\[\left(\left(\left(333.75 \cdot {y}^{6} + {x}^{2} \cdot \left(\left(\left(\left(11 \cdot {x}^{2}\right) \cdot {y}^{2} - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\right) - \left(-timeout\right) \cdot 10^{3}\]

↓

\[\left(333.75 \cdot {y}^{6} + {x}^{2} \cdot \left(\left(\left(\left(11 \cdot {x}^{2}\right) \cdot {y}^{2} - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + \left(\left(5.5 \cdot {y}^{8} + \frac{x}{2 \cdot y}\right) + timeout \cdot 10^{3}\right)\]

Error

The X axis uses an exponential scale — Bits error versus `y`

Derivation

Initial program 0.1
\[\left(\left(\left(333.75 \cdot {y}^{6} + {x}^{2} \cdot \left(\left(\left(\left(11 \cdot {x}^{2}\right) \cdot {y}^{2} - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\right) - \left(-timeout\right) \cdot 10^{3}\]
Simplified0.1
\[\leadsto \color{blue}{\left(333.75 \cdot {y}^{6} + {x}^{2} \cdot \left(\left(\left(\left(11 \cdot {x}^{2}\right) \cdot {y}^{2} - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + \left(\left(5.5 \cdot {y}^{8} + \frac{x}{2 \cdot y}\right) + timeout \cdot 10^{3}\right)}\]
Final simplification0.1
\[\leadsto \left(333.75 \cdot {y}^{6} + {x}^{2} \cdot \left(\left(\left(\left(11 \cdot {x}^{2}\right) \cdot {y}^{2} - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + \left(\left(5.5 \cdot {y}^{8} + \frac{x}{2 \cdot y}\right) + timeout \cdot 10^{3}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (y x timeout)
  :name "(- (+ (+ (+ (* 333.75 (pow y 6)) (* (pow x 2) (- (- (- (* (* 11 (pow x 2)) (pow y 2)) (pow y 6)) (* 121 (pow y 4))) 2))) (* 5.5 (pow y 8))) (/ x (* 2 y))) (* (- timeout) 1000))"
  :precision binary64
  (- (+ (+ (+ (* 333.75 (pow y 6.0)) (* (pow x 2.0) (- (- (- (* (* 11.0 (pow x 2.0)) (pow y 2.0)) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y))) (* (neg timeout) 1000.0)))