Average Error: 9.2 → 0.1
Time: 21.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r611741 = x;
        double r611742 = y;
        double r611743 = r611741 / r611742;
        double r611744 = 2.0;
        double r611745 = z;
        double r611746 = r611745 * r611744;
        double r611747 = 1.0;
        double r611748 = t;
        double r611749 = r611747 - r611748;
        double r611750 = r611746 * r611749;
        double r611751 = r611744 + r611750;
        double r611752 = r611748 * r611745;
        double r611753 = r611751 / r611752;
        double r611754 = r611743 + r611753;
        return r611754;
}
↓
double f(double x, double y, double z, double t) {
        double r611755 = 2.0;
        double r611756 = t;
        double r611757 = z;
        double r611758 = r611756 * r611757;
        double r611759 = r611755 / r611758;
        double r611760 = r611755 / r611756;
        double r611761 = r611760 - r611755;
        double r611762 = r611759 + r611761;
        double r611763 = x;
        double r611764 = y;
        double r611765 = r611763 / r611764;
        double r611766 = r611762 + r611765;
        return r611766;
}

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

Derivation

  1. Initial program 9.2

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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))))