Average Error: 3.7 → 1.8
Time: 3.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{\frac{y}{\frac{t}{z \cdot 3}}}\]
\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{1}{\frac{y}{\frac{t}{z \cdot 3}}}
double f(double x, double y, double z, double t) {
        double r846963 = x;
        double r846964 = y;
        double r846965 = z;
        double r846966 = 3.0;
        double r846967 = r846965 * r846966;
        double r846968 = r846964 / r846967;
        double r846969 = r846963 - r846968;
        double r846970 = t;
        double r846971 = r846967 * r846964;
        double r846972 = r846970 / r846971;
        double r846973 = r846969 + r846972;
        return r846973;
}
↓
double f(double x, double y, double z, double t) {
        double r846974 = x;
        double r846975 = y;
        double r846976 = z;
        double r846977 = r846975 / r846976;
        double r846978 = 3.0;
        double r846979 = r846977 / r846978;
        double r846980 = r846974 - r846979;
        double r846981 = 1.0;
        double r846982 = t;
        double r846983 = r846976 * r846978;
        double r846984 = r846982 / r846983;
        double r846985 = r846975 / r846984;
        double r846986 = r846981 / r846985;
        double r846987 = r846980 + r846986;
        return r846987;
}

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

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*1.8

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
  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 clear-num1.8

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

  8. Final simplification1.8

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

Reproduce

herbie shell --seed 2020060 
(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))))