Average Error: 29.3 → 29.4
Time: 9.0s
Precision: 64
Internal Precision: 576
\[\log \left(\left|\sin x\right| + 1\right) + \cos \left(x \cdot x\right)\]
\[\frac{\cos \left(x \cdot x\right) \cdot \left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right)\right) - \log \left(1 + \left|\sin x\right|\right) \cdot \log \left(1 + \left|\sin x\right|\right)}{\cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.3

    \[\log \left(\left|\sin x\right| + 1\right) + \cos \left(x \cdot x\right)\]
  2. Initial simplification29.3

    \[\leadsto \cos \left(x \cdot x\right) + \log \left(1 + \left|\sin x\right|\right)\]
  3. Using strategy rm
  4. Applied flip-+29.3

    \[\leadsto \color{blue}{\frac{\cos \left(x \cdot x\right) \cdot \cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right) \cdot \log \left(1 + \left|\sin x\right|\right)}{\cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right)}}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt29.4

    \[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right) \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right)} \cdot \cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right) \cdot \log \left(1 + \left|\sin x\right|\right)}{\cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right)}\]
  7. Final simplification29.4

    \[\leadsto \frac{\cos \left(x \cdot x\right) \cdot \left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \left(\sqrt[3]{\cos \left(x \cdot x\right)} \cdot \sqrt[3]{\cos \left(x \cdot x\right)}\right)\right) - \log \left(1 + \left|\sin x\right|\right) \cdot \log \left(1 + \left|\sin x\right|\right)}{\cos \left(x \cdot x\right) - \log \left(1 + \left|\sin x\right|\right)}\]

Runtime

Time bar (total: 9.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "log(abs(sin(x)) + 1) + cos(x * x)"
  (+ (log (+ (fabs (sin x)) 1)) (cos (* x x))))