Average Error: 9.5 → 0.1
Time: 3.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left({\left(\frac{\frac{2}{z} + 2}{t}\right)}^{1} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left({\left(\frac{\frac{2}{z} + 2}{t}\right)}^{1} - 2\right)
double f(double x, double y, double z, double t) {
        double r780697 = x;
        double r780698 = y;
        double r780699 = r780697 / r780698;
        double r780700 = 2.0;
        double r780701 = z;
        double r780702 = r780701 * r780700;
        double r780703 = 1.0;
        double r780704 = t;
        double r780705 = r780703 - r780704;
        double r780706 = r780702 * r780705;
        double r780707 = r780700 + r780706;
        double r780708 = r780704 * r780701;
        double r780709 = r780707 / r780708;
        double r780710 = r780699 + r780709;
        return r780710;
}
↓
double f(double x, double y, double z, double t) {
        double r780711 = x;
        double r780712 = y;
        double r780713 = r780711 / r780712;
        double r780714 = 2.0;
        double r780715 = z;
        double r780716 = r780714 / r780715;
        double r780717 = r780716 + r780714;
        double r780718 = t;
        double r780719 = r780717 / r780718;
        double r780720 = 1.0;
        double r780721 = pow(r780719, r780720);
        double r780722 = r780721 - r780714;
        double r780723 = r780713 + r780722;
        return r780723;
}

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

Original9.5
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.5

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

  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

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

  5. Applied pow10.1

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

  6. Applied pow10.1

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

  7. Applied pow-prod-down0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(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))))