Average Error: 14.3 → 13.8
Time: 43.8s
Precision: 64
Internal Precision: 576
\[2.0 \cdot \frac{f}{x + \sqrt{\left(x \cdot x\right) \cdot \left(1.0 \cdot f - y\right) + y}}\]
\[\frac{2.0 \cdot f}{x + \sqrt{y + x \cdot \left(\left(1.0 \cdot f - y\right) \cdot x\right)}}\]

Error

Bits error versus f

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

    \[2.0 \cdot \frac{f}{x + \sqrt{\left(x \cdot x\right) \cdot \left(1.0 \cdot f - y\right) + y}}\]
  2. Initial simplification14.3

    \[\leadsto \frac{2.0 \cdot f}{x + \sqrt{y + \left(f \cdot 1.0 - y\right) \cdot \left(x \cdot x\right)}}\]
  3. Using strategy rm
  4. Applied associate-*r*13.8

    \[\leadsto \frac{2.0 \cdot f}{x + \sqrt{y + \color{blue}{\left(\left(f \cdot 1.0 - y\right) \cdot x\right) \cdot x}}}\]
  5. Final simplification13.8

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

Runtime

Time bar (total: 43.8s)Debug log

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