Average Error: 8.9 → 0.1
Time: 39.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2}{z}}{t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{\frac{2}{z}}{t} - 2\right) + \frac{2}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r43319517 = x;
        double r43319518 = y;
        double r43319519 = r43319517 / r43319518;
        double r43319520 = 2.0;
        double r43319521 = z;
        double r43319522 = r43319521 * r43319520;
        double r43319523 = 1.0;
        double r43319524 = t;
        double r43319525 = r43319523 - r43319524;
        double r43319526 = r43319522 * r43319525;
        double r43319527 = r43319520 + r43319526;
        double r43319528 = r43319524 * r43319521;
        double r43319529 = r43319527 / r43319528;
        double r43319530 = r43319519 + r43319529;
        return r43319530;
}
↓
double f(double x, double y, double z, double t) {
        double r43319531 = 2.0;
        double r43319532 = z;
        double r43319533 = r43319531 / r43319532;
        double r43319534 = t;
        double r43319535 = r43319533 / r43319534;
        double r43319536 = r43319535 - r43319531;
        double r43319537 = r43319531 / r43319534;
        double r43319538 = r43319536 + r43319537;
        double r43319539 = x;
        double r43319540 = y;
        double r43319541 = r43319539 / r43319540;
        double r43319542 = r43319538 + r43319541;
        return r43319542;
}

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

Original8.9
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 8.9

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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))))