Average Error: 9.4 → 0.1
Time: 3.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r792399 = x;
        double r792400 = y;
        double r792401 = r792399 / r792400;
        double r792402 = 2.0;
        double r792403 = z;
        double r792404 = r792403 * r792402;
        double r792405 = 1.0;
        double r792406 = t;
        double r792407 = r792405 - r792406;
        double r792408 = r792404 * r792407;
        double r792409 = r792402 + r792408;
        double r792410 = r792406 * r792403;
        double r792411 = r792409 / r792410;
        double r792412 = r792401 + r792411;
        return r792412;
}
↓
double f(double x, double y, double z, double t) {
        double r792413 = x;
        double r792414 = y;
        double r792415 = r792413 / r792414;
        double r792416 = 1.0;
        double r792417 = 2.0;
        double r792418 = z;
        double r792419 = r792417 / r792418;
        double r792420 = r792419 + r792417;
        double r792421 = t;
        double r792422 = r792420 / r792421;
        double r792423 = r792416 * r792422;
        double r792424 = r792423 - r792417;
        double r792425 = r792415 + r792424;
        return r792425;
}

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

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

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

  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 *-un-lft-identity0.1

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

  6. Applied associate-*l*0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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))))