Average Error: 3.4 → 1.5
Time: 5.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]
\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{\frac{\frac{t}{z}}{3}}{y}
double f(double x, double y, double z, double t) {
        double r877395 = x;
        double r877396 = y;
        double r877397 = z;
        double r877398 = 3.0;
        double r877399 = r877397 * r877398;
        double r877400 = r877396 / r877399;
        double r877401 = r877395 - r877400;
        double r877402 = t;
        double r877403 = r877399 * r877396;
        double r877404 = r877402 / r877403;
        double r877405 = r877401 + r877404;
        return r877405;
}
↓
double f(double x, double y, double z, double t) {
        double r877406 = x;
        double r877407 = y;
        double r877408 = z;
        double r877409 = r877407 / r877408;
        double r877410 = 3.0;
        double r877411 = r877409 / r877410;
        double r877412 = r877406 - r877411;
        double r877413 = t;
        double r877414 = r877413 / r877408;
        double r877415 = r877414 / r877410;
        double r877416 = r877415 / r877407;
        double r877417 = r877412 + r877416;
        return r877417;
}

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

Original3.4
Target1.5
Herbie1.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.4

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

  3. Applied associate-/r*1.5

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

  5. Applied associate-/r*1.5

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

  7. Applied associate-/r*1.5

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

  8. Final simplification1.5

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

Reproduce

herbie shell --seed 2020065 +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))))