Average Error: 9.6 → 0.1
Time: 13.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{z \cdot t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2}{z \cdot t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r40828781 = x;
        double r40828782 = y;
        double r40828783 = r40828781 / r40828782;
        double r40828784 = 2.0;
        double r40828785 = z;
        double r40828786 = r40828785 * r40828784;
        double r40828787 = 1.0;
        double r40828788 = t;
        double r40828789 = r40828787 - r40828788;
        double r40828790 = r40828786 * r40828789;
        double r40828791 = r40828784 + r40828790;
        double r40828792 = r40828788 * r40828785;
        double r40828793 = r40828791 / r40828792;
        double r40828794 = r40828783 + r40828793;
        return r40828794;
}
↓
double f(double x, double y, double z, double t) {
        double r40828795 = 2.0;
        double r40828796 = z;
        double r40828797 = t;
        double r40828798 = r40828796 * r40828797;
        double r40828799 = r40828795 / r40828798;
        double r40828800 = r40828799 - r40828795;
        double r40828801 = r40828795 / r40828797;
        double r40828802 = r40828800 + r40828801;
        double r40828803 = x;
        double r40828804 = y;
        double r40828805 = r40828803 / r40828804;
        double r40828806 = r40828802 + r40828805;
        return r40828806;
}

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

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(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))))