Average Error: 9.7 → 0.1
Time: 3.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r840212 = x;
        double r840213 = y;
        double r840214 = r840212 / r840213;
        double r840215 = 2.0;
        double r840216 = z;
        double r840217 = r840216 * r840215;
        double r840218 = 1.0;
        double r840219 = t;
        double r840220 = r840218 - r840219;
        double r840221 = r840217 * r840220;
        double r840222 = r840215 + r840221;
        double r840223 = r840219 * r840216;
        double r840224 = r840222 / r840223;
        double r840225 = r840214 + r840224;
        return r840225;
}
↓
double f(double x, double y, double z, double t) {
        double r840226 = x;
        double r840227 = y;
        double r840228 = r840226 / r840227;
        double r840229 = 2.0;
        double r840230 = z;
        double r840231 = r840229 / r840230;
        double r840232 = r840231 + r840229;
        double r840233 = t;
        double r840234 = r840232 / r840233;
        double r840235 = r840234 - r840229;
        double r840236 = r840228 + r840235;
        return r840236;
}

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

Original9.7
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.7

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

  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

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

  5. Applied associate-*l/0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 
(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))))