Average Error: 9.3 → 0.1
Time: 19.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \left(\frac{2}{t} - 2\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r536311 = x;
        double r536312 = y;
        double r536313 = r536311 / r536312;
        double r536314 = 2.0;
        double r536315 = z;
        double r536316 = r536315 * r536314;
        double r536317 = 1.0;
        double r536318 = t;
        double r536319 = r536317 - r536318;
        double r536320 = r536316 * r536319;
        double r536321 = r536314 + r536320;
        double r536322 = r536318 * r536315;
        double r536323 = r536321 / r536322;
        double r536324 = r536313 + r536323;
        return r536324;
}
↓
double f(double x, double y, double z, double t) {
        double r536325 = 2.0;
        double r536326 = t;
        double r536327 = r536325 / r536326;
        double r536328 = z;
        double r536329 = r536327 / r536328;
        double r536330 = r536327 - r536325;
        double r536331 = r536329 + r536330;
        double r536332 = x;
        double r536333 = y;
        double r536334 = r536332 / r536333;
        double r536335 = r536331 + r536334;
        return r536335;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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))))