Rump's expression from Stadtherr's award speech

Percentage Accurate: 9.2% → 8.2%

Time: 3.9s

Alternatives: 1

Speedup: N/A×

Specification

\[x = 77617 \land y = 33096\]

Math

\[\begin{array}{l} \\ -0.8273960599468214 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -0.8273960599468214)

C

double code(double x, double y) {
	return -0.8273960599468214;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -0.8273960599468214d0
end function

Java

public static double code(double x, double y) {
	return -0.8273960599468214;
}

Python

def code(x, y):
	return -0.8273960599468214

Julia

function code(x, y)
	return -0.8273960599468214
end

MATLAB

function tmp = code(x, y)
	tmp = -0.8273960599468214;
end

Wolfram

code[x_, y_] := -0.8273960599468214

Initial Program: 9.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+
  (+
   (+
    (* 333.75 (pow y 6.0))
    (*
     (* x x)
     (-
      (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0)))
      2.0)))
   (* 5.5 (pow y 8.0)))
  (/ x (* 2.0 y))))

C

double code(double x, double y) {
	return (((333.75 * pow(y, 6.0)) + ((x * x) * (((((((11.0 * x) * x) * y) * y) - pow(y, 6.0)) - (121.0 * pow(y, 4.0))) - 2.0))) + (5.5 * pow(y, 8.0))) + (x / (2.0 * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (((333.75d0 * (y ** 6.0d0)) + ((x * x) * (((((((11.0d0 * x) * x) * y) * y) - (y ** 6.0d0)) - (121.0d0 * (y ** 4.0d0))) - 2.0d0))) + (5.5d0 * (y ** 8.0d0))) + (x / (2.0d0 * y))
end function

Java

public static double code(double x, double y) {
	return (((333.75 * Math.pow(y, 6.0)) + ((x * x) * (((((((11.0 * x) * x) * y) * y) - Math.pow(y, 6.0)) - (121.0 * Math.pow(y, 4.0))) - 2.0))) + (5.5 * Math.pow(y, 8.0))) + (x / (2.0 * y));
}

Python

def code(x, y):
	return (((333.75 * math.pow(y, 6.0)) + ((x * x) * (((((((11.0 * x) * x) * y) * y) - math.pow(y, 6.0)) - (121.0 * math.pow(y, 4.0))) - 2.0))) + (5.5 * math.pow(y, 8.0))) + (x / (2.0 * y))

Julia

function code(x, y)
	return Float64(Float64(Float64(Float64(333.75 * (y ^ 6.0)) + Float64(Float64(x * x) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(11.0 * x) * x) * y) * y) - (y ^ 6.0)) - Float64(121.0 * (y ^ 4.0))) - 2.0))) + Float64(5.5 * (y ^ 8.0))) + Float64(x / Float64(2.0 * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (((333.75 * (y ^ 6.0)) + ((x * x) * (((((((11.0 * x) * x) * y) * y) - (y ^ 6.0)) - (121.0 * (y ^ 4.0))) - 2.0))) + (5.5 * (y ^ 8.0))) + (x / (2.0 * y));
end

Wolfram

code[x_, y_] := N[(N[(N[(N[(333.75 * N[Power[y, 6.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * x), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(11.0 * x), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision] * y), $MachinePrecision] - N[Power[y, 6.0], $MachinePrecision]), $MachinePrecision] - N[(121.0 * N[Power[y, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(5.5 * N[Power[y, 8.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 8.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot y\right)\\ \left(\left(\left(t\_0 \cdot t\_0\right) \cdot 333.75 + x \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - y \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right)\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{y \cdot 2} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y y))))
   (+
    (+
     (+
      (* (* t_0 t_0) 333.75)
      (*
       x
       (-
        (-
         (- (* y (* y (* x (* x 11.0)))) (pow y 6.0))
         (* y (* (* y y) (* y 121.0))))
        2.0)))
     (* y 5.5))
    (/ x (* y 2.0)))))

