Average Error: 30.8 → 29.6
Time: 20.0s
Precision: 64
Internal Precision: 2368
\[\sin \left(x \cdot x\right) - \sin \left(x \cdot x + 1\right)\]
\[\sin \left(x \cdot x\right) - \left(\cos \left(x \cdot x\right) \cdot \sin 1 + \sqrt[3]{\cos 1 \cdot \sin \left(x \cdot x\right)} \cdot \left(\sqrt[3]{\cos 1 \cdot \sin \left(x \cdot x\right)} \cdot \sqrt[3]{\cos 1 \cdot \sin \left(x \cdot x\right)}\right)\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.8

    \[\sin \left(x \cdot x\right) - \sin \left(x \cdot x + 1\right)\]
  2. Initial simplification30.8

    \[\leadsto \sin \left(x \cdot x\right) - \sin \left(x \cdot x + 1\right)\]
  3. Using strategy rm
  4. Applied sin-sum29.6

    \[\leadsto \sin \left(x \cdot x\right) - \color{blue}{\left(\sin \left(x \cdot x\right) \cdot \cos 1 + \cos \left(x \cdot x\right) \cdot \sin 1\right)}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt29.6

    \[\leadsto \sin \left(x \cdot x\right) - \left(\color{blue}{\left(\sqrt[3]{\sin \left(x \cdot x\right) \cdot \cos 1} \cdot \sqrt[3]{\sin \left(x \cdot x\right) \cdot \cos 1}\right) \cdot \sqrt[3]{\sin \left(x \cdot x\right) \cdot \cos 1}} + \cos \left(x \cdot x\right) \cdot \sin 1\right)\]
  7. Final simplification29.6

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

Runtime

Time bar (total: 20.0s)Debug log

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