Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[0.5 \cdot \left(x \cdot x - y\right)\]
↓
\[\left(x \cdot x - y\right) \cdot 0.5\]
0.5 \cdot \left(x \cdot x - y\right)
↓
\left(x \cdot x - y\right) \cdot 0.5
double f(double x, double y) {
        double r11047 = 0.5;
        double r11048 = x;
        double r11049 = r11048 * r11048;
        double r11050 = y;
        double r11051 = r11049 - r11050;
        double r11052 = r11047 * r11051;
        return r11052;
}
↓
double f(double x, double y) {
        double r11053 = x;
        double r11054 = r11053 * r11053;
        double r11055 = y;
        double r11056 = r11054 - r11055;
        double r11057 = 0.5;
        double r11058 = r11056 * r11057;
        return r11058;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[0.5 \cdot \left(x \cdot x - y\right)\]

  2. Final simplification0.0

    \[\leadsto \left(x \cdot x - y\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  (* 0.5 (- (* x x) y)))