Average Error: 9.3 → 0.1
Time: 15.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} - 2\right) + \frac{2}{t \cdot z}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} - 2\right) + \frac{2}{t \cdot z}\right)
double f(double x, double y, double z, double t) {
        double r914977 = x;
        double r914978 = y;
        double r914979 = r914977 / r914978;
        double r914980 = 2.0;
        double r914981 = z;
        double r914982 = r914981 * r914980;
        double r914983 = 1.0;
        double r914984 = t;
        double r914985 = r914983 - r914984;
        double r914986 = r914982 * r914985;
        double r914987 = r914980 + r914986;
        double r914988 = r914984 * r914981;
        double r914989 = r914987 / r914988;
        double r914990 = r914979 + r914989;
        return r914990;
}
↓
double f(double x, double y, double z, double t) {
        double r914991 = x;
        double r914992 = y;
        double r914993 = r914991 / r914992;
        double r914994 = 2.0;
        double r914995 = t;
        double r914996 = r914994 / r914995;
        double r914997 = r914996 - r914994;
        double r914998 = z;
        double r914999 = r914995 * r914998;
        double r915000 = r914994 / r914999;
        double r915001 = r914997 + r915000;
        double r915002 = r914993 + r915001;
        return r915002;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) - 2\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(\frac{2}{t} - 2\right) + \frac{2}{t \cdot z}\right)}\]

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y)))

  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))