Average Error: 9.4 → 0.1
Time: 21.6s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r570679 = x;
        double r570680 = y;
        double r570681 = r570679 / r570680;
        double r570682 = 2.0;
        double r570683 = z;
        double r570684 = r570683 * r570682;
        double r570685 = 1.0;
        double r570686 = t;
        double r570687 = r570685 - r570686;
        double r570688 = r570684 * r570687;
        double r570689 = r570682 + r570688;
        double r570690 = r570686 * r570683;
        double r570691 = r570689 / r570690;
        double r570692 = r570681 + r570691;
        return r570692;
}
↓
double f(double x, double y, double z, double t) {
        double r570693 = x;
        double r570694 = y;
        double r570695 = r570693 / r570694;
        double r570696 = 2.0;
        double r570697 = t;
        double r570698 = r570696 / r570697;
        double r570699 = z;
        double r570700 = r570696 / r570699;
        double r570701 = r570700 / r570697;
        double r570702 = r570698 + r570701;
        double r570703 = r570702 - r570696;
        double r570704 = r570695 + r570703;
        return r570704;
}

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

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

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

  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

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

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

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

  6. Applied times-frac0.1

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

  8. Applied associate-*l/0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 
(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))))