Average Error: 9.4 → 0.1
Time: 40.6s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \frac{x}{y}\right) - 2\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \frac{x}{y}\right) - 2
double f(double x, double y, double z, double t) {
        double r37001404 = x;
        double r37001405 = y;
        double r37001406 = r37001404 / r37001405;
        double r37001407 = 2.0;
        double r37001408 = z;
        double r37001409 = r37001408 * r37001407;
        double r37001410 = 1.0;
        double r37001411 = t;
        double r37001412 = r37001410 - r37001411;
        double r37001413 = r37001409 * r37001412;
        double r37001414 = r37001407 + r37001413;
        double r37001415 = r37001411 * r37001408;
        double r37001416 = r37001414 / r37001415;
        double r37001417 = r37001406 + r37001416;
        return r37001417;
}
↓
double f(double x, double y, double z, double t) {
        double r37001418 = 2.0;
        double r37001419 = t;
        double r37001420 = r37001418 / r37001419;
        double r37001421 = z;
        double r37001422 = r37001420 / r37001421;
        double r37001423 = r37001420 + r37001422;
        double r37001424 = x;
        double r37001425 = y;
        double r37001426 = r37001424 / r37001425;
        double r37001427 = r37001423 + r37001426;
        double r37001428 = r37001427 - r37001418;
        return r37001428;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))))