Average Error: 14.8 → 0.4
Time: 11.7s
Precision: 64
Internal Precision: 1344
\[\sin \left(y - x\right) - \cos \left(x - y\right)\]
\[\cos x \cdot \sin y - \left(\left(\sin x \cdot \sin y + \cos y \cdot \cos x\right) + \sin x \cdot \cos y\right)\]

Error

Bits error versus y

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\sin \left(y - x\right) - \cos \left(x - y\right)\]
  2. Initial simplification14.8

    \[\leadsto \sin \left(y - x\right) - \cos \left(x - y\right)\]
  3. Using strategy rm
  4. Applied cos-diff14.3

    \[\leadsto \sin \left(y - x\right) - \color{blue}{\left(\cos x \cdot \cos y + \sin x \cdot \sin y\right)}\]
  5. Using strategy rm
  6. Applied sin-diff0.4

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

    \[\leadsto \color{blue}{\sin y \cdot \cos x - \left(\cos y \cdot \sin x + \left(\cos x \cdot \cos y + \sin x \cdot \sin y\right)\right)}\]
  8. Final simplification0.4

    \[\leadsto \cos x \cdot \sin y - \left(\left(\sin x \cdot \sin y + \cos y \cdot \cos x\right) + \sin x \cdot \cos y\right)\]

Runtime

Time bar (total: 11.7s)Debug log

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