Average Error: 9.2 → 0.1
Time: 38.9s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0
double f(double x, double y, double z, double t) {
        double r37535887 = x;
        double r37535888 = y;
        double r37535889 = r37535887 / r37535888;
        double r37535890 = 2.0;
        double r37535891 = z;
        double r37535892 = r37535891 * r37535890;
        double r37535893 = 1.0;
        double r37535894 = t;
        double r37535895 = r37535893 - r37535894;
        double r37535896 = r37535892 * r37535895;
        double r37535897 = r37535890 + r37535896;
        double r37535898 = r37535894 * r37535891;
        double r37535899 = r37535897 / r37535898;
        double r37535900 = r37535889 + r37535899;
        return r37535900;
}
↓
double f(double x, double y, double z, double t) {
        double r37535901 = 2.0;
        double r37535902 = t;
        double r37535903 = r37535901 / r37535902;
        double r37535904 = z;
        double r37535905 = r37535903 / r37535904;
        double r37535906 = r37535903 + r37535905;
        double r37535907 = x;
        double r37535908 = y;
        double r37535909 = r37535907 / r37535908;
        double r37535910 = r37535906 + r37535909;
        double r37535911 = r37535910 - r37535901;
        return r37535911;
}

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
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.2

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2.0}{t}, \frac{\mathsf{fma}\left(z, 1.0, 1\right)}{z}, \frac{x}{y}\right) - 2.0}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(\frac{x}{y} + \left(2.0 \cdot \frac{1}{t} + 2.0 \cdot \frac{1}{t \cdot z}\right)\right)} - 2.0\]

  4. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right)} - 2.0\]

  5. Final simplification0.1

    \[\leadsto \left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))))