Error: 32.2 → 0.1
Time: 32.6s
Precision: 64
Ground Truth: 128
\[\frac{x - \sin x}{x - \tan x}\]
⬇
\[\begin{cases} \frac{x - \sin x}{x - \tan x} & \text{when } x \le -1.8773586721409905 \cdot 10^{-08} \\ \frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right) & \text{when } x \le 108678362595.63406 \\ \frac{x - \sin x}{x - \tan x} & \text{otherwise} \end{cases}\]

Error

Bits error versus x

Derivation

    if x < -1.8773586721409905e-08 or 108678362595.63406 < x

    1. Initial program 0.3

      \[\frac{x - \sin x}{x - \tan x}\]

    if -1.8773586721409905e-08 < x < 108678362595.63406

    1. Initial program 63.1

      \[\frac{x - \sin x}{x - \tan x}\]

    2. Applied taylor 0.0

      \[\leadsto \frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)\]

    3. Taylor expanded around 0 0.0

      \[\leadsto \color{blue}{\frac{9}{40} \cdot {x}^2 - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)}\]
  1. Removed slow pow expressions

Runtime

Total time: 32.6s Debug log

Please report a bug with the following info:

herbie --seed '#(4033285044 1576463085 2929677627 151269710 2157998159 803759123)'
(FPCore (x)
  :name "NMSE problem 3.4.5"
  (/ (- x (sin x)) (- x (tan x))))