Average Error: 3.6 → 1.9
Time: 12.0s
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 r478833 = x;
        double r478834 = y;
        double r478835 = z;
        double r478836 = 3.0;
        double r478837 = r478835 * r478836;
        double r478838 = r478834 / r478837;
        double r478839 = r478833 - r478838;
        double r478840 = t;
        double r478841 = r478837 * r478834;
        double r478842 = r478840 / r478841;
        double r478843 = r478839 + r478842;
        return r478843;
}
↓
double f(double x, double y, double z, double t) {
        double r478844 = x;
        double r478845 = y;
        double r478846 = z;
        double r478847 = r478845 / r478846;
        double r478848 = 3.0;
        double r478849 = r478847 / r478848;
        double r478850 = r478844 - r478849;
        double r478851 = t;
        double r478852 = r478846 * r478848;
        double r478853 = r478851 / r478852;
        double r478854 = 1.0;
        double r478855 = r478854 / r478845;
        double r478856 = r478853 * r478855;
        double r478857 = r478850 + r478856;
        return r478857;
}

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 
(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))))