Average Error: 10.1 → 0.1
Time: 18.1s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r58871511 = x;
        double r58871512 = y;
        double r58871513 = r58871511 / r58871512;
        double r58871514 = 2.0;
        double r58871515 = z;
        double r58871516 = r58871515 * r58871514;
        double r58871517 = 1.0;
        double r58871518 = t;
        double r58871519 = r58871517 - r58871518;
        double r58871520 = r58871516 * r58871519;
        double r58871521 = r58871514 + r58871520;
        double r58871522 = r58871518 * r58871515;
        double r58871523 = r58871521 / r58871522;
        double r58871524 = r58871513 + r58871523;
        return r58871524;
}
↓
double f(double x, double y, double z, double t) {
        double r58871525 = x;
        double r58871526 = y;
        double r58871527 = r58871525 / r58871526;
        double r58871528 = 2.0;
        double r58871529 = t;
        double r58871530 = r58871528 / r58871529;
        double r58871531 = z;
        double r58871532 = r58871528 / r58871531;
        double r58871533 = r58871532 / r58871529;
        double r58871534 = r58871530 + r58871533;
        double r58871535 = r58871534 - r58871528;
        double r58871536 = r58871527 + r58871535;
        return r58871536;
}

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

Original10.1
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 10.1

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  5. Applied associate-/r*0.1

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

  7. Applied div-inv0.1

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

  9. Applied associate-*l/0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))