Average Error: 9.7 → 0.1
Time: 4.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r825794 = x;
        double r825795 = y;
        double r825796 = r825794 / r825795;
        double r825797 = 2.0;
        double r825798 = z;
        double r825799 = r825798 * r825797;
        double r825800 = 1.0;
        double r825801 = t;
        double r825802 = r825800 - r825801;
        double r825803 = r825799 * r825802;
        double r825804 = r825797 + r825803;
        double r825805 = r825801 * r825798;
        double r825806 = r825804 / r825805;
        double r825807 = r825796 + r825806;
        return r825807;
}
↓
double f(double x, double y, double z, double t) {
        double r825808 = x;
        double r825809 = y;
        double r825810 = r825808 / r825809;
        double r825811 = 1.0;
        double r825812 = t;
        double r825813 = r825811 / r825812;
        double r825814 = 2.0;
        double r825815 = z;
        double r825816 = r825814 / r825815;
        double r825817 = r825816 + r825814;
        double r825818 = r825813 * r825817;
        double r825819 = r825818 - r825814;
        double r825820 = r825810 + r825819;
        return r825820;
}

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

Original9.7
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.7

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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))))