Average Error: 4.0 → 1.8
Time: 5.8s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}
double f(double x, double y, double z, double t) {
        double r724788 = x;
        double r724789 = y;
        double r724790 = z;
        double r724791 = 3.0;
        double r724792 = r724790 * r724791;
        double r724793 = r724789 / r724792;
        double r724794 = r724788 - r724793;
        double r724795 = t;
        double r724796 = r724792 * r724789;
        double r724797 = r724795 / r724796;
        double r724798 = r724794 + r724797;
        return r724798;
}
↓
double f(double x, double y, double z, double t) {
        double r724799 = x;
        double r724800 = 1.0;
        double r724801 = z;
        double r724802 = 3.0;
        double r724803 = r724801 * r724802;
        double r724804 = y;
        double r724805 = r724803 / r724804;
        double r724806 = r724800 / r724805;
        double r724807 = r724799 - r724806;
        double r724808 = t;
        double r724809 = r724808 / r724803;
        double r724810 = r724809 / r724804;
        double r724811 = r724807 + r724810;
        return r724811;
}

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

Original4.0
Target1.7
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 4.0

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

  3. Applied associate-/r*1.7

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

  5. Applied clear-num1.8

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

  6. Final simplification1.8

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

Reproduce

herbie shell --seed 2020045 
(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))))