Average Error: 4.0 → 1.8
Time: 9.1s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}
double f(double x, double y, double z, double t) {
        double r813450 = x;
        double r813451 = y;
        double r813452 = z;
        double r813453 = 3.0;
        double r813454 = r813452 * r813453;
        double r813455 = r813451 / r813454;
        double r813456 = r813450 - r813455;
        double r813457 = t;
        double r813458 = r813454 * r813451;
        double r813459 = r813457 / r813458;
        double r813460 = r813456 + r813459;
        return r813460;
}
↓
double f(double x, double y, double z, double t) {
        double r813461 = x;
        double r813462 = 1.0;
        double r813463 = z;
        double r813464 = 3.0;
        double r813465 = r813463 * r813464;
        double r813466 = y;
        double r813467 = r813465 / r813466;
        double r813468 = r813462 / r813467;
        double r813469 = r813461 - r813468;
        double r813470 = t;
        double r813471 = r813470 / r813465;
        double r813472 = r813471 / r813466;
        double r813473 = r813469 + r813472;
        return r813473;
}

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

Original4.0
Target1.7
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 4.0

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

  3. Applied associate-/r*1.7

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

  5. Applied clear-num1.8

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

  6. Final simplification1.8

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

Reproduce

herbie shell --seed 2020045 +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))))