Average Error: 9.3 → 0.1
Time: 14.5s
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 r1076314 = x;
        double r1076315 = y;
        double r1076316 = r1076314 / r1076315;
        double r1076317 = 2.0;
        double r1076318 = z;
        double r1076319 = r1076318 * r1076317;
        double r1076320 = 1.0;
        double r1076321 = t;
        double r1076322 = r1076320 - r1076321;
        double r1076323 = r1076319 * r1076322;
        double r1076324 = r1076317 + r1076323;
        double r1076325 = r1076321 * r1076318;
        double r1076326 = r1076324 / r1076325;
        double r1076327 = r1076316 + r1076326;
        return r1076327;
}
↓
double f(double x, double y, double z, double t) {
        double r1076328 = x;
        double r1076329 = y;
        double r1076330 = r1076328 / r1076329;
        double r1076331 = 2.0;
        double r1076332 = t;
        double r1076333 = r1076331 / r1076332;
        double r1076334 = r1076333 - r1076331;
        double r1076335 = z;
        double r1076336 = r1076332 * r1076335;
        double r1076337 = r1076331 / r1076336;
        double r1076338 = r1076334 + r1076337;
        double r1076339 = r1076330 + r1076338;
        return r1076339;
}

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))))