Average Error: 9.2 → 0.1
Time: 4.4s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r901259 = x;
        double r901260 = y;
        double r901261 = r901259 / r901260;
        double r901262 = 2.0;
        double r901263 = z;
        double r901264 = r901263 * r901262;
        double r901265 = 1.0;
        double r901266 = t;
        double r901267 = r901265 - r901266;
        double r901268 = r901264 * r901267;
        double r901269 = r901262 + r901268;
        double r901270 = r901266 * r901263;
        double r901271 = r901269 / r901270;
        double r901272 = r901261 + r901271;
        return r901272;
}
↓
double f(double x, double y, double z, double t) {
        double r901273 = x;
        double r901274 = y;
        double r901275 = r901273 / r901274;
        double r901276 = 1.0;
        double r901277 = t;
        double r901278 = r901276 / r901277;
        double r901279 = 2.0;
        double r901280 = z;
        double r901281 = r901279 / r901280;
        double r901282 = r901281 + r901279;
        double r901283 = r901278 * r901282;
        double r901284 = r901283 - r901279;
        double r901285 = r901275 + r901284;
        return r901285;
}

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

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

Derivation

  1. Initial program 9.2

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

  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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))))