Average Error: 3.6 → 1.9
Time: 19.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{z \cdot 3} \cdot \frac{1}{y}\]
\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{t}{z \cdot 3} \cdot \frac{1}{y}
double f(double x, double y, double z, double t) {
        double r467617 = x;
        double r467618 = y;
        double r467619 = z;
        double r467620 = 3.0;
        double r467621 = r467619 * r467620;
        double r467622 = r467618 / r467621;
        double r467623 = r467617 - r467622;
        double r467624 = t;
        double r467625 = r467621 * r467618;
        double r467626 = r467624 / r467625;
        double r467627 = r467623 + r467626;
        return r467627;
}
↓
double f(double x, double y, double z, double t) {
        double r467628 = x;
        double r467629 = y;
        double r467630 = z;
        double r467631 = r467629 / r467630;
        double r467632 = 3.0;
        double r467633 = r467631 / r467632;
        double r467634 = r467628 - r467633;
        double r467635 = t;
        double r467636 = r467630 * r467632;
        double r467637 = r467635 / r467636;
        double r467638 = 1.0;
        double r467639 = r467638 / r467629;
        double r467640 = r467637 * r467639;
        double r467641 = r467634 + r467640;
        return r467641;
}

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

Original3.6
Target1.8
Herbie1.9
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.6

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

  3. Applied associate-/r*1.8

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

  5. Applied associate-/r*1.8

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

  7. Applied div-inv1.9

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

  8. Final simplification1.9

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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))))