Average Error: 16.8 → 16.8
Time: 19.3s
Precision: 64
Internal Precision: 832
\[\sin \left(\sqrt{x}\right) + \log x \cdot \left|\sin x \cdot \log x\right|\]
\[\sin \left(\sqrt{x}\right) + \left|\left(\log x \cdot \left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \sqrt[3]{\sqrt[3]{\sin x}}\right)\right| \cdot \log x\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.8

    \[\sin \left(\sqrt{x}\right) + \log x \cdot \left|\sin x \cdot \log x\right|\]
  2. Initial simplification16.8

    \[\leadsto \left|\log x \cdot \sin x\right| \cdot \log x + \sin \left(\sqrt{x}\right)\]
  3. Using strategy rm
  4. Applied add-cube-cbrt16.8

    \[\leadsto \left|\log x \cdot \color{blue}{\left(\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}\right)}\right| \cdot \log x + \sin \left(\sqrt{x}\right)\]
  5. Applied associate-*r*16.8

    \[\leadsto \left|\color{blue}{\left(\log x \cdot \left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)\right) \cdot \sqrt[3]{\sin x}}\right| \cdot \log x + \sin \left(\sqrt{x}\right)\]
  6. Using strategy rm
  7. Applied add-cube-cbrt16.8

    \[\leadsto \left|\left(\log x \cdot \left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}}}\right| \cdot \log x + \sin \left(\sqrt{x}\right)\]
  8. Applied cbrt-prod16.8

    \[\leadsto \left|\left(\log x \cdot \left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \sqrt[3]{\sqrt[3]{\sin x}}\right)}\right| \cdot \log x + \sin \left(\sqrt{x}\right)\]
  9. Final simplification16.8

    \[\leadsto \sin \left(\sqrt{x}\right) + \left|\left(\log x \cdot \left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}} \cdot \sqrt[3]{\sqrt[3]{\sin x}}\right)\right| \cdot \log x\]

Runtime

Time bar (total: 19.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sin(sqrt(x)) + log(x) * abs(sin(x) * log(x))"
  (+ (sin (sqrt x)) (* (log x) (fabs (* (sin x) (log x))))))