Average Error: 9.2 → 0.1
Time: 13.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{x}{y} + \left(\frac{2}{t \cdot z} + \frac{2}{t}\right)\right) - 2\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{x}{y} + \left(\frac{2}{t \cdot z} + \frac{2}{t}\right)\right) - 2
double f(double x, double y, double z, double t) {
        double r429508 = x;
        double r429509 = y;
        double r429510 = r429508 / r429509;
        double r429511 = 2.0;
        double r429512 = z;
        double r429513 = r429512 * r429511;
        double r429514 = 1.0;
        double r429515 = t;
        double r429516 = r429514 - r429515;
        double r429517 = r429513 * r429516;
        double r429518 = r429511 + r429517;
        double r429519 = r429515 * r429512;
        double r429520 = r429518 / r429519;
        double r429521 = r429510 + r429520;
        return r429521;
}
↓
double f(double x, double y, double z, double t) {
        double r429522 = x;
        double r429523 = y;
        double r429524 = r429522 / r429523;
        double r429525 = 2.0;
        double r429526 = t;
        double r429527 = z;
        double r429528 = r429526 * r429527;
        double r429529 = r429525 / r429528;
        double r429530 = r429525 / r429526;
        double r429531 = r429529 + r429530;
        double r429532 = r429524 + r429531;
        double r429533 = r429532 - r429525;
        return r429533;
}

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

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

Derivation

  1. Initial program 9.2

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

  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

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

  5. Applied associate-+r-0.1

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

  6. Applied associate-+r-0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +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))))