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

   if -1.9999999999999999e33 < (*.f64 y 9)

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 96.0%

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

      1. associate-*r* 96.0%

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

      2. *-commutative 96.0%

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

      3. associate-*r* 93.7%

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

   4. Simplified 93.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;9 \cdot y \leq -2 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - z \cdot \left(t \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 5: 47.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-238}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-139}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))) (t_2 (* -9.0 (* y (* z t)))))
   (if (<= z -7.2e-15)
     t_2
     (if (<= z -1.16e-238)
       (* 27.0 (* a b))
       (if (<= z 5.5e-139)
         (* x 2.0)
         (if (<= z 1.05e-20)
           t_1
           (if (<= z 3.2e+39) (* x 2.0) (if (<= z 2.05e+46) t_1 t_2))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -7.2e-15) {
		tmp = t_2;
	} else if (z <= -1.16e-238) {
		tmp = 27.0 * (a * b);
	} else if (z <= 5.5e-139) {
		tmp = x * 2.0;
	} else if (z <= 1.05e-20) {
		tmp = t_1;
	} else if (z <= 3.2e+39) {
		tmp = x * 2.0;
	} else if (z <= 2.05e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    t_2 = (-9.0d0) * (y * (z * t))
    if (z <= (-7.2d-15)) then
        tmp = t_2
    else if (z <= (-1.16d-238)) then
        tmp = 27.0d0 * (a * b)
    else if (z <= 5.5d-139) then
        tmp = x * 2.0d0
    else if (z <= 1.05d-20) then
        tmp = t_1
    else if (z <= 3.2d+39) then
        tmp = x * 2.0d0
    else if (z <= 2.05d+46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double t_2 = -9.0 * (y * (z * t));
	double tmp;
	if (z <= -7.2e-15) {
		tmp = t_2;
	} else if (z <= -1.16e-238) {
		tmp = 27.0 * (a * b);
	} else if (z <= 5.5e-139) {
		tmp = x * 2.0;
	} else if (z <= 1.05e-20) {
		tmp = t_1;
	} else if (z <= 3.2e+39) {
		tmp = x * 2.0;
	} else if (z <= 2.05e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	t_2 = -9.0 * (y * (z * t))
	tmp = 0
	if z <= -7.2e-15:
		tmp = t_2
	elif z <= -1.16e-238:
		tmp = 27.0 * (a * b)
	elif z <= 5.5e-139:
		tmp = x * 2.0
	elif z <= 1.05e-20:
		tmp = t_1
	elif z <= 3.2e+39:
		tmp = x * 2.0
	elif z <= 2.05e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	t_2 = Float64(-9.0 * Float64(y * Float64(z * t)))
	tmp = 0.0
	if (z <= -7.2e-15)
		tmp = t_2;
	elseif (z <= -1.16e-238)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (z <= 5.5e-139)
		tmp = Float64(x * 2.0);
	elseif (z <= 1.05e-20)
		tmp = t_1;
	elseif (z <= 3.2e+39)
		tmp = Float64(x * 2.0);
	elseif (z <= 2.05e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	t_2 = -9.0 * (y * (z * t));
	tmp = 0.0;
	if (z <= -7.2e-15)
		tmp = t_2;
	elseif (z <= -1.16e-238)
		tmp = 27.0 * (a * b);
	elseif (z <= 5.5e-139)
		tmp = x * 2.0;
	elseif (z <= 1.05e-20)
		tmp = t_1;
	elseif (z <= 3.2e+39)
		tmp = x * 2.0;
	elseif (z <= 2.05e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-15], t$95$2, If[LessEqual[z, -1.16e-238], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-139], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 1.05e-20], t$95$1, If[LessEqual[z, 3.2e+39], N[(x * 2.0), $MachinePrecision], If[LessEqual[z, 2.05e+46], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2000000000000002e-15 or 2.05e46 < z

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0 73.6%

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

   3. Taylor expanded in a around 0 58.3%

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

   if -7.2000000000000002e-15 < z < -1.1600000000000001e-238

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-*l* 96.6%

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

      3. fma-def 96.5%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

      1. associate-*r* 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 96.5%

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

      4. cancel-sign-sub-inv 96.5%

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

      5. associate-*l* 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in a around inf 50.2%

