Average Error: 9.6 → 0.1
Time: 18.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{\frac{2}{t}}{z} - 2\right)\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{\frac{2}{t}}{z} - 2\right)\right)
double f(double x, double y, double z, double t) {
        double r584917 = x;
        double r584918 = y;
        double r584919 = r584917 / r584918;
        double r584920 = 2.0;
        double r584921 = z;
        double r584922 = r584921 * r584920;
        double r584923 = 1.0;
        double r584924 = t;
        double r584925 = r584923 - r584924;
        double r584926 = r584922 * r584925;
        double r584927 = r584920 + r584926;
        double r584928 = r584924 * r584921;
        double r584929 = r584927 / r584928;
        double r584930 = r584919 + r584929;
        return r584930;
}
↓
double f(double x, double y, double z, double t) {
        double r584931 = x;
        double r584932 = y;
        double r584933 = r584931 / r584932;
        double r584934 = 2.0;
        double r584935 = t;
        double r584936 = r584934 / r584935;
        double r584937 = z;
        double r584938 = r584936 / r584937;
        double r584939 = r584938 - r584934;
        double r584940 = r584936 + r584939;
        double r584941 = r584933 + r584940;
        return r584941;
}

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. 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

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 +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))))