Average Error: 0.5 → 0.5
Time: 35.9s
Precision: 64
Internal Precision: 576
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{\frac{1 - \left(\left(v \cdot v\right) \cdot 5\right) \cdot \left(\left(v \cdot v\right) \cdot 5\right)}{\left(v \cdot v\right) \cdot 5 + 1}}{v \cdot v - 1}\right)\]

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 flip--0.5

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

  4. Final simplification0.5

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

Runtime

Time bar (total: 35.9s)Debug logProfile

herbie shell --seed 2018254 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))