Average Error: 3.6 → 1.8
Time: 13.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}
double f(double x, double y, double z, double t) {
        double r660831 = x;
        double r660832 = y;
        double r660833 = z;
        double r660834 = 3.0;
        double r660835 = r660833 * r660834;
        double r660836 = r660832 / r660835;
        double r660837 = r660831 - r660836;
        double r660838 = t;
        double r660839 = r660835 * r660832;
        double r660840 = r660838 / r660839;
        double r660841 = r660837 + r660840;
        return r660841;
}
↓
double f(double x, double y, double z, double t) {
        double r660842 = x;
        double r660843 = y;
        double r660844 = z;
        double r660845 = 3.0;
        double r660846 = r660844 * r660845;
        double r660847 = r660843 / r660846;
        double r660848 = r660842 - r660847;
        double r660849 = t;
        double r660850 = r660849 / r660844;
        double r660851 = r660850 / r660845;
        double r660852 = r660851 / r660843;
        double r660853 = r660848 + r660852;
        return r660853;
}

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

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

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

  6. Final simplification1.8

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

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))))