Average Error: 9.3 → 0.1
Time: 16.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)\]
\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{\frac{2}{t}}{z}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r125325268 = x;
        double r125325269 = y;
        double r125325270 = r125325268 / r125325269;
        double r125325271 = 2.0;
        double r125325272 = z;
        double r125325273 = r125325272 * r125325271;
        double r125325274 = 1.0;
        double r125325275 = t;
        double r125325276 = r125325274 - r125325275;
        double r125325277 = r125325273 * r125325276;
        double r125325278 = r125325271 + r125325277;
        double r125325279 = r125325275 * r125325272;
        double r125325280 = r125325278 / r125325279;
        double r125325281 = r125325270 + r125325280;
        return r125325281;
}
↓
double f(double x, double y, double z, double t) {
        double r125325282 = x;
        double r125325283 = y;
        double r125325284 = r125325282 / r125325283;
        double r125325285 = 2.0;
        double r125325286 = t;
        double r125325287 = r125325285 / r125325286;
        double r125325288 = z;
        double r125325289 = r125325287 / r125325288;
        double r125325290 = r125325287 + r125325289;
        double r125325291 = r125325290 - r125325285;
        double r125325292 = r125325284 + r125325291;
        return r125325292;
}

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

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

  3. Simplified0.1

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))