Average Error: 3.5 → 1.6
Time: 13.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\frac{\frac{t}{3.0} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3.0}\right)
double f(double x, double y, double z, double t) {
        double r27474680 = x;
        double r27474681 = y;
        double r27474682 = z;
        double r27474683 = 3.0;
        double r27474684 = r27474682 * r27474683;
        double r27474685 = r27474681 / r27474684;
        double r27474686 = r27474680 - r27474685;
        double r27474687 = t;
        double r27474688 = r27474684 * r27474681;
        double r27474689 = r27474687 / r27474688;
        double r27474690 = r27474686 + r27474689;
        return r27474690;
}
↓
double f(double x, double y, double z, double t) {
        double r27474691 = t;
        double r27474692 = 3.0;
        double r27474693 = r27474691 / r27474692;
        double r27474694 = 1.0;
        double r27474695 = z;
        double r27474696 = r27474694 / r27474695;
        double r27474697 = r27474693 * r27474696;
        double r27474698 = y;
        double r27474699 = r27474697 / r27474698;
        double r27474700 = x;
        double r27474701 = r27474698 / r27474692;
        double r27474702 = r27474696 * r27474701;
        double r27474703 = r27474700 - r27474702;
        double r27474704 = r27474699 + r27474703;
        return r27474704;
}

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

Original3.5
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 3.5

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

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

  6. Applied times-frac1.6

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

  8. Applied *-un-lft-identity1.6

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

  9. Applied times-frac1.6

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

  10. Final simplification1.6

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

Reproduce

herbie shell --seed 2019163 +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))))