Average Error: 0.5 → 0.5
Time: 57.1s
Precision: 64
Internal Precision: 576
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{v \cdot v - 1}\right)\right)}\]

Error

Bits error versus v

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.5

    \[\leadsto \cos^{-1} \left(\frac{1 - \color{blue}{\log \left(e^{5 \cdot \left(v \cdot v\right)}\right)}}{v \cdot v - 1}\right)\]
  4. Using strategy rm

  5. Applied add-exp-log0.5

    \[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{5 \cdot \left(v \cdot v\right)}\right)}{v \cdot v - 1}\right)\right)}}\]

  6. Final simplification0.5

    \[\leadsto e^{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{v \cdot v - 1}\right)\right)}\]

Runtime

Time bar (total: 57.1s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.50.50.50.00%
herbie shell --seed 2018263 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))