Average Error: 9.4 → 0.1
Time: 9.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{x}{y} + \frac{2}{t}\right) - \left(2 - \frac{2}{t \cdot z}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{x}{y} + \frac{2}{t}\right) - \left(2 - \frac{2}{t \cdot z}\right)
double f(double x, double y, double z, double t) {
        double r867445 = x;
        double r867446 = y;
        double r867447 = r867445 / r867446;
        double r867448 = 2.0;
        double r867449 = z;
        double r867450 = r867449 * r867448;
        double r867451 = 1.0;
        double r867452 = t;
        double r867453 = r867451 - r867452;
        double r867454 = r867450 * r867453;
        double r867455 = r867448 + r867454;
        double r867456 = r867452 * r867449;
        double r867457 = r867455 / r867456;
        double r867458 = r867447 + r867457;
        return r867458;
}
↓
double f(double x, double y, double z, double t) {
        double r867459 = x;
        double r867460 = y;
        double r867461 = r867459 / r867460;
        double r867462 = 2.0;
        double r867463 = t;
        double r867464 = r867462 / r867463;
        double r867465 = r867461 + r867464;
        double r867466 = z;
        double r867467 = r867463 * r867466;
        double r867468 = r867462 / r867467;
        double r867469 = r867462 - r867468;
        double r867470 = r867465 - r867469;
        return r867470;
}

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

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

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

  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

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

  5. Applied associate-+l-0.1

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

  6. Applied associate-+r-0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))))