Average Error: 3.6 → 3.4
Time: 30.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{\frac{1}{z}}{\frac{y}{t}}}{3.0} + \left(x - \frac{y}{z \cdot 3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{\frac{1}{z}}{\frac{y}{t}}}{3.0} + \left(x - \frac{y}{z \cdot 3.0}\right)
double f(double x, double y, double z, double t) {
        double r31874984 = x;
        double r31874985 = y;
        double r31874986 = z;
        double r31874987 = 3.0;
        double r31874988 = r31874986 * r31874987;
        double r31874989 = r31874985 / r31874988;
        double r31874990 = r31874984 - r31874989;
        double r31874991 = t;
        double r31874992 = r31874988 * r31874985;
        double r31874993 = r31874991 / r31874992;
        double r31874994 = r31874990 + r31874993;
        return r31874994;
}
↓
double f(double x, double y, double z, double t) {
        double r31874995 = 1.0;
        double r31874996 = z;
        double r31874997 = r31874995 / r31874996;
        double r31874998 = y;
        double r31874999 = t;
        double r31875000 = r31874998 / r31874999;
        double r31875001 = r31874997 / r31875000;
        double r31875002 = 3.0;
        double r31875003 = r31875001 / r31875002;
        double r31875004 = x;
        double r31875005 = r31874996 * r31875002;
        double r31875006 = r31874998 / r31875005;
        double r31875007 = r31875004 - r31875006;
        double r31875008 = r31875003 + r31875007;
        return r31875008;
}

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
Target1.6
Herbie3.4
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

Derivation

  1. Initial program 3.6

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

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

  6. Applied times-frac1.6

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

  7. Applied associate-/l*3.4

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

  9. Applied associate-/r/3.4

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

  10. Applied associate-/r*3.4

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

  11. Final simplification3.4

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

Reproduce

herbie shell --seed 2019162 +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))))