Average Error: 9.0 → 0.1
Time: 24.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)
double f(double x, double y, double z, double t) {
        double r514911 = x;
        double r514912 = y;
        double r514913 = r514911 / r514912;
        double r514914 = 2.0;
        double r514915 = z;
        double r514916 = r514915 * r514914;
        double r514917 = 1.0;
        double r514918 = t;
        double r514919 = r514917 - r514918;
        double r514920 = r514916 * r514919;
        double r514921 = r514914 + r514920;
        double r514922 = r514918 * r514915;
        double r514923 = r514921 / r514922;
        double r514924 = r514913 + r514923;
        return r514924;
}
↓
double f(double x, double y, double z, double t) {
        double r514925 = 2.0;
        double r514926 = t;
        double r514927 = r514925 / r514926;
        double r514928 = z;
        double r514929 = r514927 / r514928;
        double r514930 = r514927 + r514929;
        double r514931 = x;
        double r514932 = y;
        double r514933 = r514931 / r514932;
        double r514934 = r514933 - r514925;
        double r514935 = r514930 + r514934;
        return r514935;
}

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

Original9.0
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.0

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))))