Average Error: 3.5 → 1.6
Time: 15.1s
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 r31155629 = x;
        double r31155630 = y;
        double r31155631 = z;
        double r31155632 = 3.0;
        double r31155633 = r31155631 * r31155632;
        double r31155634 = r31155630 / r31155633;
        double r31155635 = r31155629 - r31155634;
        double r31155636 = t;
        double r31155637 = r31155633 * r31155630;
        double r31155638 = r31155636 / r31155637;
        double r31155639 = r31155635 + r31155638;
        return r31155639;
}
↓
double f(double x, double y, double z, double t) {
        double r31155640 = t;
        double r31155641 = 3.0;
        double r31155642 = r31155640 / r31155641;
        double r31155643 = 1.0;
        double r31155644 = z;
        double r31155645 = r31155643 / r31155644;
        double r31155646 = r31155642 * r31155645;
        double r31155647 = y;
        double r31155648 = r31155646 / r31155647;
        double r31155649 = x;
        double r31155650 = r31155647 / r31155641;
        double r31155651 = r31155645 * r31155650;
        double r31155652 = r31155649 - r31155651;
        double r31155653 = r31155648 + r31155652;
        return r31155653;
}

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 
(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))))