Average Error: 9.3 → 0.1
Time: 3.2s
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 r794338 = x;
        double r794339 = y;
        double r794340 = r794338 / r794339;
        double r794341 = 2.0;
        double r794342 = z;
        double r794343 = r794342 * r794341;
        double r794344 = 1.0;
        double r794345 = t;
        double r794346 = r794344 - r794345;
        double r794347 = r794343 * r794346;
        double r794348 = r794341 + r794347;
        double r794349 = r794345 * r794342;
        double r794350 = r794348 / r794349;
        double r794351 = r794340 + r794350;
        return r794351;
}
↓
double f(double x, double y, double z, double t) {
        double r794352 = x;
        double r794353 = y;
        double r794354 = r794352 / r794353;
        double r794355 = 1.0;
        double r794356 = t;
        double r794357 = r794355 / r794356;
        double r794358 = 2.0;
        double r794359 = z;
        double r794360 = r794358 / r794359;
        double r794361 = r794360 + r794358;
        double r794362 = r794357 * r794361;
        double r794363 = r794362 - r794358;
        double r794364 = r794354 + r794363;
        return r794364;
}

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

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

  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 2020062 
(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))))