Average Error: 9.2 → 0.1
Time: 12.5s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{t} - 2.0\right) + \frac{\frac{2.0}{z}}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2.0}{t} - 2.0\right) + \frac{\frac{2.0}{z}}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r42905271 = x;
        double r42905272 = y;
        double r42905273 = r42905271 / r42905272;
        double r42905274 = 2.0;
        double r42905275 = z;
        double r42905276 = r42905275 * r42905274;
        double r42905277 = 1.0;
        double r42905278 = t;
        double r42905279 = r42905277 - r42905278;
        double r42905280 = r42905276 * r42905279;
        double r42905281 = r42905274 + r42905280;
        double r42905282 = r42905278 * r42905275;
        double r42905283 = r42905281 / r42905282;
        double r42905284 = r42905273 + r42905283;
        return r42905284;
}
↓
double f(double x, double y, double z, double t) {
        double r42905285 = 2.0;
        double r42905286 = t;
        double r42905287 = r42905285 / r42905286;
        double r42905288 = r42905287 - r42905285;
        double r42905289 = z;
        double r42905290 = r42905285 / r42905289;
        double r42905291 = r42905290 / r42905286;
        double r42905292 = r42905288 + r42905291;
        double r42905293 = x;
        double r42905294 = y;
        double r42905295 = r42905293 / r42905294;
        double r42905296 = r42905292 + r42905295;
        return r42905296;
}

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
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.2

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2.0 \cdot \frac{1}{t} + 2.0 \cdot \frac{1}{t \cdot z}\right) - 2.0\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2.0}{z \cdot t} + \left(\frac{2.0}{t} - 2.0\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-/r*0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{\frac{2.0}{z}}{t}} + \left(\frac{2.0}{t} - 2.0\right)\right)\]

  6. Final simplification0.1

    \[\leadsto \left(\left(\frac{2.0}{t} - 2.0\right) + \frac{\frac{2.0}{z}}{t}\right) + \frac{x}{y}\]

Reproduce

herbie shell --seed 2019168 
(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))))