Average Error: 9.3 → 0.1
Time: 21.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{\left(1 - t\right) \cdot 2 + \frac{2}{z}}{t} + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{\left(1 - t\right) \cdot 2 + \frac{2}{z}}{t} + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r660728 = x;
        double r660729 = y;
        double r660730 = r660728 / r660729;
        double r660731 = 2.0;
        double r660732 = z;
        double r660733 = r660732 * r660731;
        double r660734 = 1.0;
        double r660735 = t;
        double r660736 = r660734 - r660735;
        double r660737 = r660733 * r660736;
        double r660738 = r660731 + r660737;
        double r660739 = r660735 * r660732;
        double r660740 = r660738 / r660739;
        double r660741 = r660730 + r660740;
        return r660741;
}
↓
double f(double x, double y, double z, double t) {
        double r660742 = 1.0;
        double r660743 = t;
        double r660744 = r660742 - r660743;
        double r660745 = 2.0;
        double r660746 = r660744 * r660745;
        double r660747 = z;
        double r660748 = r660745 / r660747;
        double r660749 = r660746 + r660748;
        double r660750 = r660749 / r660743;
        double r660751 = x;
        double r660752 = y;
        double r660753 = r660751 / r660752;
        double r660754 = r660750 + r660753;
        return r660754;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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))))