Average Error: 0.0 → 0.0
Time: 14.5s
Precision: 64
Internal Precision: 320
\[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
↓
\[\log \left(\frac{\log \left(e^{\sqrt{1 - x \cdot x}}\right)}{x} + \frac{1}{x}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]

  2. Initial simplification0.0

    \[\leadsto \log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
  3. Using strategy rm

  4. Applied add-log-exp0.0

    \[\leadsto \log \left(\frac{1}{x} + \frac{\color{blue}{\log \left(e^{\sqrt{1 - x \cdot x}}\right)}}{x}\right)\]

  5. Final simplification0.0

    \[\leadsto \log \left(\frac{\log \left(e^{\sqrt{1 - x \cdot x}}\right)}{x} + \frac{1}{x}\right)\]

Runtime

Time bar (total: 14.5s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.0100%
herbie shell --seed 2018297 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))