Average Error: 9.9 → 0.1
Time: 15.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} - 2\right) + \left(\frac{\frac{2}{z}}{t} + \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} - 2\right) + \left(\frac{\frac{2}{z}}{t} + \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r648740 = x;
        double r648741 = y;
        double r648742 = r648740 / r648741;
        double r648743 = 2.0;
        double r648744 = z;
        double r648745 = r648744 * r648743;
        double r648746 = 1.0;
        double r648747 = t;
        double r648748 = r648746 - r648747;
        double r648749 = r648745 * r648748;
        double r648750 = r648743 + r648749;
        double r648751 = r648747 * r648744;
        double r648752 = r648750 / r648751;
        double r648753 = r648742 + r648752;
        return r648753;
}
↓
double f(double x, double y, double z, double t) {
        double r648754 = 2.0;
        double r648755 = t;
        double r648756 = r648754 / r648755;
        double r648757 = r648756 - r648754;
        double r648758 = z;
        double r648759 = r648754 / r648758;
        double r648760 = r648759 / r648755;
        double r648761 = x;
        double r648762 = y;
        double r648763 = r648761 / r648762;
        double r648764 = r648760 + r648763;
        double r648765 = r648757 + r648764;
        return r648765;
}

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

Original9.9
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.9

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

  2. Simplified9.9

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied *-un-lft-identity0.1

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

  8. Applied distribute-lft-out0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(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))))