Average Error: 3.6 → 1.8
Time: 14.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z} \cdot t}{y \cdot 3}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z} \cdot t}{y \cdot 3}
double f(double x, double y, double z, double t) {
        double r513728 = x;
        double r513729 = y;
        double r513730 = z;
        double r513731 = 3.0;
        double r513732 = r513730 * r513731;
        double r513733 = r513729 / r513732;
        double r513734 = r513728 - r513733;
        double r513735 = t;
        double r513736 = r513732 * r513729;
        double r513737 = r513735 / r513736;
        double r513738 = r513734 + r513737;
        return r513738;
}
↓
double f(double x, double y, double z, double t) {
        double r513739 = x;
        double r513740 = y;
        double r513741 = z;
        double r513742 = 3.0;
        double r513743 = r513741 * r513742;
        double r513744 = r513740 / r513743;
        double r513745 = r513739 - r513744;
        double r513746 = 1.0;
        double r513747 = r513746 / r513741;
        double r513748 = t;
        double r513749 = r513747 * r513748;
        double r513750 = r513740 * r513742;
        double r513751 = r513749 / r513750;
        double r513752 = r513745 + r513751;
        return r513752;
}

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
Target1.8
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.6

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

  3. Applied associate-/r*1.8

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

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

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

  6. Applied times-frac1.8

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

  8. Applied associate-*r/1.8

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

  9. Applied associate-/l/1.8

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

  10. Final simplification1.8

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))