(- (* (- 1 (cos x)) (pow x 2)) (* (- timeout) 10))

Average Error: 2.4 → 2.4

Time: 2.8s

Precision: binary64

Math

\[\left(1 - \cos x\right) \cdot {x}^{2} - \left(-timeout\right) \cdot 10\]

↓

\[timeout \cdot 10 + \left(1 - \cos x\right) \cdot {x}^{2}\]

Error

Bits error versus x

Bits error versus timeout

Derivation

1. Initial program 2.4

   \[\left(1 - \cos x\right) \cdot {x}^{2} - \left(-timeout\right) \cdot 10\]

2. Simplified 2.4

   \[\leadsto \color{blue}{timeout \cdot 10 + \left(1 - \cos x\right) \cdot {x}^{2}}\]

3. Final simplification 2.4

   \[\leadsto timeout \cdot 10 + \left(1 - \cos x\right) \cdot {x}^{2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x timeout)
  :name "(- (* (- 1 (cos x)) (pow x 2)) (* (- timeout) 10))"
  :precision binary64
  (- (* (- 1.0 (cos x)) (pow x 2.0)) (* (neg timeout) 10.0)))