Average Error: 3.8 → 1.9
Time: 18.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\frac{\frac{t}{3} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\frac{\frac{t}{3} \cdot \frac{1}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)
double f(double x, double y, double z, double t) {
        double r21116865 = x;
        double r21116866 = y;
        double r21116867 = z;
        double r21116868 = 3.0;
        double r21116869 = r21116867 * r21116868;
        double r21116870 = r21116866 / r21116869;
        double r21116871 = r21116865 - r21116870;
        double r21116872 = t;
        double r21116873 = r21116869 * r21116866;
        double r21116874 = r21116872 / r21116873;
        double r21116875 = r21116871 + r21116874;
        return r21116875;
}
↓
double f(double x, double y, double z, double t) {
        double r21116876 = t;
        double r21116877 = 3.0;
        double r21116878 = r21116876 / r21116877;
        double r21116879 = 1.0;
        double r21116880 = z;
        double r21116881 = r21116879 / r21116880;
        double r21116882 = r21116878 * r21116881;
        double r21116883 = y;
        double r21116884 = r21116882 / r21116883;
        double r21116885 = x;
        double r21116886 = r21116883 / r21116877;
        double r21116887 = r21116881 * r21116886;
        double r21116888 = r21116885 - r21116887;
        double r21116889 = r21116884 + r21116888;
        return r21116889;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

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Target

Original3.8
Target1.9
Herbie1.9
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.8

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

  3. Applied associate-/r*1.9

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

  5. Applied *-un-lft-identity1.9

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

  6. Applied times-frac1.9

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

  8. Applied *-un-lft-identity1.9

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

  9. Applied times-frac1.9

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

  10. Final simplification1.9

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

Reproduce

herbie shell --seed 2019171 
(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))))