Average Error: 9.2 → 0.1
Time: 27.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) + \left(\frac{x}{y} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) + \left(\frac{x}{y} - 2\right)
double f(double x, double y, double z, double t) {
        double r499281 = x;
        double r499282 = y;
        double r499283 = r499281 / r499282;
        double r499284 = 2.0;
        double r499285 = z;
        double r499286 = r499285 * r499284;
        double r499287 = 1.0;
        double r499288 = t;
        double r499289 = r499287 - r499288;
        double r499290 = r499286 * r499289;
        double r499291 = r499284 + r499290;
        double r499292 = r499288 * r499285;
        double r499293 = r499291 / r499292;
        double r499294 = r499283 + r499293;
        return r499294;
}
↓
double f(double x, double y, double z, double t) {
        double r499295 = 2.0;
        double r499296 = t;
        double r499297 = z;
        double r499298 = r499296 * r499297;
        double r499299 = r499295 / r499298;
        double r499300 = r499295 / r499296;
        double r499301 = r499299 + r499300;
        double r499302 = x;
        double r499303 = y;
        double r499304 = r499302 / r499303;
        double r499305 = r499304 - r499295;
        double r499306 = r499301 + r499305;
        return r499306;
}

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

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

Derivation

  1. Initial program 9.2

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 +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))))