Average Error: 31.3 → 0.7
Time: 1.2m
Precision: 64
Ground Truth: 128
\[\frac{1 - \cos x}{{x}^2}\]
⬇
\[\frac{1}{\left(1 + \cos x\right) \cdot {\left(\frac{x}{\sin x}\right)}^2}\]

Error

Bits error versus x

Derivation

  1. Initial program 31.3

    \[\frac{1 - \cos x}{{x}^2}\]
  2. Using strategy rm

  3. Applied flip-- 31.4

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

  4. Applied simplify 15.7

    \[\leadsto \frac{\frac{\color{blue}{\sin x \cdot \sin x}}{1 + \cos x}}{{x}^2}\]
  5. Using strategy rm

  6. Applied clear-num 15.7

    \[\leadsto \color{blue}{\frac{1}{\frac{{x}^2}{\frac{\sin x \cdot \sin x}{1 + \cos x}}}}\]

  7. Applied simplify 0.7

    \[\leadsto \frac{1}{\color{blue}{\left(1 + \cos x\right) \cdot {\left(\frac{x}{\sin x}\right)}^2}}\]
  8. Removed slow pow expressions

Runtime

Total time: 1.2m Debug log

Please include this information when filing a bug report:

herbie --seed '#(3687061469 319650801 1141741595 1577272311 577064297 1181464521)'
(FPCore (x)
  :name "NMSE problem 3.4.1"
  (/ (- 1 (cos x)) (sqr x)))