Average Error: 9.6 → 0.1
Time: 17.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r513680 = x;
        double r513681 = y;
        double r513682 = r513680 / r513681;
        double r513683 = 2.0;
        double r513684 = z;
        double r513685 = r513684 * r513683;
        double r513686 = 1.0;
        double r513687 = t;
        double r513688 = r513686 - r513687;
        double r513689 = r513685 * r513688;
        double r513690 = r513683 + r513689;
        double r513691 = r513687 * r513684;
        double r513692 = r513690 / r513691;
        double r513693 = r513682 + r513692;
        return r513693;
}
↓
double f(double x, double y, double z, double t) {
        double r513694 = 2.0;
        double r513695 = t;
        double r513696 = r513694 / r513695;
        double r513697 = z;
        double r513698 = r513696 / r513697;
        double r513699 = r513696 - r513694;
        double r513700 = r513698 + r513699;
        double r513701 = x;
        double r513702 = y;
        double r513703 = r513701 / r513702;
        double r513704 = r513700 + r513703;
        return r513704;
}

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. 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. Using strategy rm

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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))))