Average Error: 9.2 → 0.1
Time: 39.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{t}}{z}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{t}}{z}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r40067485 = x;
        double r40067486 = y;
        double r40067487 = r40067485 / r40067486;
        double r40067488 = 2.0;
        double r40067489 = z;
        double r40067490 = r40067489 * r40067488;
        double r40067491 = 1.0;
        double r40067492 = t;
        double r40067493 = r40067491 - r40067492;
        double r40067494 = r40067490 * r40067493;
        double r40067495 = r40067488 + r40067494;
        double r40067496 = r40067492 * r40067489;
        double r40067497 = r40067495 / r40067496;
        double r40067498 = r40067487 + r40067497;
        return r40067498;
}
↓
double f(double x, double y, double z, double t) {
        double r40067499 = 2.0;
        double r40067500 = t;
        double r40067501 = r40067499 / r40067500;
        double r40067502 = r40067501 - r40067499;
        double r40067503 = z;
        double r40067504 = r40067501 / r40067503;
        double r40067505 = r40067502 + r40067504;
        double r40067506 = x;
        double r40067507 = y;
        double r40067508 = r40067506 / r40067507;
        double r40067509 = r40067505 + r40067508;
        return r40067509;
}

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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))