Average Error: 3.5 → 1.6
Time: 15.9s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r34264875 = x;
        double r34264876 = y;
        double r34264877 = z;
        double r34264878 = 3.0;
        double r34264879 = r34264877 * r34264878;
        double r34264880 = r34264876 / r34264879;
        double r34264881 = r34264875 - r34264880;
        double r34264882 = t;
        double r34264883 = r34264879 * r34264876;
        double r34264884 = r34264882 / r34264883;
        double r34264885 = r34264881 + r34264884;
        return r34264885;
}
↓
double f(double x, double y, double z, double t) {
        double r34264886 = t;
        double r34264887 = 3.0;
        double r34264888 = r34264886 / r34264887;
        double r34264889 = 1.0;
        double r34264890 = z;
        double r34264891 = r34264889 / r34264890;
        double r34264892 = r34264888 * r34264891;
        double r34264893 = y;
        double r34264894 = r34264892 / r34264893;
        double r34264895 = x;
        double r34264896 = r34264893 / r34264887;
        double r34264897 = r34264891 * r34264896;
        double r34264898 = r34264895 - r34264897;
        double r34264899 = r34264894 + r34264898;
        return r34264899;
}

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

Original3.5
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

Derivation

  1. Initial program 3.5

    \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3.0}}{y}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.6

    \[\leadsto \left(x - \frac{\color{blue}{1 \cdot y}}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

  6. Applied times-frac1.6

    \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3.0}}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity1.6

    \[\leadsto \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right) + \frac{\frac{\color{blue}{1 \cdot t}}{z \cdot 3.0}}{y}\]

  9. Applied times-frac1.6

    \[\leadsto \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right) + \frac{\color{blue}{\frac{1}{z} \cdot \frac{t}{3.0}}}{y}\]

  10. Final simplification1.6

    \[\leadsto \frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))