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

   if -1.1600000000000001e-238 < z < 5.4999999999999997e-139 or 1.0499999999999999e-20 < z < 3.19999999999999993e39

   1. Initial program 96.6%

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

      1. associate-+l- 96.6%

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

      2. fma-neg 96.6%

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

      3. neg-sub0 96.6%

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

      4. associate-+l- 96.6%

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

      5. neg-sub0 96.6%

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

      6. *-commutative 96.6%

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

      7. distribute-rgt-neg-in 96.6%

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

      8. fma-def 96.6%

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

      9. *-commutative 96.6%

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

      10. associate-*r* 96.6%

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

      11. distribute-rgt-neg-in 96.6%

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

      12. *-commutative 96.6%

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

      13. metadata-eval 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 39.9%

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

   if 5.4999999999999997e-139 < z < 1.0499999999999999e-20 or 3.19999999999999993e39 < z < 2.05e46

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. cancel-sign-sub-inv 99.7%

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

      5. associate-*l* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around inf 59.9%

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

      1. associate-*r* 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

      4. *-commutative 59.8%

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

   8. Simplified 59.8%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-238}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-139}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 6: 97.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 7.8 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \end{array} \]

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 7.8e+93)
   (+ (* b (* a 27.0)) (- (* x 2.0) (* y (* 9.0 (* z t)))))
   (- (* x 2.0) (* t (* y (* z 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 <= 7.8e+93) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = (x * 2.0) - (t * (y * (z * 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 <= 7.8d+93) then
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (y * (9.0d0 * (z * t))))
    else
        tmp = (x * 2.0d0) - (t * (y * (z * 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 <= 7.8e+93) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = (x * 2.0) - (t * (y * (z * 9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 7.8e+93:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))))
	else:
		tmp = (x * 2.0) - (t * (y * (z * 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 <= 7.8e+93)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 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 <= 7.8e+93)
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))));
	else
		tmp = (x * 2.0) - (t * (y * (z * 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, 7.8e+93], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.8000000000000005e93

   1. Initial program 92.7%

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

   2. Taylor expanded in y around 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*r* 97.4%

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

   4. Simplified 97.4%

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

   if 7.8000000000000005e93 < z

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-*l* 90.0%

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

      3. fma-def 89.9%

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

      4. associate-*l* 89.9%

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

      5. *-commutative 89.9%

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

      6. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

      1. associate-*r* 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*r* 89.9%

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

      4. cancel-sign-sub-inv 89.9%

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

      5. associate-*l* 90.0%

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

   5. Applied egg-rr 90.0%

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

      1. fma-udef 90.0%

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

      2. associate-*l* 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*l* 90.0%

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

      5. cancel-sign-sub-inv 90.0%

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

      6. +-commutative 90.0%

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

      7. associate-+l- 90.0%

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

      8. associate-*l* 90.0%

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

      9. *-commutative 90.0%

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

      10. associate-*l* 90.0%

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

   7. Applied egg-rr 90.0%

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

      1. add-sqr-sqrt 47.4%

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

      2. pow2 47.4%

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

   9. Applied egg-rr 47.4%

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

   10. Taylor expanded in y around inf 73.5%

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

       1. associate-*r* 73.6%

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

       2. *-commutative 73.6%

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

       3. associate-*l* 72.0%

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

       4. *-commutative 72.0%

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

       5. *-commutative 72.0%

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

       6. associate-*l* 72.0%

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

       7. *-commutative 72.0%

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

   12. Simplified 72.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.8 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \]

Alternative 7: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq 3.05 \cdot 10^{-139}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= z 3.05e-139)
     (+ t_1 (- (* x 2.0) (* y (* 9.0 (* z t)))))
     (+ t_1 (- (* x 2.0) (* t (* z (* 9.0 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);
	double tmp;
	if (z <= 3.05e-139) {
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (z * (9.0 * 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)
    if (z <= 3.05d-139) then
        tmp = t_1 + ((x * 2.0d0) - (y * (9.0d0 * (z * t))))
    else
        tmp = t_1 + ((x * 2.0d0) - (t * (z * (9.0d0 * 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);
	double tmp;
	if (z <= 3.05e-139) {
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (z * (9.0 * 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)
	tmp = 0
	if z <= 3.05e-139:
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))))
	else:
		tmp = t_1 + ((x * 2.0) - (t * (z * (9.0 * y))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (z <= 3.05e-139)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(t * Float64(z * Float64(9.0 * 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);
	tmp = 0.0;
	if (z <= 3.05e-139)
		tmp = t_1 + ((x * 2.0) - (y * (9.0 * (z * t))));
	else
		tmp = t_1 + ((x * 2.0) - (t * (z * (9.0 * 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[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 3.05e-139], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 3.0499999999999999e-139

