Average Error: 9.2 → 0.1
Time: 2.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r618359 = x;
        double r618360 = y;
        double r618361 = r618359 / r618360;
        double r618362 = 2.0;
        double r618363 = z;
        double r618364 = r618363 * r618362;
        double r618365 = 1.0;
        double r618366 = t;
        double r618367 = r618365 - r618366;
        double r618368 = r618364 * r618367;
        double r618369 = r618362 + r618368;
        double r618370 = r618366 * r618363;
        double r618371 = r618369 / r618370;
        double r618372 = r618361 + r618371;
        return r618372;
}
↓
double f(double x, double y, double z, double t) {
        double r618373 = x;
        double r618374 = y;
        double r618375 = r618373 / r618374;
        double r618376 = 1.0;
        double r618377 = 2.0;
        double r618378 = z;
        double r618379 = r618377 / r618378;
        double r618380 = r618379 + r618377;
        double r618381 = t;
        double r618382 = r618380 / r618381;
        double r618383 = r618376 * r618382;
        double r618384 = r618383 - r618377;
        double r618385 = r618375 + r618384;
        return r618385;
}

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

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

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

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

  6. Applied associate-*l*0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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))))