Average Error: 3.7 → 1.7
Time: 23.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\frac{\frac{\frac{t}{3}}{z}}{y} + \left(\left(\frac{\frac{y}{3}}{z} + \left(-\frac{\frac{y}{3}}{z}\right)\right) + \left(x - \frac{\frac{y}{3}}{z}\right)\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\frac{\frac{\frac{t}{3}}{z}}{y} + \left(\left(\frac{\frac{y}{3}}{z} + \left(-\frac{\frac{y}{3}}{z}\right)\right) + \left(x - \frac{\frac{y}{3}}{z}\right)\right)
double f(double x, double y, double z, double t) {
        double r30959908 = x;
        double r30959909 = y;
        double r30959910 = z;
        double r30959911 = 3.0;
        double r30959912 = r30959910 * r30959911;
        double r30959913 = r30959909 / r30959912;
        double r30959914 = r30959908 - r30959913;
        double r30959915 = t;
        double r30959916 = r30959912 * r30959909;
        double r30959917 = r30959915 / r30959916;
        double r30959918 = r30959914 + r30959917;
        return r30959918;
}
↓
double f(double x, double y, double z, double t) {
        double r30959919 = t;
        double r30959920 = 3.0;
        double r30959921 = r30959919 / r30959920;
        double r30959922 = z;
        double r30959923 = r30959921 / r30959922;
        double r30959924 = y;
        double r30959925 = r30959923 / r30959924;
        double r30959926 = r30959924 / r30959920;
        double r30959927 = r30959926 / r30959922;
        double r30959928 = -r30959927;
        double r30959929 = r30959927 + r30959928;
        double r30959930 = x;
        double r30959931 = r30959930 - r30959927;
        double r30959932 = r30959929 + r30959931;
        double r30959933 = r30959925 + r30959932;
        return r30959933;
}

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

Enter valid numbers for all inputs

Target

Original3.7
Target1.7
Herbie1.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.7

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  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 associate-/r*1.7

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

  7. Applied *-un-lft-identity1.7

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

  8. Applied associate-/r*1.7

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

  9. Simplified1.7

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

  11. Applied *-un-lft-identity1.7

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

  12. Applied times-frac1.7

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

  13. Applied add-sqr-sqrt33.2

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

  14. Applied prod-diff33.2

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

  15. Simplified1.7

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

  16. Simplified1.7

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

  17. Final simplification1.7

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

Reproduce

herbie shell --seed 2019169 +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))))