   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. Taylor expanded in y around 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*r* 97.4%

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

   4. Simplified 97.4%

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

   if 3.0499999999999999e-139 < z

   1. Initial program 95.1%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.05 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 8: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 3.05 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

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 3.05e-127)
   (+ (* b (* a 27.0)) (- (* x 2.0) (* y (* 9.0 (* z t)))))
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* t (* y (* z 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 <= 3.05e-127) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (t * (y * (z * 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 <= 3.05d-127) then
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (y * (9.0d0 * (z * t))))
    else
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - (t * (y * (z * 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 <= 3.05e-127) {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))));
	} else {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (t * (y * (z * 9.0))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 3.05e-127:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))))
	else:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (t * (y * (z * 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 <= 3.05e-127)
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(t * Float64(y * Float64(z * 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 <= 3.05e-127)
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (y * (9.0 * (z * t))));
	else
		tmp = (x * 2.0) + ((a * (27.0 * b)) - (t * (y * (z * 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, 3.05e-127], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.0499999999999999e-127

   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. Taylor expanded in y around 0 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*r* 97.4%

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

   4. Simplified 97.4%

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

   if 3.0499999999999999e-127 < z

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-*l* 95.1%

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

      3. fma-def 95.1%

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

      4. associate-*l* 93.9%

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

      5. *-commutative 93.9%

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

      6. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

      1. associate-*r* 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*r* 95.1%

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

      4. cancel-sign-sub-inv 95.1%

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

      5. associate-*l* 95.1%

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

   5. Applied egg-rr 95.1%

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

      1. fma-udef 95.1%

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

      2. associate-*l* 95.1%

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

      3. *-commutative 95.1%

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

      4. associate-*l* 95.1%

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

      5. cancel-sign-sub-inv 95.1%

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

      6. +-commutative 95.1%

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

      7. associate-+l- 95.1%

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

      8. associate-*l* 95.1%

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

      9. *-commutative 95.1%

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

      10. associate-*l* 95.1%

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

   7. Applied egg-rr 95.1%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.05 \cdot 10^{-127}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 9: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+77} \lor \neg \left(a \leq 4.4 \cdot 10^{-96}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(z \cdot 9\right)\right)\\ \end{array} \end{array} \]

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 (or (<= a -3.1e+77) (not (<= a 4.4e-96)))
   (- (* 27.0 (* a b)) (* 9.0 (* y (* z t))))
   (- (* x 2.0) (* y (* t (* z 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 ((a <= -3.1e+77) || !(a <= 4.4e-96)) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (y * (t * (z * 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 ((a <= (-3.1d+77)) .or. (.not. (a <= 4.4d-96))) then
        tmp = (27.0d0 * (a * b)) - (9.0d0 * (y * (z * t)))
    else
        tmp = (x * 2.0d0) - (y * (t * (z * 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 ((a <= -3.1e+77) || !(a <= 4.4e-96)) {
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (y * (t * (z * 9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.1e+77) or not (a <= 4.4e-96):
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) - (y * (t * (z * 9.0)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.1e+77) || !(a <= 4.4e-96))
		tmp = Float64(Float64(27.0 * Float64(a * b)) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(y * Float64(t * Float64(z * 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 ((a <= -3.1e+77) || ~((a <= 4.4e-96)))
		tmp = (27.0 * (a * b)) - (9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) - (y * (t * (z * 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[Or[LessEqual[a, -3.1e+77], N[Not[LessEqual[a, 4.4e-96]], $MachinePrecision]], N[(N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.09999999999999999e77 or 4.39999999999999959e-96 < a

