Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[\sqrt{x + y}\]
↓
\[\sqrt{y + x}\]
\sqrt{x + y}
↓
\sqrt{y + x}
double f(double x, double y) {
        double r3207141 = x;
        double r3207142 = y;
        double r3207143 = r3207141 + r3207142;
        double r3207144 = sqrt(r3207143);
        return r3207144;
}
↓
double f(double x, double y) {
        double r3207145 = y;
        double r3207146 = x;
        double r3207147 = r3207145 + r3207146;
        double r3207148 = sqrt(r3207147);
        return r3207148;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[\sqrt{x + y}\]

  2. Final simplification0.0

    \[\leadsto \sqrt{y + x}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A"
  (sqrt (+ x y)))