Average Error: 9.3 → 0.1
Time: 11.6s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\left(-2\right) + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\left(-2\right) + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\right) + \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r632160 = x;
        double r632161 = y;
        double r632162 = r632160 / r632161;
        double r632163 = 2.0;
        double r632164 = z;
        double r632165 = r632164 * r632163;
        double r632166 = 1.0;
        double r632167 = t;
        double r632168 = r632166 - r632167;
        double r632169 = r632165 * r632168;
        double r632170 = r632163 + r632169;
        double r632171 = r632167 * r632164;
        double r632172 = r632170 / r632171;
        double r632173 = r632162 + r632172;
        return r632173;
}
↓
double f(double x, double y, double z, double t) {
        double r632174 = 2.0;
        double r632175 = -r632174;
        double r632176 = t;
        double r632177 = r632174 / r632176;
        double r632178 = z;
        double r632179 = r632174 / r632178;
        double r632180 = r632179 / r632176;
        double r632181 = r632177 + r632180;
        double r632182 = r632175 + r632181;
        double r632183 = x;
        double r632184 = y;
        double r632185 = r632183 / r632184;
        double r632186 = r632182 + r632185;
        return r632186;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  2. Simplified9.3

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied sub-neg0.1

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

  7. Applied associate-+r+0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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))))