Average Error: 9.1 → 0.1
Time: 15.5s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2.0}{z}}{t} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{\frac{2.0}{z}}{t} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r36000415 = x;
        double r36000416 = y;
        double r36000417 = r36000415 / r36000416;
        double r36000418 = 2.0;
        double r36000419 = z;
        double r36000420 = r36000419 * r36000418;
        double r36000421 = 1.0;
        double r36000422 = t;
        double r36000423 = r36000421 - r36000422;
        double r36000424 = r36000420 * r36000423;
        double r36000425 = r36000418 + r36000424;
        double r36000426 = r36000422 * r36000419;
        double r36000427 = r36000425 / r36000426;
        double r36000428 = r36000417 + r36000427;
        return r36000428;
}
↓
double f(double x, double y, double z, double t) {
        double r36000429 = 2.0;
        double r36000430 = z;
        double r36000431 = r36000429 / r36000430;
        double r36000432 = t;
        double r36000433 = r36000431 / r36000432;
        double r36000434 = r36000433 - r36000429;
        double r36000435 = r36000429 / r36000432;
        double r36000436 = r36000434 + r36000435;
        double r36000437 = x;
        double r36000438 = y;
        double r36000439 = r36000437 / r36000438;
        double r36000440 = r36000436 + r36000439;
        return r36000440;
}

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

Original9.1
Target0.1
Herbie0.1
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.1

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2.0 \cdot \frac{1}{t} + 2.0 \cdot \frac{1}{t \cdot z}\right) - 2.0\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(\frac{2.0}{z \cdot t} - 2.0\right) + \frac{2.0}{t}\right)}\]
  4. Using strategy rm

  5. Applied associate-/r*0.1

    \[\leadsto \frac{x}{y} + \left(\left(\color{blue}{\frac{\frac{2.0}{z}}{t}} - 2.0\right) + \frac{2.0}{t}\right)\]

  6. Final simplification0.1

    \[\leadsto \left(\left(\frac{\frac{2.0}{z}}{t} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}\]

Reproduce

herbie shell --seed 2019163 
(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))))