Average Error: 3.7 → 1.6
Time: 2.8s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}
double f(double x, double y, double z, double t) {
        double r650343 = x;
        double r650344 = y;
        double r650345 = z;
        double r650346 = 3.0;
        double r650347 = r650345 * r650346;
        double r650348 = r650344 / r650347;
        double r650349 = r650343 - r650348;
        double r650350 = t;
        double r650351 = r650347 * r650344;
        double r650352 = r650350 / r650351;
        double r650353 = r650349 + r650352;
        return r650353;
}
↓
double f(double x, double y, double z, double t) {
        double r650354 = x;
        double r650355 = y;
        double r650356 = z;
        double r650357 = r650355 / r650356;
        double r650358 = 3.0;
        double r650359 = r650357 / r650358;
        double r650360 = r650354 - r650359;
        double r650361 = 1.0;
        double r650362 = 0.3333333333333333;
        double r650363 = t;
        double r650364 = r650363 / r650356;
        double r650365 = r650362 * r650364;
        double r650366 = r650355 / r650365;
        double r650367 = r650361 / r650366;
        double r650368 = r650360 + r650367;
        return r650368;
}

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

Original3.7
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.7

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]

  4. Taylor expanded around 0 1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{0.333333333333333315 \cdot \frac{t}{z}}}{y}\]
  5. Using strategy rm

  6. Applied associate-/r*1.6

    \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{z}}{3}}\right) + \frac{0.333333333333333315 \cdot \frac{t}{z}}{y}\]
  7. Using strategy rm

  8. Applied clear-num1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{\frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}}\]

  9. Final simplification1.6

    \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{0.333333333333333315 \cdot \frac{t}{z}}}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))