Average Error: 8.8 → 0.1
Time: 15.1s
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 r38128290 = x;
        double r38128291 = y;
        double r38128292 = r38128290 / r38128291;
        double r38128293 = 2.0;
        double r38128294 = z;
        double r38128295 = r38128294 * r38128293;
        double r38128296 = 1.0;
        double r38128297 = t;
        double r38128298 = r38128296 - r38128297;
        double r38128299 = r38128295 * r38128298;
        double r38128300 = r38128293 + r38128299;
        double r38128301 = r38128297 * r38128294;
        double r38128302 = r38128300 / r38128301;
        double r38128303 = r38128292 + r38128302;
        return r38128303;
}
↓
double f(double x, double y, double z, double t) {
        double r38128304 = 2.0;
        double r38128305 = z;
        double r38128306 = r38128304 / r38128305;
        double r38128307 = t;
        double r38128308 = r38128306 / r38128307;
        double r38128309 = r38128308 - r38128304;
        double r38128310 = r38128304 / r38128307;
        double r38128311 = r38128309 + r38128310;
        double r38128312 = x;
        double r38128313 = y;
        double r38128314 = r38128312 / r38128313;
        double r38128315 = r38128311 + r38128314;
        return r38128315;
}

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

Original8.8
Target0.1
Herbie0.1
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 8.8

    \[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]

  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

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

  5. Applied div-inv0.1

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

  7. Applied associate-*l/0.1

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

  8. Simplified0.1

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

  9. 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 2019162 
(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))))