Average Error: 29.5 → 0.4
Time: 29.7s
Precision: 64
Internal Precision: 1344
\[\sin \left(x + 1\right) - \sin x\]
\[\left(\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1} + \cos x \cdot \sin 1\right) - \sin x\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.5

    \[\sin \left(x + 1\right) - \sin x\]
  2. Using strategy rm
  3. Applied sin-sum0.4

    \[\leadsto \color{blue}{\left(\sin x \cdot \cos 1 + \cos x \cdot \sin 1\right)} - \sin x\]
  4. Using strategy rm
  5. Applied add-cube-cbrt0.4

    \[\leadsto \left(\sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} + \cos x \cdot \sin 1\right) - \sin x\]
  6. Applied associate-*r*0.4

    \[\leadsto \left(\color{blue}{\left(\sin x \cdot \left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right)\right) \cdot \sqrt[3]{\cos 1}} + \cos x \cdot \sin 1\right) - \sin x\]

Runtime

Time bar (total: 29.7s)Debug log

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