Average Error: 30.0 → 0.6
Time: 16.3s
Precision: 64
Internal Precision: 1344
\[e^{\sin x} - e^{\sin \left(x + 1\right)}\]
\[\sqrt[3]{\left(e^{\sin x} - e^{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}\right) \cdot \left(\left(e^{\sin x} - e^{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}\right) \cdot \left(e^{\sin x} - e^{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}\right)\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.0

    \[e^{\sin x} - e^{\sin \left(x + 1\right)}\]
  2. Using strategy rm
  3. Applied sin-sum1.0

    \[\leadsto e^{\sin x} - e^{\color{blue}{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}}\]
  4. Using strategy rm
  5. Applied add-cbrt-cube0.6

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(e^{\sin x} - e^{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}\right) \cdot \left(e^{\sin x} - e^{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}\right)\right) \cdot \left(e^{\sin x} - e^{\sin x \cdot \cos 1 + \cos x \cdot \sin 1}\right)}}\]
  6. Final simplification0.6

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

Runtime

Time bar (total: 16.3s)Debug log

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