Average Error: 9.1 → 0.1
Time: 14.2s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\left(\left(\frac{\frac{2.0}{z}}{t} - 2.0\right) + \frac{2.0}{t}\right) + \frac{x}{y}\]
\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 r38631167 = x;
        double r38631168 = y;
        double r38631169 = r38631167 / r38631168;
        double r38631170 = 2.0;
        double r38631171 = z;
        double r38631172 = r38631171 * r38631170;
        double r38631173 = 1.0;
        double r38631174 = t;
        double r38631175 = r38631173 - r38631174;
        double r38631176 = r38631172 * r38631175;
        double r38631177 = r38631170 + r38631176;
        double r38631178 = r38631174 * r38631171;
        double r38631179 = r38631177 / r38631178;
        double r38631180 = r38631169 + r38631179;
        return r38631180;
}
↓
double f(double x, double y, double z, double t) {
        double r38631181 = 2.0;
        double r38631182 = z;
        double r38631183 = r38631181 / r38631182;
        double r38631184 = t;
        double r38631185 = r38631183 / r38631184;
        double r38631186 = r38631185 - r38631181;
        double r38631187 = r38631181 / r38631184;
        double r38631188 = r38631186 + r38631187;
        double r38631189 = x;
        double r38631190 = y;
        double r38631191 = r38631189 / r38631190;
        double r38631192 = r38631188 + r38631191;
        return r38631192;
}

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))))