Average Error: 3.4 → 1.6
Time: 17.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{t}{z}}{y \cdot 3.0} + \left(x - \frac{\frac{y}{z}}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{t}{z}}{y \cdot 3.0} + \left(x - \frac{\frac{y}{z}}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r13410040 = x;
        double r13410041 = y;
        double r13410042 = z;
        double r13410043 = 3.0;
        double r13410044 = r13410042 * r13410043;
        double r13410045 = r13410041 / r13410044;
        double r13410046 = r13410040 - r13410045;
        double r13410047 = t;
        double r13410048 = r13410044 * r13410041;
        double r13410049 = r13410047 / r13410048;
        double r13410050 = r13410046 + r13410049;
        return r13410050;
}
↓
double f(double x, double y, double z, double t) {
        double r13410051 = t;
        double r13410052 = z;
        double r13410053 = r13410051 / r13410052;
        double r13410054 = y;
        double r13410055 = 3.0;
        double r13410056 = r13410054 * r13410055;
        double r13410057 = r13410053 / r13410056;
        double r13410058 = x;
        double r13410059 = r13410054 / r13410052;
        double r13410060 = r13410059 / r13410055;
        double r13410061 = r13410058 - r13410060;
        double r13410062 = r13410057 + r13410061;
        return r13410062;
}

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

Original3.4
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 3.4

    \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
  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 associate-/r*1.6

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

  7. Applied associate-/r*1.6

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

  9. Applied associate-/l/1.6

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

  10. Final simplification1.6

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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))))