C

double code(double x, double y) {
	double t_0 = y * (y * y);
	return ((((t_0 * t_0) * 333.75) + (x * ((((y * (y * (x * (x * 11.0)))) - pow(y, 6.0)) - (y * ((y * y) * (y * 121.0)))) - 2.0))) + (y * 5.5)) + (x / (y * 2.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = y * (y * y)
    code = ((((t_0 * t_0) * 333.75d0) + (x * ((((y * (y * (x * (x * 11.0d0)))) - (y ** 6.0d0)) - (y * ((y * y) * (y * 121.0d0)))) - 2.0d0))) + (y * 5.5d0)) + (x / (y * 2.0d0))
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (y * y);
	return ((((t_0 * t_0) * 333.75) + (x * ((((y * (y * (x * (x * 11.0)))) - Math.pow(y, 6.0)) - (y * ((y * y) * (y * 121.0)))) - 2.0))) + (y * 5.5)) + (x / (y * 2.0));
}

Python

def code(x, y):
	t_0 = y * (y * y)
	return ((((t_0 * t_0) * 333.75) + (x * ((((y * (y * (x * (x * 11.0)))) - math.pow(y, 6.0)) - (y * ((y * y) * (y * 121.0)))) - 2.0))) + (y * 5.5)) + (x / (y * 2.0))

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * y))
	return Float64(Float64(Float64(Float64(Float64(t_0 * t_0) * 333.75) + Float64(x * Float64(Float64(Float64(Float64(y * Float64(y * Float64(x * Float64(x * 11.0)))) - (y ^ 6.0)) - Float64(y * Float64(Float64(y * y) * Float64(y * 121.0)))) - 2.0))) + Float64(y * 5.5)) + Float64(x / Float64(y * 2.0)))
end

MATLAB

function tmp = code(x, y)
	t_0 = y * (y * y);
	tmp = ((((t_0 * t_0) * 333.75) + (x * ((((y * (y * (x * (x * 11.0)))) - (y ^ 6.0)) - (y * ((y * y) * (y * 121.0)))) - 2.0))) + (y * 5.5)) + (x / (y * 2.0));
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] * 333.75), $MachinePrecision] + N[(x * N[(N[(N[(N[(y * N[(y * N[(x * N[(x * 11.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Power[y, 6.0], $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(y * y), $MachinePrecision] * N[(y * 121.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.5), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 9.2%

   \[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sqr-pow N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot \color{blue}{\left({y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}\right)}\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   2. associate-*r* N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \color{blue}{\left(121 \cdot {y}^{\left(\frac{4}{2}\right)}\right) \cdot {y}^{\left(\frac{4}{2}\right)}}\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   3. metadata-eval N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(121 \cdot {y}^{\left(\frac{4}{2}\right)}\right) \cdot {y}^{\color{blue}{2}}\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   4. unpow2 N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(121 \cdot {y}^{\left(\frac{4}{2}\right)}\right) \cdot \color{blue}{\left(y \cdot y\right)}\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \color{blue}{\left(\left(121 \cdot {y}^{\left(\frac{4}{2}\right)}\right) \cdot y\right) \cdot y}\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \color{blue}{\left(\left(121 \cdot {y}^{\left(\frac{4}{2}\right)}\right) \cdot y\right) \cdot y}\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   7. *-commutative N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\color{blue}{\left({y}^{\left(\frac{4}{2}\right)} \cdot 121\right)} \cdot y\right) \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   8. associate-*l* N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \color{blue}{\left({y}^{\left(\frac{4}{2}\right)} \cdot \left(121 \cdot y\right)\right)} \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left({y}^{\left(\frac{4}{2}\right)} \cdot \color{blue}{\left(y \cdot 121\right)}\right) \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   10. lower-*.f64 N/A

       \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \color{blue}{\left({y}^{\left(\frac{4}{2}\right)} \cdot \left(y \cdot 121\right)\right)} \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   11. metadata-eval N/A

       \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left({y}^{\color{blue}{2}} \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   12. unpow2 N/A

       \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\color{blue}{\left(y \cdot y\right)} \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   13. lower-*.f64 N/A

       \[\leadsto \left(\left(\frac{1335}{4} \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\color{blue}{\left(y \cdot y\right)} \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + \frac{11}{2} \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

   14. lower-*.f64 9.2

       \[\leadsto \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \color{blue}{\left(y \cdot 121\right)}\right) \cdot y\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

4. Applied egg-rr 9.2%

   \[\leadsto \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \color{blue}{\left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y} \]

6. Applied egg-rr 7.9%

   \[\leadsto \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + \color{blue}{y \cdot 5.5}\right) + \frac{x}{2 \cdot y} \]
7. Step-by-step derivation

