Average Error: 0.1 → 0.3
Time: 17.0s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot x + \left(\sqrt{\sqrt{z}} \cdot y\right) \cdot \left(\sqrt{\sqrt{z}} \cdot \frac{1}{2}\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot x + \left(\sqrt{\sqrt{z}} \cdot y\right) \cdot \left(\sqrt{\sqrt{z}} \cdot \frac{1}{2}\right)
double f(double x, double y, double z) {
        double r9320889 = 1.0;
        double r9320890 = 2.0;
        double r9320891 = r9320889 / r9320890;
        double r9320892 = x;
        double r9320893 = y;
        double r9320894 = z;
        double r9320895 = sqrt(r9320894);
        double r9320896 = r9320893 * r9320895;
        double r9320897 = r9320892 + r9320896;
        double r9320898 = r9320891 * r9320897;
        return r9320898;
}
↓
double f(double x, double y, double z) {
        double r9320899 = 1.0;
        double r9320900 = 2.0;
        double r9320901 = r9320899 / r9320900;
        double r9320902 = x;
        double r9320903 = r9320901 * r9320902;
        double r9320904 = z;
        double r9320905 = sqrt(r9320904);
        double r9320906 = sqrt(r9320905);
        double r9320907 = y;
        double r9320908 = r9320906 * r9320907;
        double r9320909 = r9320906 * r9320901;
        double r9320910 = r9320908 * r9320909;
        double r9320911 = r9320903 + r9320910;
        return r9320911;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \sqrt{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}\right)\]

  4. Applied sqrt-prod0.3

    \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \color{blue}{\left(\sqrt{\sqrt{z}} \cdot \sqrt{\sqrt{z}}\right)}\right)\]

  5. Applied associate-*r*0.3

    \[\leadsto \frac{1}{2} \cdot \left(x + \color{blue}{\left(y \cdot \sqrt{\sqrt{z}}\right) \cdot \sqrt{\sqrt{z}}}\right)\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.3

    \[\leadsto \frac{1}{2} \cdot \left(x + \left(y \cdot \sqrt{\sqrt{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}\right) \cdot \sqrt{\sqrt{z}}\right)\]

  8. Applied sqrt-prod0.3

    \[\leadsto \frac{1}{2} \cdot \left(x + \left(y \cdot \sqrt{\color{blue}{\sqrt{\sqrt{z}} \cdot \sqrt{\sqrt{z}}}}\right) \cdot \sqrt{\sqrt{z}}\right)\]

  9. Applied sqrt-prod0.4

    \[\leadsto \frac{1}{2} \cdot \left(x + \left(y \cdot \color{blue}{\left(\sqrt{\sqrt{\sqrt{z}}} \cdot \sqrt{\sqrt{\sqrt{z}}}\right)}\right) \cdot \sqrt{\sqrt{z}}\right)\]

  10. Applied associate-*r*0.4

    \[\leadsto \frac{1}{2} \cdot \left(x + \color{blue}{\left(\left(y \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right)} \cdot \sqrt{\sqrt{z}}\right)\]
  11. Using strategy rm

  12. Applied add-sqr-sqrt0.4

    \[\leadsto \frac{1}{2} \cdot \left(x + \left(\left(y \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}}\right)\]

  13. Applied sqrt-prod0.4

    \[\leadsto \frac{1}{2} \cdot \left(x + \left(\left(y \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\color{blue}{\sqrt{\sqrt{z}} \cdot \sqrt{\sqrt{z}}}}\right)\]

  14. Applied sqrt-prod0.5

    \[\leadsto \frac{1}{2} \cdot \left(x + \left(\left(y \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \color{blue}{\left(\sqrt{\sqrt{\sqrt{z}}} \cdot \sqrt{\sqrt{\sqrt{z}}}\right)}\right)\]

  15. Applied associate-*r*0.5

    \[\leadsto \frac{1}{2} \cdot \left(x + \color{blue}{\left(\left(\left(y \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}}\right)\]

  16. Simplified0.4

    \[\leadsto \frac{1}{2} \cdot \left(x + \color{blue}{\left(\left(y \cdot \sqrt{\sqrt{z}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right)} \cdot \sqrt{\sqrt{\sqrt{z}}}\right)\]
  17. Using strategy rm

  18. Applied distribute-lft-in0.4

    \[\leadsto \color{blue}{\frac{1}{2} \cdot x + \frac{1}{2} \cdot \left(\left(\left(y \cdot \sqrt{\sqrt{z}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right) \cdot \sqrt{\sqrt{\sqrt{z}}}\right)}\]

  19. Simplified0.3

    \[\leadsto \frac{1}{2} \cdot x + \color{blue}{\left(\sqrt{\sqrt{z}} \cdot y\right) \cdot \left(\sqrt{\sqrt{z}} \cdot \frac{1}{2}\right)}\]

  20. Final simplification0.3

    \[\leadsto \frac{1}{2} \cdot x + \left(\sqrt{\sqrt{z}} \cdot y\right) \cdot \left(\sqrt{\sqrt{z}} \cdot \frac{1}{2}\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))