Average Error: 9.1 → 0.1
Time: 16.2s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\left(\left(\frac{2.0}{t} + \frac{\frac{2.0}{t}}{z}\right) + \frac{x}{y}\right) - 2.0
double f(double x, double y, double z, double t) {
        double r33782398 = x;
        double r33782399 = y;
        double r33782400 = r33782398 / r33782399;
        double r33782401 = 2.0;
        double r33782402 = z;
        double r33782403 = r33782402 * r33782401;
        double r33782404 = 1.0;
        double r33782405 = t;
        double r33782406 = r33782404 - r33782405;
        double r33782407 = r33782403 * r33782406;
        double r33782408 = r33782401 + r33782407;
        double r33782409 = r33782405 * r33782402;
        double r33782410 = r33782408 / r33782409;
        double r33782411 = r33782400 + r33782410;
        return r33782411;
}
↓
double f(double x, double y, double z, double t) {
        double r33782412 = 2.0;
        double r33782413 = t;
        double r33782414 = r33782412 / r33782413;
        double r33782415 = z;
        double r33782416 = r33782414 / r33782415;
        double r33782417 = r33782414 + r33782416;
        double r33782418 = x;
        double r33782419 = y;
        double r33782420 = r33782418 / r33782419;
        double r33782421 = r33782417 + r33782420;
        double r33782422 = r33782421 - r33782412;
        return r33782422;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2.0}{t}, \frac{\mathsf{fma}\left(z, 1.0, 1\right)}{z}, \frac{x}{y}\right) - 2.0}\]

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +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))))