Average Error: 9.8 → 0.1
Time: 7.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{2}{t \cdot z} - 2\right)\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{2}{t \cdot z} - 2\right)\right)
double f(double x, double y, double z, double t) {
        double r1083739 = x;
        double r1083740 = y;
        double r1083741 = r1083739 / r1083740;
        double r1083742 = 2.0;
        double r1083743 = z;
        double r1083744 = r1083743 * r1083742;
        double r1083745 = 1.0;
        double r1083746 = t;
        double r1083747 = r1083745 - r1083746;
        double r1083748 = r1083744 * r1083747;
        double r1083749 = r1083742 + r1083748;
        double r1083750 = r1083746 * r1083743;
        double r1083751 = r1083749 / r1083750;
        double r1083752 = r1083741 + r1083751;
        return r1083752;
}
↓
double f(double x, double y, double z, double t) {
        double r1083753 = x;
        double r1083754 = y;
        double r1083755 = r1083753 / r1083754;
        double r1083756 = 2.0;
        double r1083757 = t;
        double r1083758 = r1083756 / r1083757;
        double r1083759 = z;
        double r1083760 = r1083757 * r1083759;
        double r1083761 = r1083756 / r1083760;
        double r1083762 = r1083761 - r1083756;
        double r1083763 = r1083758 + r1083762;
        double r1083764 = r1083755 + r1083763;
        return r1083764;
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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))))