Average Error: 9.1 → 0.1
Time: 14.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{2}{t \cdot z}\right) - 2\right)\]
\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} + \frac{2}{t \cdot z}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r608250 = x;
        double r608251 = y;
        double r608252 = r608250 / r608251;
        double r608253 = 2.0;
        double r608254 = z;
        double r608255 = r608254 * r608253;
        double r608256 = 1.0;
        double r608257 = t;
        double r608258 = r608256 - r608257;
        double r608259 = r608255 * r608258;
        double r608260 = r608253 + r608259;
        double r608261 = r608257 * r608254;
        double r608262 = r608260 / r608261;
        double r608263 = r608252 + r608262;
        return r608263;
}
↓
double f(double x, double y, double z, double t) {
        double r608264 = x;
        double r608265 = y;
        double r608266 = r608264 / r608265;
        double r608267 = 2.0;
        double r608268 = t;
        double r608269 = r608267 / r608268;
        double r608270 = z;
        double r608271 = r608268 * r608270;
        double r608272 = r608267 / r608271;
        double r608273 = r608269 + r608272;
        double r608274 = r608273 - r608267;
        double r608275 = r608266 + r608274;
        return r608275;
}

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

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

Derivation

  1. Initial program 9.1

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(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))))