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 78.1%

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

   if -3.09999999999999999e77 < a < 4.39999999999999959e-96

   1. Initial program 91.1%

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

   2. Taylor expanded in a around 0 84.2%

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

      1. *-commutative 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-*r* 84.3%

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

      4. cancel-sign-sub-inv 84.3%

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

      5. associate-*l* 83.5%

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

      6. *-commutative 83.5%

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

   4. Applied egg-rr 83.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+77} \lor \neg \left(a \leq 4.4 \cdot 10^{-96}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(t \cdot \left(z \cdot 9\right)\right)\\ \end{array} \]

Alternative 10: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-37} \lor \neg \left(z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e-37) (not (<= z 4e-15)))
   (+ (* x 2.0) (* -9.0 (* z (* y t))))
   (- (* x 2.0) (* (* a b) -27.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-37) || !(z <= 4e-15)) {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	} else {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.2d-37)) .or. (.not. (z <= 4d-15))) then
        tmp = (x * 2.0d0) + ((-9.0d0) * (z * (y * t)))
    else
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-37) || !(z <= 4e-15)) {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	} else {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e-37) or not (z <= 4e-15):
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)))
	else:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e-37) || !(z <= 4e-15))
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(z * Float64(y * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e-37) || ~((z <= 4e-15)))
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	else
		tmp = (x * 2.0) - ((a * b) * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e-37], N[Not[LessEqual[z, 4e-15]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999995e-37 or 4.0000000000000003e-15 < z

   1. Initial program 87.3%

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

   2. Taylor expanded in a around 0 74.7%

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

      1. cancel-sign-sub-inv 74.7%

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

      2. *-commutative 74.7%

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

      3. metadata-eval 74.7%

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

      4. associate-*r* 77.1%

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

   4. Applied egg-rr 77.1%

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

   if -1.19999999999999995e-37 < z < 4.0000000000000003e-15

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. metadata-eval 97.5%

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

      8. *-lft-identity 97.5%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-37} \lor \neg \left(z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \end{array} \]

Alternative 11: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.1e-37)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= z 5.4e-15)
     (- (* x 2.0) (* (* a b) -27.0))
     (+ (* x 2.0) (* -9.0 (* z (* y t)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.1e-37) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 5.4e-15) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.1d-37)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (z <= 5.4d-15) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (x * 2.0d0) + ((-9.0d0) * (z * (y * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.1e-37) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 5.4e-15) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.1e-37:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif z <= 5.4e-15:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.1e-37)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 5.4e-15)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(-9.0 * Float64(z * Float64(y * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.1e-37)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (z <= 5.4e-15)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (x * 2.0) + (-9.0 * (z * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.1e-37], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-15], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(-9.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999998e-37

   1. Initial program 82.1%

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

   2. Taylor expanded in a around 0 77.3%

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

   if -4.0999999999999998e-37 < z < 5.40000000000000018e-15

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. metadata-eval 97.5%

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

      8. *-lft-identity 97.5%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   if 5.40000000000000018e-15 < z

   1. Initial program 93.5%

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

   2. Taylor expanded in a around 0 71.7%

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

      1. cancel-sign-sub-inv 71.7%

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

      2. *-commutative 71.7%

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

      3. metadata-eval 71.7%

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

      4. associate-*r* 76.9%

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

   4. Applied egg-rr 76.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 12: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-37}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \end{array} \]

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 -2.7e-37)
   (- (* x 2.0) (* 9.0 (* y (* z t))))
   (if (<= z 3.8e-15)
     (- (* x 2.0) (* (* a b) -27.0))
     (- (* x 2.0) (* t (* y (* z 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 <= -2.7e-37) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 3.8e-15) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (t * (y * (z * 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 <= (-2.7d-37)) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else if (z <= 3.8d-15) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (x * 2.0d0) - (t * (y * (z * 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 <= -2.7e-37) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else if (z <= 3.8e-15) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (t * (y * (z * 9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.7e-37:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	elif z <= 3.8e-15:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (x * 2.0) - (t * (y * (z * 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 <= -2.7e-37)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	elseif (z <= 3.8e-15)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 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 <= -2.7e-37)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	elseif (z <= 3.8e-15)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (x * 2.0) - (t * (y * (z * 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, -2.7e-37], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-15], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000016e-37

