Average Error: 9.4 → 0.1
Time: 11.3s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{2}{t \cdot z}\right) - \left(2 - \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \frac{2}{t \cdot z}\right) - \left(2 - \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r799269 = x;
        double r799270 = y;
        double r799271 = r799269 / r799270;
        double r799272 = 2.0;
        double r799273 = z;
        double r799274 = r799273 * r799272;
        double r799275 = 1.0;
        double r799276 = t;
        double r799277 = r799275 - r799276;
        double r799278 = r799274 * r799277;
        double r799279 = r799272 + r799278;
        double r799280 = r799276 * r799273;
        double r799281 = r799279 / r799280;
        double r799282 = r799271 + r799281;
        return r799282;
}
↓
double f(double x, double y, double z, double t) {
        double r799283 = 2.0;
        double r799284 = t;
        double r799285 = r799283 / r799284;
        double r799286 = z;
        double r799287 = r799284 * r799286;
        double r799288 = r799283 / r799287;
        double r799289 = r799285 + r799288;
        double r799290 = x;
        double r799291 = y;
        double r799292 = r799290 / r799291;
        double r799293 = r799283 - r799292;
        double r799294 = r799289 - r799293;
        return r799294;
}

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. Simplified0.1

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

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

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

  5. Applied add-cube-cbrt0.7

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{2}{z} + 1 \cdot 2} \cdot \sqrt[3]{\frac{2}{z} + 1 \cdot 2}\right) \cdot \sqrt[3]{\frac{2}{z} + 1 \cdot 2}}}{1 \cdot t} - \left(2 - \frac{x}{y}\right)\]

  6. Applied times-frac0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{2}{z} + 1 \cdot 2} \cdot \sqrt[3]{\frac{2}{z} + 1 \cdot 2}}{1} \cdot \frac{\sqrt[3]{\frac{2}{z} + 1 \cdot 2}}{t}} - \left(2 - \frac{x}{y}\right)\]

  7. Simplified0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{2}{z} + 1 \cdot 2} \cdot \sqrt[3]{\frac{2}{z} + 1 \cdot 2}\right)} \cdot \frac{\sqrt[3]{\frac{2}{z} + 1 \cdot 2}}{t} - \left(2 - \frac{x}{y}\right)\]

  8. Taylor expanded around 0 0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))))