Rump's expression from Stadtherr's award speech

Average Error: 58.1 → 57.1

Time: 2.2min

Precision: binary64

Cost: 704

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

Math

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

↓

\[\left(x \cdot x\right) \cdot -2 + 0.5 \cdot \frac{x}{y}\]

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))))

↓

(FPCore (x y) :precision binary64 (+ (* (* x x) -2.0) (* 0.5 (/ x 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));
}

↓

double code(double x, double y) {
	return ((x * x) * -2.0) + (0.5 * (x / y));
}

Alternative 1
Accuracy	58.1
Cost	15040

\[\frac{\left({\left(5.5 \cdot {y}^{8}\right)}^{3} + \left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) \cdot {\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right)}^{2}\right) \cdot \left(y \cdot 2\right) + x \cdot \left(30.25 \cdot {y}^{16} + \left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) \cdot \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) - 5.5 \cdot {y}^{8}\right)\right)}{\left(y \cdot 2\right) \cdot \left(30.25 \cdot {y}^{16} + \left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) \cdot \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) - 5.5 \cdot {y}^{8}\right)\right)}\]

Alternative 2
Accuracy	58.1
Cost	12992

\[\frac{\left({\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right)}^{3} + {\left(5.5 \cdot {y}^{8}\right)}^{3}\right) \cdot \left(y \cdot 2\right) + x \cdot \left(30.25 \cdot {y}^{16} + \left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) \cdot \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) - 5.5 \cdot {y}^{8}\right)\right)}{\left(y \cdot 2\right) \cdot \left(30.25 \cdot {y}^{16} + \left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) \cdot \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(y \cdot \left(x \cdot \left(x \cdot 11\right)\right)\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) - 5.5 \cdot {y}^{8}\right)\right)}\]

Alternative 3
Accuracy	58.1
Cost	2752

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

Derivation

1. Initial program 58.1

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

2. Taylor expanded around 0 57.1

   \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}}\]

3. Simplified 57.1

   \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot -2 + 0.5 \cdot \frac{x}{y}}\]

4. Final simplification 57.1

   \[\leadsto \left(x \cdot x\right) \cdot -2 + 0.5 \cdot \frac{x}{y}\]

Reproduce

herbie shell --seed 2020322 
(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))))