   1. Initial program 82.1%

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

   2. Taylor expanded in a around 0 77.3%

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

   if -2.70000000000000016e-37 < z < 3.8000000000000002e-15

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. metadata-eval 97.5%

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

      8. *-lft-identity 97.5%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   if 3.8000000000000002e-15 < z

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-*l* 93.5%

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

      3. fma-def 93.5%

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

      4. associate-*l* 91.8%

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

      5. *-commutative 91.8%

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

      6. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. associate-*r* 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r* 93.5%

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

      4. cancel-sign-sub-inv 93.5%

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

      5. associate-*l* 93.5%

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

   5. Applied egg-rr 93.5%

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

      1. fma-udef 93.5%

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

      2. associate-*l* 93.5%

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

      3. *-commutative 93.5%

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

      4. associate-*l* 93.5%

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

      5. cancel-sign-sub-inv 93.5%

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

      6. +-commutative 93.5%

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

      7. associate-+l- 93.5%

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

      8. associate-*l* 93.5%

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

      9. *-commutative 93.5%

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

      10. associate-*l* 93.5%

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

   7. Applied egg-rr 93.5%

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

      1. add-sqr-sqrt 52.5%

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

      2. pow2 52.5%

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

   9. Applied egg-rr 52.5%

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

   10. Taylor expanded in y around inf 71.7%

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

       1. associate-*r* 71.8%

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

       2. *-commutative 71.8%

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

       3. associate-*l* 72.4%

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

       4. *-commutative 72.4%

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

       5. *-commutative 72.4%

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

       6. associate-*l* 72.4%

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

       7. *-commutative 72.4%

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

   12. Simplified 72.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-37}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \]

Alternative 13: 80.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \end{array} \]

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 -8.6e-36)
   (- (* x 2.0) (* (* z 9.0) (* y t)))
   (if (<= z 5.8e-16)
     (- (* x 2.0) (* (* a b) -27.0))
     (- (* x 2.0) (* t (* y (* z 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 <= -8.6e-36) {
		tmp = (x * 2.0) - ((z * 9.0) * (y * t));
	} else if (z <= 5.8e-16) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (t * (y * (z * 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 <= (-8.6d-36)) then
        tmp = (x * 2.0d0) - ((z * 9.0d0) * (y * t))
    else if (z <= 5.8d-16) then
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    else
        tmp = (x * 2.0d0) - (t * (y * (z * 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 <= -8.6e-36) {
		tmp = (x * 2.0) - ((z * 9.0) * (y * t));
	} else if (z <= 5.8e-16) {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	} else {
		tmp = (x * 2.0) - (t * (y * (z * 9.0)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.6e-36:
		tmp = (x * 2.0) - ((z * 9.0) * (y * t))
	elif z <= 5.8e-16:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	else:
		tmp = (x * 2.0) - (t * (y * (z * 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 <= -8.6e-36)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(z * 9.0) * Float64(y * t)));
	elseif (z <= 5.8e-16)
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 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 <= -8.6e-36)
		tmp = (x * 2.0) - ((z * 9.0) * (y * t));
	elseif (z <= 5.8e-16)
		tmp = (x * 2.0) - ((a * b) * -27.0);
	else
		tmp = (x * 2.0) - (t * (y * (z * 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, -8.6e-36], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-16], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000004e-36

