Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

Average Error: 0.1 → 0.1

Time: 3.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y) {
        double r130134 = x;
        double r130135 = y;
        double r130136 = r130134 + r130135;
        double r130137 = r130135 + r130135;
        double r130138 = r130136 / r130137;
        return r130138;
}

↓

double f(double x, double y) {
        double r130139 = x;
        double r130140 = y;
        double r130141 = r130139 + r130140;
        double r130142 = r130140 + r130140;
        double r130143 = r130141 / r130142;
        return r130143;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.1
Target	0.0
Herbie	0.1

\[0.5 \cdot \frac{x}{y} + 0.5\]

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

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