Average Error: 9.7 → 0.1
Time: 3.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r1022362 = x;
        double r1022363 = y;
        double r1022364 = r1022362 / r1022363;
        double r1022365 = 2.0;
        double r1022366 = z;
        double r1022367 = r1022366 * r1022365;
        double r1022368 = 1.0;
        double r1022369 = t;
        double r1022370 = r1022368 - r1022369;
        double r1022371 = r1022367 * r1022370;
        double r1022372 = r1022365 + r1022371;
        double r1022373 = r1022369 * r1022366;
        double r1022374 = r1022372 / r1022373;
        double r1022375 = r1022364 + r1022374;
        return r1022375;
}
↓
double f(double x, double y, double z, double t) {
        double r1022376 = x;
        double r1022377 = y;
        double r1022378 = r1022376 / r1022377;
        double r1022379 = 1.0;
        double r1022380 = t;
        double r1022381 = r1022379 / r1022380;
        double r1022382 = 2.0;
        double r1022383 = z;
        double r1022384 = r1022382 / r1022383;
        double r1022385 = r1022384 + r1022382;
        double r1022386 = r1022381 * r1022385;
        double r1022387 = r1022386 - r1022382;
        double r1022388 = r1022378 + r1022387;
        return r1022388;
}

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

Original9.7
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.7

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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))))