Average Error: 0.1 → 0.1
Time: 31.5s
Precision: 64
Internal Precision: 128
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(e^{\left(\left(b - a\right) + \left(b - a\right)\right) \cdot \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)\]

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]

  2. Initial simplification0.1

    \[\leadsto \sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.1

    \[\leadsto \sin \left({\color{blue}{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}}^{\left(b - a\right)}\right)\]

  5. Applied unpow-prod-down0.1

    \[\leadsto \sin \color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\]
  6. Using strategy rm

  7. Applied add-exp-log0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\color{blue}{\left(e^{\log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)}}^{\left(b - a\right)}\right)\]

  8. Applied pow-exp0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \color{blue}{e^{\log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \left(b - a\right)}}\right)\]

  9. Applied add-exp-log0.1

    \[\leadsto \sin \left(\color{blue}{e^{\log \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}} \cdot e^{\log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \left(b - a\right)}\right)\]

  10. Applied prod-exp0.1

    \[\leadsto \sin \color{blue}{\left(e^{\log \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right) + \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \left(b - a\right)}\right)}\]

  11. Simplified0.1

    \[\leadsto \sin \left(e^{\color{blue}{\log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \left(\left(b - a\right) + \left(b - a\right)\right)}}\right)\]

  12. Final simplification0.1

    \[\leadsto \sin \left(e^{\left(\left(b - a\right) + \left(b - a\right)\right) \cdot \log \left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}\right)\]

Runtime

Time bar (total: 31.5s)Debug logProfile

herbie shell --seed 2018336 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))