Average Error: 9.6 → 0.1
Time: 48.1s
Precision: 64
\[\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2.0}{t} + \frac{1}{z} \cdot \frac{2.0}{t}\right) - 2.0\right)\]
\frac{x}{y} + \frac{2.0 + \left(z \cdot 2.0\right) \cdot \left(1.0 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2.0}{t} + \frac{1}{z} \cdot \frac{2.0}{t}\right) - 2.0\right)
double f(double x, double y, double z, double t) {
        double r41255254 = x;
        double r41255255 = y;
        double r41255256 = r41255254 / r41255255;
        double r41255257 = 2.0;
        double r41255258 = z;
        double r41255259 = r41255258 * r41255257;
        double r41255260 = 1.0;
        double r41255261 = t;
        double r41255262 = r41255260 - r41255261;
        double r41255263 = r41255259 * r41255262;
        double r41255264 = r41255257 + r41255263;
        double r41255265 = r41255261 * r41255258;
        double r41255266 = r41255264 / r41255265;
        double r41255267 = r41255256 + r41255266;
        return r41255267;
}
↓
double f(double x, double y, double z, double t) {
        double r41255268 = x;
        double r41255269 = y;
        double r41255270 = r41255268 / r41255269;
        double r41255271 = 2.0;
        double r41255272 = t;
        double r41255273 = r41255271 / r41255272;
        double r41255274 = 1.0;
        double r41255275 = z;
        double r41255276 = r41255274 / r41255275;
        double r41255277 = r41255276 * r41255273;
        double r41255278 = r41255273 + r41255277;
        double r41255279 = r41255278 - r41255271;
        double r41255280 = r41255270 + r41255279;
        return r41255280;
}

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

Original9.6
Target0.1
Herbie0.1
\[\frac{\frac{2.0}{z} + 2.0}{t} - \left(2.0 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.6

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

  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

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

  5. Applied div-inv0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(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))))