Average Error: 58.6 → 0.0
Time: 28.0s
Precision: 64
Internal Precision: 1344
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
↓
\[\log_* (1 + \left(-\varepsilon\right)) - \log_* (1 + \varepsilon)\]

Error

Bits error versus eps

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original58.6
Target0.2
Herbie0.0
\[-2 \cdot \left(\left(\varepsilon + \frac{{\varepsilon}^{3}}{3}\right) + \frac{{\varepsilon}^{5}}{5}\right)\]

Derivation

  1. Initial program 58.6

    \[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]

  2. Initial simplification0.0

    \[\leadsto \log_* (1 + \left(-\varepsilon\right)) - \log_* (1 + \varepsilon)\]

  3. Final simplification0.0

    \[\leadsto \log_* (1 + \left(-\varepsilon\right)) - \log_* (1 + \varepsilon)\]

Runtime

Time bar (total: 28.0s)Debug logProfile

herbie shell --seed 2018221 +o rules:numerics
(FPCore (eps)
  :name "logq (problem 3.4.3)"

  :herbie-target
  (* -2 (+ (+ eps (/ (pow eps 3) 3)) (/ (pow eps 5) 5)))

  (log (/ (- 1 eps) (+ 1 eps))))