Average Error: 45.1 → 42.9
Time: 7.5s
Precision: 64
Internal Precision: 2368
\[\cos \left(\left(x + y\right) \cdot \left(x - y\right)\right)\]
\[1\]

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 45.1

    \[\cos \left(\left(x + y\right) \cdot \left(x - y\right)\right)\]
  2. Taylor expanded around 0 42.9

    \[\leadsto \color{blue}{1}\]
  3. Final simplification42.9

    \[\leadsto 1\]

Runtime

Time bar (total: 7.5s)Debug log

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