Average Error: 9.3 → 0.1
Time: 10.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - \left(2 - \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - \left(2 - \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r874740 = x;
        double r874741 = y;
        double r874742 = r874740 / r874741;
        double r874743 = 2.0;
        double r874744 = z;
        double r874745 = r874744 * r874743;
        double r874746 = 1.0;
        double r874747 = t;
        double r874748 = r874746 - r874747;
        double r874749 = r874745 * r874748;
        double r874750 = r874743 + r874749;
        double r874751 = r874747 * r874744;
        double r874752 = r874750 / r874751;
        double r874753 = r874742 + r874752;
        return r874753;
}
↓
double f(double x, double y, double z, double t) {
        double r874754 = 2.0;
        double r874755 = t;
        double r874756 = r874754 / r874755;
        double r874757 = z;
        double r874758 = r874756 / r874757;
        double r874759 = r874756 + r874758;
        double r874760 = x;
        double r874761 = y;
        double r874762 = r874760 / r874761;
        double r874763 = r874754 - r874762;
        double r874764 = r874759 - r874763;
        return r874764;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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))))