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-*l* 82.1%

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

      3. fma-def 85.0%

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

      4. associate-*l* 97.1%

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

      5. *-commutative 97.1%

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

      6. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

      1. associate-*r* 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*r* 85.0%

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

      4. cancel-sign-sub-inv 85.0%

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

      5. associate-*l* 83.6%

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

   5. Applied egg-rr 83.6%

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

      1. fma-udef 80.8%

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

      2. associate-*l* 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-*l* 82.2%

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

      5. cancel-sign-sub-inv 82.2%

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

      6. +-commutative 82.2%

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

      7. associate-+l- 82.2%

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

      8. associate-*l* 80.8%

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

      9. *-commutative 80.8%

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

      10. associate-*l* 80.8%

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

   7. Applied egg-rr 80.8%

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

      1. add-sqr-sqrt 42.5%

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

      2. pow2 42.5%

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

   9. Applied egg-rr 42.5%

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

   10. Taylor expanded in y around inf 77.3%

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

       1. associate-*r* 77.3%

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

       2. *-commutative 77.3%

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

       3. associate-*r* 77.3%

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

       4. *-commutative 77.3%

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

       5. *-commutative 77.3%

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

       6. *-commutative 77.3%

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

       7. associate-*l* 76.0%

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

       8. *-commutative 76.0%

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

       9. associate-*r* 76.2%

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

       10. *-commutative 76.2%

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

   12. Simplified 76.2%

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

   if -8.6000000000000004e-36 < z < 5.7999999999999996e-16

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. sub-neg 97.5%

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

      3. neg-mul-1 97.5%

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

      4. metadata-eval 97.5%

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

      5. metadata-eval 97.5%

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

      6. cancel-sign-sub-inv 97.5%

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

      7. metadata-eval 97.5%

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

      8. *-lft-identity 97.5%

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

      9. associate-*l* 99.6%

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

      10. associate-*l* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   if 5.7999999999999996e-16 < z

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-*l* 93.5%

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

      3. fma-def 93.5%

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

      4. associate-*l* 91.8%

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

      5. *-commutative 91.8%

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

      6. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. associate-*r* 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r* 93.5%

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

      4. cancel-sign-sub-inv 93.5%

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

      5. associate-*l* 93.5%

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

   5. Applied egg-rr 93.5%

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

      1. fma-udef 93.5%

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

      2. associate-*l* 93.5%

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

      3. *-commutative 93.5%

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

      4. associate-*l* 93.5%

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

      5. cancel-sign-sub-inv 93.5%

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

      6. +-commutative 93.5%

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

      7. associate-+l- 93.5%

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

      8. associate-*l* 93.5%

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

      9. *-commutative 93.5%

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

      10. associate-*l* 93.5%

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

   7. Applied egg-rr 93.5%

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

      1. add-sqr-sqrt 52.5%

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

      2. pow2 52.5%

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

   9. Applied egg-rr 52.5%

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

   10. Taylor expanded in y around inf 71.7%

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

       1. associate-*r* 71.8%

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

       2. *-commutative 71.8%

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

       3. associate-*l* 72.4%

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

       4. *-commutative 72.4%

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

       5. *-commutative 72.4%

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

       6. associate-*l* 72.4%

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

       7. *-commutative 72.4%

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

   12. Simplified 72.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-16}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\\ \end{array} \]

Alternative 14: 73.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-15} \lor \neg \left(z \leq 7.6 \cdot 10^{+97}\right):\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e-15) (not (<= z 7.6e+97)))
   (* -9.0 (* y (* z t)))
   (+ (* x 2.0) (* a (* 27.0 b)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-15) || !(z <= 7.6e+97)) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = (x * 2.0) + (a * (27.0 * b));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.5d-15)) .or. (.not. (z <= 7.6d+97))) then
        tmp = (-9.0d0) * (y * (z * t))
    else
        tmp = (x * 2.0d0) + (a * (27.0d0 * b))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-15) || !(z <= 7.6e+97)) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = (x * 2.0) + (a * (27.0 * b));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e-15) or not (z <= 7.6e+97):
		tmp = -9.0 * (y * (z * t))
	else:
		tmp = (x * 2.0) + (a * (27.0 * b))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e-15) || !(z <= 7.6e+97))
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	else
		tmp = Float64(Float64(x * 2.0) + Float64(a * Float64(27.0 * b)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e-15) || ~((z <= 7.6e+97)))
		tmp = -9.0 * (y * (z * t));
	else
		tmp = (x * 2.0) + (a * (27.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e-15], N[Not[LessEqual[z, 7.6e+97]], $MachinePrecision]], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000007e-15 or 7.60000000000000071e97 < z

   1. Initial program 84.5%

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

   2. Taylor expanded in x around 0 73.4%

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

   3. Taylor expanded in a around 0 58.8%

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

   if -8.50000000000000007e-15 < z < 7.60000000000000071e97

   1. Initial program 97.9%

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

      1. associate-+l- 97.9%

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

      2. sub-neg 97.9%

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

      3. neg-mul-1 97.9%

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

      4. metadata-eval 97.9%

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

      5. metadata-eval 97.9%

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

      6. cancel-sign-sub-inv 97.9%

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

      7. metadata-eval 97.9%

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

      8. *-lft-identity 97.9%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 77.6%

