Average Error: 9.6 → 0.1
Time: 17.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r1250501 = x;
        double r1250502 = y;
        double r1250503 = r1250501 / r1250502;
        double r1250504 = 2.0;
        double r1250505 = z;
        double r1250506 = r1250505 * r1250504;
        double r1250507 = 1.0;
        double r1250508 = t;
        double r1250509 = r1250507 - r1250508;
        double r1250510 = r1250506 * r1250509;
        double r1250511 = r1250504 + r1250510;
        double r1250512 = r1250508 * r1250505;
        double r1250513 = r1250511 / r1250512;
        double r1250514 = r1250503 + r1250513;
        return r1250514;
}
↓
double f(double x, double y, double z, double t) {
        double r1250515 = 2.0;
        double r1250516 = t;
        double r1250517 = r1250515 / r1250516;
        double r1250518 = z;
        double r1250519 = r1250517 / r1250518;
        double r1250520 = r1250517 - r1250515;
        double r1250521 = r1250519 + r1250520;
        double r1250522 = x;
        double r1250523 = y;
        double r1250524 = r1250522 / r1250523;
        double r1250525 = r1250521 + r1250524;
        return r1250525;
}

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

Original9.6
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.6

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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))))