Average Error: 0.1 → 0.2
Time: 23.8s
Precision: 64
Internal Precision: 128
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[(e^{\log_* (1 + \sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}\right))} - 1)^*\]

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. Using strategy rm

  3. Applied expm1-log1p-u0.2

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

  5. Applied add-cube-cbrt0.2

    \[\leadsto (e^{\log_* (1 + \sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right) \cdot \sqrt[3]{b - a}\right)}}\right))} - 1)^*\]

  6. Applied pow-unpow0.2

    \[\leadsto (e^{\log_* (1 + \sin \color{blue}{\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}\right)})} - 1)^*\]

  7. Final simplification0.2

    \[\leadsto (e^{\log_* (1 + \sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}\right))} - 1)^*\]

Runtime

Time bar (total: 23.8s)Debug logProfile

herbie shell --seed 2018304 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))