Average Error: 9.1 → 0.1
Time: 12.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2}{z}}{t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{\frac{2}{z}}{t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r1232241 = x;
        double r1232242 = y;
        double r1232243 = r1232241 / r1232242;
        double r1232244 = 2.0;
        double r1232245 = z;
        double r1232246 = r1232245 * r1232244;
        double r1232247 = 1.0;
        double r1232248 = t;
        double r1232249 = r1232247 - r1232248;
        double r1232250 = r1232246 * r1232249;
        double r1232251 = r1232244 + r1232250;
        double r1232252 = r1232248 * r1232245;
        double r1232253 = r1232251 / r1232252;
        double r1232254 = r1232243 + r1232253;
        return r1232254;
}
↓
double f(double x, double y, double z, double t) {
        double r1232255 = 2.0;
        double r1232256 = z;
        double r1232257 = r1232255 / r1232256;
        double r1232258 = t;
        double r1232259 = r1232257 / r1232258;
        double r1232260 = r1232259 - r1232255;
        double r1232261 = r1232255 / r1232258;
        double r1232262 = r1232260 + r1232261;
        double r1232263 = x;
        double r1232264 = y;
        double r1232265 = r1232263 / r1232264;
        double r1232266 = r1232262 + r1232265;
        return r1232266;
}

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

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

  3. Simplified0.1

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

  4. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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))))