Average Error: 9.2 → 0.1
Time: 17.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right)
double f(double x, double y, double z, double t) {
        double r511440 = x;
        double r511441 = y;
        double r511442 = r511440 / r511441;
        double r511443 = 2.0;
        double r511444 = z;
        double r511445 = r511444 * r511443;
        double r511446 = 1.0;
        double r511447 = t;
        double r511448 = r511446 - r511447;
        double r511449 = r511445 * r511448;
        double r511450 = r511443 + r511449;
        double r511451 = r511447 * r511444;
        double r511452 = r511450 / r511451;
        double r511453 = r511442 + r511452;
        return r511453;
}
↓
double f(double x, double y, double z, double t) {
        double r511454 = x;
        double r511455 = y;
        double r511456 = r511454 / r511455;
        double r511457 = 2.0;
        double r511458 = t;
        double r511459 = r511457 / r511458;
        double r511460 = z;
        double r511461 = r511459 / r511460;
        double r511462 = r511459 - r511457;
        double r511463 = r511461 + r511462;
        double r511464 = r511456 + r511463;
        return r511464;
}

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

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

Derivation

  1. Initial program 9.2

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

  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

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(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))))