Average Error: 9.2 → 0.1
Time: 4.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t \cdot z} + \frac{2}{t}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r1041281 = x;
        double r1041282 = y;
        double r1041283 = r1041281 / r1041282;
        double r1041284 = 2.0;
        double r1041285 = z;
        double r1041286 = r1041285 * r1041284;
        double r1041287 = 1.0;
        double r1041288 = t;
        double r1041289 = r1041287 - r1041288;
        double r1041290 = r1041286 * r1041289;
        double r1041291 = r1041284 + r1041290;
        double r1041292 = r1041288 * r1041285;
        double r1041293 = r1041291 / r1041292;
        double r1041294 = r1041283 + r1041293;
        return r1041294;
}
↓
double f(double x, double y, double z, double t) {
        double r1041295 = x;
        double r1041296 = y;
        double r1041297 = r1041295 / r1041296;
        double r1041298 = 2.0;
        double r1041299 = t;
        double r1041300 = z;
        double r1041301 = r1041299 * r1041300;
        double r1041302 = r1041298 / r1041301;
        double r1041303 = r1041298 / r1041299;
        double r1041304 = r1041302 + r1041303;
        double r1041305 = r1041304 - r1041298;
        double r1041306 = r1041297 + r1041305;
        return r1041306;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(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))))