Average Error: 3.6 → 1.6
Time: 19.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{\frac{t}{z}}{3.0}}{y} + \left(x - \frac{\frac{y}{z}}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{\frac{t}{z}}{3.0}}{y} + \left(x - \frac{\frac{y}{z}}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r37584729 = x;
        double r37584730 = y;
        double r37584731 = z;
        double r37584732 = 3.0;
        double r37584733 = r37584731 * r37584732;
        double r37584734 = r37584730 / r37584733;
        double r37584735 = r37584729 - r37584734;
        double r37584736 = t;
        double r37584737 = r37584733 * r37584730;
        double r37584738 = r37584736 / r37584737;
        double r37584739 = r37584735 + r37584738;
        return r37584739;
}
↓
double f(double x, double y, double z, double t) {
        double r37584740 = t;
        double r37584741 = z;
        double r37584742 = r37584740 / r37584741;
        double r37584743 = 3.0;
        double r37584744 = r37584742 / r37584743;
        double r37584745 = y;
        double r37584746 = r37584744 / r37584745;
        double r37584747 = x;
        double r37584748 = r37584745 / r37584741;
        double r37584749 = r37584748 / r37584743;
        double r37584750 = r37584747 - r37584749;
        double r37584751 = r37584746 + r37584750;
        return r37584751;
}

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

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

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

  6. Applied associate-/r*1.6

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

  7. Simplified1.6

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

  9. Applied associate-/r*1.6

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

  10. Final simplification1.6

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

Reproduce

herbie shell --seed 2019162 
(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))))