Average Error: 0.3 → 0.3
Time: 19.4s
Precision: 64
Internal Precision: 576
\[\sin x - {\left(\cos x\right)}^{2}\]
\[\sin x - \sqrt[3]{{\left(\cos x \cdot \cos x\right)}^{3}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\sin x - {\left(\cos x\right)}^{2}\]
  2. Using strategy rm
  3. Applied add-cbrt-cube0.3

    \[\leadsto \sin x - \color{blue}{\sqrt[3]{\left({\left(\cos x\right)}^{2} \cdot {\left(\cos x\right)}^{2}\right) \cdot {\left(\cos x\right)}^{2}}}\]
  4. Applied simplify0.3

    \[\leadsto \sin x - \sqrt[3]{\color{blue}{{\left(\cos x \cdot \cos x\right)}^{3}}}\]

Runtime

Time bar (total: 19.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sin(x) - cos(x)^2"
  (- (sin x) (pow (cos x) 2)))