Average Error: 0 → 0
Time: 2.6s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y\right)\]
↓
\[\left(y + x\right) \cdot \frac{1}{2}\]
\frac{1}{2} \cdot \left(x + y\right)
↓
\left(y + x\right) \cdot \frac{1}{2}
double f(double x, double y) {
        double r17902774 = 1.0;
        double r17902775 = 2.0;
        double r17902776 = r17902774 / r17902775;
        double r17902777 = x;
        double r17902778 = y;
        double r17902779 = r17902777 + r17902778;
        double r17902780 = r17902776 * r17902779;
        return r17902780;
}
↓
double f(double x, double y) {
        double r17902781 = y;
        double r17902782 = x;
        double r17902783 = r17902781 + r17902782;
        double r17902784 = 1.0;
        double r17902785 = 2.0;
        double r17902786 = r17902784 / r17902785;
        double r17902787 = r17902783 * r17902786;
        return r17902787;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0
Target0
Herbie0
\[\frac{x + y}{2}\]

Derivation

  1. Initial program 0

    \[\frac{1}{2} \cdot \left(x + y\right)\]

  2. Final simplification0

    \[\leadsto \left(y + x\right) \cdot \frac{1}{2}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, G"

  :herbie-target
  (/ (+ x y) 2.0)

  (* (/ 1.0 2.0) (+ x y)))