Average Error: 4.0 → 1.8
Time: 7.1s
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 r682920 = x;
        double r682921 = y;
        double r682922 = z;
        double r682923 = 3.0;
        double r682924 = r682922 * r682923;
        double r682925 = r682921 / r682924;
        double r682926 = r682920 - r682925;
        double r682927 = t;
        double r682928 = r682924 * r682921;
        double r682929 = r682927 / r682928;
        double r682930 = r682926 + r682929;
        return r682930;
}
↓
double f(double x, double y, double z, double t) {
        double r682931 = x;
        double r682932 = 1.0;
        double r682933 = z;
        double r682934 = 3.0;
        double r682935 = r682933 * r682934;
        double r682936 = y;
        double r682937 = r682935 / r682936;
        double r682938 = r682932 / r682937;
        double r682939 = r682931 - r682938;
        double r682940 = t;
        double r682941 = r682940 / r682935;
        double r682942 = r682941 / r682936;
        double r682943 = r682939 + r682942;
        return r682943;
}

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))))