Average Error: 0.1 → 0.1
Time: 19.4s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[x + \frac{x - y}{2}\]
x + \frac{x - y}{2}
↓
x + \frac{x - y}{2}
double f(double x, double y) {
        double r491940 = x;
        double r491941 = y;
        double r491942 = r491940 - r491941;
        double r491943 = 2.0;
        double r491944 = r491942 / r491943;
        double r491945 = r491940 + r491944;
        return r491945;
}
↓
double f(double x, double y) {
        double r491946 = x;
        double r491947 = y;
        double r491948 = r491946 - r491947;
        double r491949 = 2.0;
        double r491950 = r491948 / r491949;
        double r491951 = r491946 + r491950;
        return r491951;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[1.5 \cdot x - 0.5 \cdot y\]

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2}\]

  2. Final simplification0.1

    \[\leadsto x + \frac{x - y}{2}\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

  (+ x (/ (- x y) 2)))