   1. lift-pow.f64 N/A

      \[\leadsto \left(\left(\frac{1335}{4} \cdot \color{blue}{{y}^{6}} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\color{blue}{{y}^{6} \cdot \frac{1335}{4}} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   3. lower-*.f64 7.9

      \[\leadsto \left(\left(\color{blue}{{y}^{6} \cdot 333.75} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{2 \cdot y} \]

   4. lift-pow.f64 N/A

      \[\leadsto \left(\left(\color{blue}{{y}^{6}} \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   5. sqr-pow N/A

      \[\leadsto \left(\left(\color{blue}{\left({y}^{\left(\frac{6}{2}\right)} \cdot {y}^{\left(\frac{6}{2}\right)}\right)} \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\color{blue}{\left({y}^{\left(\frac{6}{2}\right)} \cdot {y}^{\left(\frac{6}{2}\right)}\right)} \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   7. metadata-eval N/A

      \[\leadsto \left(\left(\left({y}^{\color{blue}{3}} \cdot {y}^{\left(\frac{6}{2}\right)}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   8. cube-mult N/A

      \[\leadsto \left(\left(\left(\color{blue}{\left(y \cdot \left(y \cdot y\right)\right)} \cdot {y}^{\left(\frac{6}{2}\right)}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   9. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\color{blue}{\left(y \cdot \left(y \cdot y\right)\right)} \cdot {y}^{\left(\frac{6}{2}\right)}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   10. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \color{blue}{\left(y \cdot y\right)}\right) \cdot {y}^{\left(\frac{6}{2}\right)}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   11. metadata-eval N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot {y}^{\color{blue}{3}}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   12. cube-mult N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(y \cdot \left(y \cdot y\right)\right)}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   13. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \color{blue}{\left(y \cdot \left(y \cdot y\right)\right)}\right) \cdot \frac{1335}{4} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   14. lower-*.f64 7.9

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \color{blue}{\left(y \cdot y\right)}\right)\right) \cdot 333.75 + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{2 \cdot y} \]

8. Applied egg-rr 7.9%

   \[\leadsto \left(\left(\color{blue}{\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot 333.75} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{2 \cdot y} \]
9. Step-by-step derivation

   1. rem-exp-log N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + \left(\color{blue}{e^{\log x}} \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   2. rem-exp-log N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + \left(e^{\log x} \cdot \color{blue}{e^{\log x}}\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   3. prod-exp N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + \color{blue}{e^{\log x + \log x}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   4. flip-+ N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\color{blue}{\frac{\log x \cdot \log x - \log x \cdot \log x}{\log x - \log x}}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   5. +-inverses N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\frac{\color{blue}{0}}{\log x - \log x}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   6. +-inverses N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\frac{\color{blue}{\log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}}{\log x - \log x}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   7. +-inverses N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\frac{\log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}{\color{blue}{0}}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   8. +-inverses N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\frac{\log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) \cdot \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}{\color{blue}{\log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) - \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   9. flip-+ N/A

      \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\color{blue}{\log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right) + \log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   10. log-prod N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\color{blue}{\log \left({x}^{\left(\frac{\frac{2}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{2}{2}}{2}\right)}\right)}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   11. sqr-pow N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\log \color{blue}{\left({x}^{\left(\frac{2}{2}\right)}\right)}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   12. metadata-eval N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\log \left({x}^{\color{blue}{1}}\right)} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   13. unpow1 N/A

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot \frac{1335}{4} + e^{\log \color{blue}{x}} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot \frac{11}{2}\right) + \frac{x}{2 \cdot y} \]

   14. rem-exp-log 8.2

       \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot 333.75 + \color{blue}{x} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{2 \cdot y} \]

10. Applied egg-rr 8.2%

    \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot 333.75 + \color{blue}{x} \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right) \cdot y\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{2 \cdot y} \]

11. Final simplification 8.2%

    \[\leadsto \left(\left(\left(\left(y \cdot \left(y \cdot y\right)\right) \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) \cdot 333.75 + x \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - y \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot 121\right)\right)\right) - 2\right)\right) + y \cdot 5.5\right) + \frac{x}{y \cdot 2} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y)
  :name "Rump's expression from Stadtherr's award speech"
  :precision binary64
  :pre (and (== x 77617.0) (== y 33096.0))
  (+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y))))