Average Error: 9.8 → 0.1
Time: 16.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{z}}{t}\right) + \frac{x}{y}\]
\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}{z}}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r41941879 = x;
        double r41941880 = y;
        double r41941881 = r41941879 / r41941880;
        double r41941882 = 2.0;
        double r41941883 = z;
        double r41941884 = r41941883 * r41941882;
        double r41941885 = 1.0;
        double r41941886 = t;
        double r41941887 = r41941885 - r41941886;
        double r41941888 = r41941884 * r41941887;
        double r41941889 = r41941882 + r41941888;
        double r41941890 = r41941886 * r41941883;
        double r41941891 = r41941889 / r41941890;
        double r41941892 = r41941881 + r41941891;
        return r41941892;
}
↓
double f(double x, double y, double z, double t) {
        double r41941893 = 2.0;
        double r41941894 = t;
        double r41941895 = r41941893 / r41941894;
        double r41941896 = r41941895 - r41941893;
        double r41941897 = z;
        double r41941898 = r41941893 / r41941897;
        double r41941899 = r41941898 / r41941894;
        double r41941900 = r41941896 + r41941899;
        double r41941901 = x;
        double r41941902 = y;
        double r41941903 = r41941901 / r41941902;
        double r41941904 = r41941900 + r41941903;
        return r41941904;
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(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))))