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

# Try it out

Results

 In Out
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

$\leadsto \color{blue}{\left(\sqrt{ax \cdot ax + ay \cdot ay} \cdot \sqrt{ax \cdot ax + ay \cdot ay}\right)} \cdot \left(by - cy\right)$
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)))