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

      1. *-commutative 77.6%

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

   6. Simplified 77.6%

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

      1. *-commutative 77.6%

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

      2. cancel-sign-sub-inv 77.6%

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

      3. metadata-eval 77.6%

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

      4. *-commutative 77.6%

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

      5. associate-*r* 77.0%

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

      6. *-commutative 77.0%

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

   8. Applied egg-rr 77.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-15} \lor \neg \left(z \leq 7.6 \cdot 10^{+97}\right):\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 15: 73.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-15} \lor \neg \left(z \leq 1.35 \cdot 10^{+95}\right):\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.7e-15) (not (<= z 1.35e+95)))
   (* -9.0 (* y (* z t)))
   (- (* x 2.0) (* (* a b) -27.0))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.7e-15) || !(z <= 1.35e+95)) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.7d-15)) .or. (.not. (z <= 1.35d+95))) then
        tmp = (-9.0d0) * (y * (z * t))
    else
        tmp = (x * 2.0d0) - ((a * b) * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.7e-15) || !(z <= 1.35e+95)) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = (x * 2.0) - ((a * b) * -27.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.7e-15) or not (z <= 1.35e+95):
		tmp = -9.0 * (y * (z * t))
	else:
		tmp = (x * 2.0) - ((a * b) * -27.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.7e-15) || !(z <= 1.35e+95))
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(Float64(a * b) * -27.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.7e-15) || ~((z <= 1.35e+95)))
		tmp = -9.0 * (y * (z * t));
	else
		tmp = (x * 2.0) - ((a * b) * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.7e-15], N[Not[LessEqual[z, 1.35e+95]], $MachinePrecision]], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.70000000000000001e-15 or 1.35e95 < z

   1. Initial program 84.5%

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

   2. Taylor expanded in x around 0 73.4%

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

   3. Taylor expanded in a around 0 58.8%

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

   if -6.70000000000000001e-15 < z < 1.35e95

   1. Initial program 97.9%

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

      1. associate-+l- 97.9%

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

      2. sub-neg 97.9%

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

      3. neg-mul-1 97.9%

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

      4. metadata-eval 97.9%

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

      5. metadata-eval 97.9%

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

      6. cancel-sign-sub-inv 97.9%

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

      7. metadata-eval 97.9%

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

      8. *-lft-identity 97.9%

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

      9. associate-*l* 99.0%

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

      10. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 77.6%

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

      1. *-commutative 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-15} \lor \neg \left(z \leq 1.35 \cdot 10^{+95}\right):\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - \left(a \cdot b\right) \cdot -27\\ \end{array} \]

Alternative 16: 45.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+78} \lor \neg \left(a \leq 7.2 \cdot 10^{-96}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

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 -9.2e+78) (not (<= a 7.2e-96))) (* 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 <= -9.2e+78) || !(a <= 7.2e-96)) {
		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 <= (-9.2d+78)) .or. (.not. (a <= 7.2d-96))) 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 <= -9.2e+78) || !(a <= 7.2e-96)) {
		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 <= -9.2e+78) or not (a <= 7.2e-96):
		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 <= -9.2e+78) || !(a <= 7.2e-96))
		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 <= -9.2e+78) || ~((a <= 7.2e-96)))
		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, -9.2e+78], N[Not[LessEqual[a, 7.2e-96]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.2000000000000008e78 or 7.20000000000000016e-96 < a

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-*l* 92.7%

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

      3. fma-def 94.1%

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

      4. associate-*l* 95.5%

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

      5. *-commutative 95.5%

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

      6. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-*r* 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 94.1%

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

      4. cancel-sign-sub-inv 94.1%

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

      5. associate-*l* 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in a around inf 56.9%

