Average Error: 9.8 → 0.1
Time: 7.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{2}{t \cdot z} - 2\right)\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{2}{t \cdot z} - 2\right)\right)
double f(double x, double y, double z, double t) {
        double r1443364 = x;
        double r1443365 = y;
        double r1443366 = r1443364 / r1443365;
        double r1443367 = 2.0;
        double r1443368 = z;
        double r1443369 = r1443368 * r1443367;
        double r1443370 = 1.0;
        double r1443371 = t;
        double r1443372 = r1443370 - r1443371;
        double r1443373 = r1443369 * r1443372;
        double r1443374 = r1443367 + r1443373;
        double r1443375 = r1443371 * r1443368;
        double r1443376 = r1443374 / r1443375;
        double r1443377 = r1443366 + r1443376;
        return r1443377;
}
↓
double f(double x, double y, double z, double t) {
        double r1443378 = x;
        double r1443379 = y;
        double r1443380 = r1443378 / r1443379;
        double r1443381 = 2.0;
        double r1443382 = t;
        double r1443383 = r1443381 / r1443382;
        double r1443384 = z;
        double r1443385 = r1443382 * r1443384;
        double r1443386 = r1443381 / r1443385;
        double r1443387 = r1443386 - r1443381;
        double r1443388 = r1443383 + r1443387;
        double r1443389 = r1443380 + r1443388;
        return r1443389;
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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))))