Average Error: 3.5 → 1.6
Time: 17.8s
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 r34205693 = x;
        double r34205694 = y;
        double r34205695 = z;
        double r34205696 = 3.0;
        double r34205697 = r34205695 * r34205696;
        double r34205698 = r34205694 / r34205697;
        double r34205699 = r34205693 - r34205698;
        double r34205700 = t;
        double r34205701 = r34205697 * r34205694;
        double r34205702 = r34205700 / r34205701;
        double r34205703 = r34205699 + r34205702;
        return r34205703;
}
↓
double f(double x, double y, double z, double t) {
        double r34205704 = t;
        double r34205705 = 3.0;
        double r34205706 = r34205704 / r34205705;
        double r34205707 = 1.0;
        double r34205708 = z;
        double r34205709 = r34205707 / r34205708;
        double r34205710 = r34205706 * r34205709;
        double r34205711 = y;
        double r34205712 = r34205710 / r34205711;
        double r34205713 = x;
        double r34205714 = r34205711 / r34205705;
        double r34205715 = r34205709 * r34205714;
        double r34205716 = r34205713 - r34205715;
        double r34205717 = r34205712 + r34205716;
        return r34205717;
}

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))))