Average Error: 12.9 → 12.9
Time: 18.2s
Precision: 64
Internal Precision: 576
\[{sin}^{2} \cdot x + {cos}^{2} \cdot x\]
\[\sqrt{cos \cdot cos + sin \cdot sin} \cdot \left(x \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right)\]

Error

Bits error versus sin

Bits error versus x

Bits error versus cos

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.9

    \[{sin}^{2} \cdot x + {cos}^{2} \cdot x\]
  2. Initial simplification12.9

    \[\leadsto x \cdot \left(cos \cdot cos + sin \cdot sin\right)\]
  3. Using strategy rm
  4. Applied add-sqr-sqrt12.9

    \[\leadsto x \cdot \color{blue}{\left(\sqrt{cos \cdot cos + sin \cdot sin} \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right)}\]
  5. Applied associate-*r*12.9

    \[\leadsto \color{blue}{\left(x \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right) \cdot \sqrt{cos \cdot cos + sin \cdot sin}}\]
  6. Final simplification12.9

    \[\leadsto \sqrt{cos \cdot cos + sin \cdot sin} \cdot \left(x \cdot \sqrt{cos \cdot cos + sin \cdot sin}\right)\]

Runtime

Time bar (total: 18.2s)Debug log

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