Average Error: 0.1 → 0.0
Time: 4.4s
Precision: 64
\[\frac{x + y}{y + y}\]
↓
\[\frac{1}{2} + \frac{x}{y} \cdot \frac{1}{2}\]
\frac{x + y}{y + y}
↓
\frac{1}{2} + \frac{x}{y} \cdot \frac{1}{2}
double f(double x, double y) {
        double r38083076 = x;
        double r38083077 = y;
        double r38083078 = r38083076 + r38083077;
        double r38083079 = r38083077 + r38083077;
        double r38083080 = r38083078 / r38083079;
        return r38083080;
}
↓
double f(double x, double y) {
        double r38083081 = 0.5;
        double r38083082 = x;
        double r38083083 = y;
        double r38083084 = r38083082 / r38083083;
        double r38083085 = r38083084 * r38083081;
        double r38083086 = r38083081 + r38083085;
        return r38083086;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}\]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}}\]

  3. Final simplification0.0

    \[\leadsto \frac{1}{2} + \frac{x}{y} \cdot \frac{1}{2}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"

  :herbie-target
  (+ (* 1/2 (/ x y)) 1/2)

  (/ (+ x y) (+ y y)))