Average Error: 26.5 → 26.5
Time: 20.6s
Precision: 64
Internal Precision: 1344
\[\frac{2.0}{x + \sqrt{\left(x \cdot x\right) \cdot \left(1.0 - y\right) + y}}\]
\[\frac{2.0}{x + \sqrt{y + \left(x \cdot x\right) \cdot \left(1.0 - y\right)}}\]

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 26.5

    \[\frac{2.0}{x + \sqrt{\left(x \cdot x\right) \cdot \left(1.0 - y\right) + y}}\]
  2. Final simplification26.5

    \[\leadsto \frac{2.0}{x + \sqrt{y + \left(x \cdot x\right) \cdot \left(1.0 - y\right)}}\]

Runtime

Time bar (total: 20.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name " 2.0 / (x + sqrt(x*x * (1.0 - y) + y))"
  (/ 2.0 (+ x (sqrt (+ (* (* x x) (- 1.0 y)) y)))))