Average Error: 3.7 → 1.6
Time: 8.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x + \frac{-\frac{y}{3}}{z}\right) + \frac{\frac{t}{z}}{3} \cdot \frac{1}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x + \frac{-\frac{y}{3}}{z}\right) + \frac{\frac{t}{z}}{3} \cdot \frac{1}{y}
double f(double x, double y, double z, double t) {
        double r928623 = x;
        double r928624 = y;
        double r928625 = z;
        double r928626 = 3.0;
        double r928627 = r928625 * r928626;
        double r928628 = r928624 / r928627;
        double r928629 = r928623 - r928628;
        double r928630 = t;
        double r928631 = r928627 * r928624;
        double r928632 = r928630 / r928631;
        double r928633 = r928629 + r928632;
        return r928633;
}
↓
double f(double x, double y, double z, double t) {
        double r928634 = x;
        double r928635 = y;
        double r928636 = 3.0;
        double r928637 = r928635 / r928636;
        double r928638 = -r928637;
        double r928639 = z;
        double r928640 = r928638 / r928639;
        double r928641 = r928634 + r928640;
        double r928642 = t;
        double r928643 = r928642 / r928639;
        double r928644 = r928643 / r928636;
        double r928645 = 1.0;
        double r928646 = r928645 / r928635;
        double r928647 = r928644 * r928646;
        double r928648 = r928641 + r928647;
        return r928648;
}

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. Using strategy rm

  5. Applied div-inv1.7

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

  7. Applied sub-neg1.7

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

  8. Simplified1.6

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

  10. Applied associate-/r*1.6

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

  11. Final simplification1.6

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

Reproduce

herbie shell --seed 2020042 +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))))