Average Error: 3.9 → 1.7
Time: 1.1m
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\frac{1}{\frac{y}{\frac{\frac{t}{z}}{3}}} + \left(x - \frac{y}{z \cdot 3}\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\frac{1}{\frac{y}{\frac{\frac{t}{z}}{3}}} + \left(x - \frac{y}{z \cdot 3}\right)
double f(double x, double y, double z, double t) {
        double r39796945 = x;
        double r39796946 = y;
        double r39796947 = z;
        double r39796948 = 3.0;
        double r39796949 = r39796947 * r39796948;
        double r39796950 = r39796946 / r39796949;
        double r39796951 = r39796945 - r39796950;
        double r39796952 = t;
        double r39796953 = r39796949 * r39796946;
        double r39796954 = r39796952 / r39796953;
        double r39796955 = r39796951 + r39796954;
        return r39796955;
}
↓
double f(double x, double y, double z, double t) {
        double r39796956 = 1.0;
        double r39796957 = y;
        double r39796958 = t;
        double r39796959 = z;
        double r39796960 = r39796958 / r39796959;
        double r39796961 = 3.0;
        double r39796962 = r39796960 / r39796961;
        double r39796963 = r39796957 / r39796962;
        double r39796964 = r39796956 / r39796963;
        double r39796965 = x;
        double r39796966 = r39796959 * r39796961;
        double r39796967 = r39796957 / r39796966;
        double r39796968 = r39796965 - r39796967;
        double r39796969 = r39796964 + r39796968;
        return r39796969;
}

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

Original3.9
Target1.6
Herbie1.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.9

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  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 *-un-lft-identity1.6

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

  6. Applied associate-/r*1.6

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

  7. Simplified1.6

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

  9. Applied clear-num1.7

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

  10. Final simplification1.7

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

Reproduce

herbie shell --seed 2019200 
(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))))