Average Error: 0.1 → 0.2
Time: 43.4s
Precision: 64
\[x - \frac{3}{8} \cdot y\]
↓
\[\frac{3}{8} \cdot \left(\left(-y\right) + y\right) + \left(x - \frac{\frac{1}{\sqrt{\sqrt{8}}}}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{8}}{3}}}\right)\]
x - \frac{3}{8} \cdot y
↓
\frac{3}{8} \cdot \left(\left(-y\right) + y\right) + \left(x - \frac{\frac{1}{\sqrt{\sqrt{8}}}}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{8}}{3}}}\right)
double f(double x, double y) {
        double r8587819 = x;
        double r8587820 = 3.0;
        double r8587821 = 8.0;
        double r8587822 = r8587820 / r8587821;
        double r8587823 = y;
        double r8587824 = r8587822 * r8587823;
        double r8587825 = r8587819 - r8587824;
        return r8587825;
}
↓
double f(double x, double y) {
        double r8587826 = 3.0;
        double r8587827 = 8.0;
        double r8587828 = r8587826 / r8587827;
        double r8587829 = y;
        double r8587830 = -r8587829;
        double r8587831 = r8587830 + r8587829;
        double r8587832 = r8587828 * r8587831;
        double r8587833 = x;
        double r8587834 = 1.0;
        double r8587835 = sqrt(r8587827);
        double r8587836 = sqrt(r8587835);
        double r8587837 = r8587834 / r8587836;
        double r8587838 = r8587827 / r8587826;
        double r8587839 = sqrt(r8587838);
        double r8587840 = r8587837 / r8587839;
        double r8587841 = r8587835 / r8587826;
        double r8587842 = sqrt(r8587841);
        double r8587843 = r8587829 / r8587842;
        double r8587844 = r8587840 * r8587843;
        double r8587845 = r8587833 - r8587844;
        double r8587846 = r8587832 + r8587845;
        return r8587846;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x - \frac{3}{8} \cdot y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} - \frac{3}{8} \cdot y\]

  4. Applied prod-diff0.8

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, -y \cdot \frac{3}{8}\right) + \mathsf{fma}\left(-y, \frac{3}{8}, y \cdot \frac{3}{8}\right)}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{\left(x - \frac{y}{\frac{8}{3}}\right)} + \mathsf{fma}\left(-y, \frac{3}{8}, y \cdot \frac{3}{8}\right)\]

  6. Simplified0.2

    \[\leadsto \left(x - \frac{y}{\frac{8}{3}}\right) + \color{blue}{\frac{3}{8} \cdot \left(\left(-y\right) + y\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.2

    \[\leadsto \left(x - \frac{y}{\color{blue}{\sqrt{\frac{8}{3}} \cdot \sqrt{\frac{8}{3}}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  9. Applied *-un-lft-identity0.2

    \[\leadsto \left(x - \frac{\color{blue}{1 \cdot y}}{\sqrt{\frac{8}{3}} \cdot \sqrt{\frac{8}{3}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  10. Applied times-frac0.3

    \[\leadsto \left(x - \color{blue}{\frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\frac{8}{3}}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]
  11. Using strategy rm

  12. Applied *-un-lft-identity0.3

    \[\leadsto \left(x - \frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\frac{8}{\color{blue}{1 \cdot 3}}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  13. Applied add-sqr-sqrt0.6

    \[\leadsto \left(x - \frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\frac{\color{blue}{\sqrt{8} \cdot \sqrt{8}}}{1 \cdot 3}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  14. Applied times-frac0.3

    \[\leadsto \left(x - \frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\color{blue}{\frac{\sqrt{8}}{1} \cdot \frac{\sqrt{8}}{3}}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  15. Applied sqrt-prod0.6

    \[\leadsto \left(x - \frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\color{blue}{\sqrt{\frac{\sqrt{8}}{1}} \cdot \sqrt{\frac{\sqrt{8}}{3}}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  16. Applied *-un-lft-identity0.6

    \[\leadsto \left(x - \frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{\color{blue}{1 \cdot y}}{\sqrt{\frac{\sqrt{8}}{1}} \cdot \sqrt{\frac{\sqrt{8}}{3}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  17. Applied times-frac0.5

    \[\leadsto \left(x - \frac{1}{\sqrt{\frac{8}{3}}} \cdot \color{blue}{\left(\frac{1}{\sqrt{\frac{\sqrt{8}}{1}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{8}}{3}}}\right)}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  18. Applied associate-*r*0.6

    \[\leadsto \left(x - \color{blue}{\left(\frac{1}{\sqrt{\frac{8}{3}}} \cdot \frac{1}{\sqrt{\frac{\sqrt{8}}{1}}}\right) \cdot \frac{y}{\sqrt{\frac{\sqrt{8}}{3}}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  19. Simplified0.2

    \[\leadsto \left(x - \color{blue}{\frac{\frac{1}{\sqrt{\sqrt{8}}}}{\sqrt{\frac{8}{3}}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{8}}{3}}}\right) + \frac{3}{8} \cdot \left(\left(-y\right) + y\right)\]

  20. Final simplification0.2

    \[\leadsto \frac{3}{8} \cdot \left(\left(-y\right) + y\right) + \left(x - \frac{\frac{1}{\sqrt{\sqrt{8}}}}{\sqrt{\frac{8}{3}}} \cdot \frac{y}{\sqrt{\frac{\sqrt{8}}{3}}}\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  (- x (* (/ 3.0 8.0) y)))