Average Error: 9.5 → 0.1
Time: 10.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) - 2\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) - 2
double f(double x, double y, double z, double t) {
        double r489502 = x;
        double r489503 = y;
        double r489504 = r489502 / r489503;
        double r489505 = 2.0;
        double r489506 = z;
        double r489507 = r489506 * r489505;
        double r489508 = 1.0;
        double r489509 = t;
        double r489510 = r489508 - r489509;
        double r489511 = r489507 * r489510;
        double r489512 = r489505 + r489511;
        double r489513 = r489509 * r489506;
        double r489514 = r489512 / r489513;
        double r489515 = r489504 + r489514;
        return r489515;
}
↓
double f(double x, double y, double z, double t) {
        double r489516 = 2.0;
        double r489517 = z;
        double r489518 = r489516 / r489517;
        double r489519 = r489518 + r489516;
        double r489520 = t;
        double r489521 = r489519 / r489520;
        double r489522 = x;
        double r489523 = y;
        double r489524 = r489522 / r489523;
        double r489525 = r489521 + r489524;
        double r489526 = r489525 - r489516;
        return r489526;
}

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

Original9.5
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.5

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

  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. Using strategy rm

  5. Applied sub-neg0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(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))))