Average Error: 29.5 → 0.3
Time: 15.3s
Precision: 64
Internal Precision: 1344
\[\sin \left(x + 1\right) - \sin x\]
\[\cos x \cdot \sin 1 + \left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \left(\sin x \cdot \sqrt[3]{\cos 1}\right) - \sin x\right)\]

Error

Bits error versus x

Try it out

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. Initial simplification29.5

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

    \[\leadsto \color{blue}{\left(\sin 1 \cdot \cos x + \cos 1 \cdot \sin x\right)} - \sin x\]
  5. Applied associate--l+0.4

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

    \[\leadsto \sin 1 \cdot \cos x + \left(\color{blue}{\left(\left(\sqrt[3]{\cos 1} \cdot \sqrt[3]{\cos 1}\right) \cdot \sqrt[3]{\cos 1}\right)} \cdot \sin x - \sin x\right)\]
  8. Applied associate-*l*0.3

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

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

Runtime

Time bar (total: 15.3s)Debug log

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