Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
Internal Precision: 320
\[\sqrt{\left(1 + x\right) \cdot \left(1 - x\right)}\]
\[\sqrt{1 - {x}^{2}}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[\sqrt{\left(1 + x\right) \cdot \left(1 - x\right)}\]
  2. Initial simplification0.0

    \[\leadsto \sqrt{\left(x + 1\right) \cdot \left(1 - x\right)}\]
  3. Taylor expanded around -inf 0.0

    \[\leadsto \sqrt{\color{blue}{1 - {x}^{2}}}\]
  4. Final simplification0.0

    \[\leadsto \sqrt{1 - {x}^{2}}\]

Runtime

Time bar (total: 12.8s)Debug log

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