Average Error: 9.8 → 0.1
Time: 12.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{\frac{2}{t}}{z} - 2\right)\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{2}{t} + \left(\frac{\frac{2}{t}}{z} - 2\right)\right)
double f(double x, double y, double z, double t) {
        double r889162 = x;
        double r889163 = y;
        double r889164 = r889162 / r889163;
        double r889165 = 2.0;
        double r889166 = z;
        double r889167 = r889166 * r889165;
        double r889168 = 1.0;
        double r889169 = t;
        double r889170 = r889168 - r889169;
        double r889171 = r889167 * r889170;
        double r889172 = r889165 + r889171;
        double r889173 = r889169 * r889166;
        double r889174 = r889172 / r889173;
        double r889175 = r889164 + r889174;
        return r889175;
}
↓
double f(double x, double y, double z, double t) {
        double r889176 = x;
        double r889177 = y;
        double r889178 = r889176 / r889177;
        double r889179 = 2.0;
        double r889180 = t;
        double r889181 = r889179 / r889180;
        double r889182 = z;
        double r889183 = r889181 / r889182;
        double r889184 = r889183 - r889179;
        double r889185 = r889181 + r889184;
        double r889186 = r889178 + r889185;
        return r889186;
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y)))

  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))