Average Error: 9.5 → 0.1
Time: 2.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\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 r1331442 = x;
        double r1331443 = y;
        double r1331444 = r1331442 / r1331443;
        double r1331445 = 2.0;
        double r1331446 = z;
        double r1331447 = r1331446 * r1331445;
        double r1331448 = 1.0;
        double r1331449 = t;
        double r1331450 = r1331448 - r1331449;
        double r1331451 = r1331447 * r1331450;
        double r1331452 = r1331445 + r1331451;
        double r1331453 = r1331449 * r1331446;
        double r1331454 = r1331452 / r1331453;
        double r1331455 = r1331444 + r1331454;
        return r1331455;
}
↓
double f(double x, double y, double z, double t) {
        double r1331456 = x;
        double r1331457 = y;
        double r1331458 = r1331456 / r1331457;
        double r1331459 = 1.0;
        double r1331460 = 2.0;
        double r1331461 = z;
        double r1331462 = r1331460 / r1331461;
        double r1331463 = r1331462 + r1331460;
        double r1331464 = t;
        double r1331465 = r1331463 / r1331464;
        double r1331466 = r1331459 * r1331465;
        double r1331467 = r1331466 - r1331460;
        double r1331468 = r1331458 + r1331467;
        return r1331468;
}

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

Original9.5
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.5

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

  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

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

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

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

  7. Applied times-frac0.1

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

  8. Applied associate-*l*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(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))))