Average Error: 9.1 → 9.1
Time: 46.8s
Precision: 64
Internal Precision: 576
\[\left(ax \cdot ax + ay \cdot ay\right) \cdot \left(by - cy\right)\]
\[\sqrt{ax \cdot ax + ay \cdot ay} \cdot \left(\sqrt{ax \cdot ax + ay \cdot ay} \cdot \left(by - cy\right)\right)\]

Error

Bits error versus ax

Bits error versus ay

Bits error versus by

Bits error versus cy

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 9.1

    \[\left(ax \cdot ax + ay \cdot ay\right) \cdot \left(by - cy\right)\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt9.1

    \[\leadsto \color{blue}{\left(\sqrt{ax \cdot ax + ay \cdot ay} \cdot \sqrt{ax \cdot ax + ay \cdot ay}\right)} \cdot \left(by - cy\right)\]
  4. Applied associate-*l*9.1

    \[\leadsto \color{blue}{\sqrt{ax \cdot ax + ay \cdot ay} \cdot \left(\sqrt{ax \cdot ax + ay \cdot ay} \cdot \left(by - cy\right)\right)}\]
  5. Final simplification9.1

    \[\leadsto \sqrt{ax \cdot ax + ay \cdot ay} \cdot \left(\sqrt{ax \cdot ax + ay \cdot ay} \cdot \left(by - cy\right)\right)\]

Runtime

Time bar (total: 46.8s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (ax ay by cy)
  :name "(ax*ax + ay*ay)*(by - cy)"
  (* (+ (* ax ax) (* ay ay)) (- by cy)))