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

   if -9.2000000000000008e78 < a < 7.20000000000000016e-96

   1. Initial program 91.2%

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

      1. associate-+l- 91.2%

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

      2. fma-neg 91.2%

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

      3. neg-sub0 91.2%

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

      4. associate-+l- 91.2%

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

      5. neg-sub0 91.2%

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

      6. *-commutative 91.2%

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

      7. distribute-rgt-neg-in 91.2%

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

      8. fma-def 91.2%

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

      9. *-commutative 91.2%

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

      10. associate-*r* 91.3%

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

      11. distribute-rgt-neg-in 91.3%

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

      12. *-commutative 91.3%

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

      13. metadata-eval 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 37.2%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+78} \lor \neg \left(a \leq 7.2 \cdot 10^{-96}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 17: 45.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+77}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.4e+77)
   (* 27.0 (* a b))
   (if (<= a 7.2e-96) (* x 2.0) (* b (* a 27.0)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.4e+77) {
		tmp = 27.0 * (a * b);
	} else if (a <= 7.2e-96) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.4d+77)) then
        tmp = 27.0d0 * (a * b)
    else if (a <= 7.2d-96) then
        tmp = x * 2.0d0
    else
        tmp = b * (a * 27.0d0)
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.4e+77) {
		tmp = 27.0 * (a * b);
	} else if (a <= 7.2e-96) {
		tmp = x * 2.0;
	} else {
		tmp = b * (a * 27.0);
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.4e+77:
		tmp = 27.0 * (a * b)
	elif a <= 7.2e-96:
		tmp = x * 2.0
	else:
		tmp = b * (a * 27.0)
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.4e+77)
		tmp = Float64(27.0 * Float64(a * b));
	elseif (a <= 7.2e-96)
		tmp = Float64(x * 2.0);
	else
		tmp = Float64(b * Float64(a * 27.0));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.4e+77)
		tmp = 27.0 * (a * b);
	elseif (a <= 7.2e-96)
		tmp = x * 2.0;
	else
		tmp = b * (a * 27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.4e+77], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-96], N[(x * 2.0), $MachinePrecision], N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4000000000000001e77

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*l* 93.4%

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

      3. fma-def 93.3%

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

      4. associate-*l* 96.5%

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

      5. *-commutative 96.5%

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

      6. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

      1. associate-*r* 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*r* 93.3%

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

      4. cancel-sign-sub-inv 93.3%

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

      5. associate-*l* 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in a around inf 56.8%

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

   if -4.4000000000000001e77 < a < 7.20000000000000016e-96

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. fma-neg 91.1%

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

      3. neg-sub0 91.1%

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

      4. associate-+l- 91.1%

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

      5. neg-sub0 91.1%

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

      6. *-commutative 91.1%

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

      7. distribute-rgt-neg-in 91.1%

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

      8. fma-def 91.1%

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

      9. *-commutative 91.1%

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

      10. associate-*r* 91.2%

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

      11. distribute-rgt-neg-in 91.2%

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

      12. *-commutative 91.2%

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

      13. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 37.5%

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

   if 7.20000000000000016e-96 < a

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-*l* 92.2%

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

      3. fma-def 94.8%

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

      4. associate-*l* 94.8%

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

      5. *-commutative 94.8%

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

      6. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

      1. associate-*r* 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-*r* 94.8%

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

      4. cancel-sign-sub-inv 94.8%

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

      5. associate-*l* 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in a around inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. *-commutative 56.2%

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

      3. *-commutative 56.2%

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

      4. *-commutative 56.2%

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

   8. Simplified 56.2%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+77}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-96}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \end{array} \]

Alternative 18: 30.4% 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 92.3%

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

   1. associate-+l- 92.3%

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

   2. fma-neg 92.3%

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

   3. neg-sub0 92.3%

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

   4. associate-+l- 92.3%

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

   5. neg-sub0 92.3%

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

   6. *-commutative 92.3%

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

   7. distribute-rgt-neg-in 92.3%

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

   8. fma-def 93.1%

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

   9. *-commutative 93.1%

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

   10. associate-*r* 93.1%

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

   11. distribute-rgt-neg-in 93.1%

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

   12. *-commutative 93.1%

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

   13. metadata-eval 93.1%

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

3. Simplified 93.1%

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

4. Taylor expanded in x around inf 27.4%

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

5. Final simplification 27.4%

   \[\leadsto x \cdot 2 \]

Developer target: 94.6% 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 2023229 
(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)))