Average Error: 0.2 → 0.3
Time: 26.5s
Precision: 64
Internal Precision: 576
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\sqrt[3]{\sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}} \cdot \sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}}} \cdot a\right)\]

Error

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{a}{-\cos^{-1} a}\]
  2. Using strategy rm

  3. Applied clear-num0.4

    \[\leadsto \color{blue}{\frac{1}{\frac{-\cos^{-1} a}{a}}}\]
  4. Using strategy rm

  5. Applied div-inv0.4

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

  6. Applied associate-/r*0.4

    \[\leadsto \color{blue}{\frac{\frac{1}{-\cos^{-1} a}}{\frac{1}{a}}}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube0.7

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\frac{1}{-\cos^{-1} a} \cdot \frac{1}{-\cos^{-1} a}\right) \cdot \frac{1}{-\cos^{-1} a}}}}{\frac{1}{a}}\]

  9. Applied simplify0.7

    \[\leadsto \frac{\sqrt[3]{\color{blue}{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{\frac{1}{a}}\]
  10. Using strategy rm

  11. Applied *-un-lft-identity0.7

    \[\leadsto \frac{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}{\color{blue}{1 \cdot \frac{1}{a}}}\]

  12. Applied add-cube-cbrt0.7

    \[\leadsto \frac{\sqrt[3]{\color{blue}{\left(\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}} \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}\right) \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}}{1 \cdot \frac{1}{a}}\]

  13. Applied cbrt-prod0.5

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}} \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}}{1 \cdot \frac{1}{a}}\]

  14. Applied times-frac0.4

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}} \cdot \sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{1} \cdot \frac{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{\frac{1}{a}}}\]

  15. Applied simplify0.4

    \[\leadsto \color{blue}{\sqrt[3]{\sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}} \cdot \sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{\frac{1}{\left(\cos^{-1} a \cdot \cos^{-1} a\right) \cdot \left(-\cos^{-1} a\right)}}}}{\frac{1}{a}}\]

  16. Applied simplify0.3

    \[\leadsto \sqrt[3]{\sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}} \cdot \sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}}} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\frac{\frac{1}{\cos^{-1} a \cdot \cos^{-1} a}}{-\cos^{-1} a}}} \cdot a\right)}\]

Runtime

Time bar (total: 26.5s)Debug logProfile

herbie shell --seed 2019053 
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))