Average Error: 9.5 → 0.1
Time: 3.7s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r812417 = x;
        double r812418 = y;
        double r812419 = r812417 / r812418;
        double r812420 = 2.0;
        double r812421 = z;
        double r812422 = r812421 * r812420;
        double r812423 = 1.0;
        double r812424 = t;
        double r812425 = r812423 - r812424;
        double r812426 = r812422 * r812425;
        double r812427 = r812420 + r812426;
        double r812428 = r812424 * r812421;
        double r812429 = r812427 / r812428;
        double r812430 = r812419 + r812429;
        return r812430;
}
↓
double f(double x, double y, double z, double t) {
        double r812431 = 2.0;
        double r812432 = z;
        double r812433 = r812431 / r812432;
        double r812434 = r812433 + r812431;
        double r812435 = t;
        double r812436 = r812434 / r812435;
        double r812437 = x;
        double r812438 = y;
        double r812439 = r812437 / r812438;
        double r812440 = r812431 - r812439;
        double r812441 = r812436 - r812440;
        return r812441;
}

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

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

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

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

  7. Applied distribute-lft-out0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(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))))