Average Error: 0.0 → 0.0
Time: 2.8s
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 r35732107 = x;
        double r35732108 = y;
        double r35732109 = r35732107 + r35732108;
        double r35732110 = r35732108 + r35732108;
        double r35732111 = r35732109 / r35732110;
        return r35732111;
}
↓
double f(double x, double y) {
        double r35732112 = 0.5;
        double r35732113 = x;
        double r35732114 = y;
        double r35732115 = r35732113 / r35732114;
        double r35732116 = r35732115 * r35732112;
        double r35732117 = r35732112 + r35732116;
        return r35732117;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.0

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

  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 2019162 
(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)))