Average Error: 0.1 → 0.1
Time: 38.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c} \cdot \sqrt{\sqrt{\sqrt{c}}}\right) + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c} \cdot \sqrt{\sqrt{\sqrt{c}}}\right) + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r72981 = x;
        double r72982 = y;
        double r72983 = log(r72982);
        double r72984 = r72981 * r72983;
        double r72985 = z;
        double r72986 = r72984 + r72985;
        double r72987 = t;
        double r72988 = r72986 + r72987;
        double r72989 = a;
        double r72990 = r72988 + r72989;
        double r72991 = b;
        double r72992 = 0.5;
        double r72993 = r72991 - r72992;
        double r72994 = c;
        double r72995 = log(r72994);
        double r72996 = r72993 * r72995;
        double r72997 = r72990 + r72996;
        double r72998 = i;
        double r72999 = r72982 * r72998;
        double r73000 = r72997 + r72999;
        return r73000;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73001 = x;
        double r73002 = y;
        double r73003 = log(r73002);
        double r73004 = r73001 * r73003;
        double r73005 = z;
        double r73006 = r73004 + r73005;
        double r73007 = t;
        double r73008 = r73006 + r73007;
        double r73009 = a;
        double r73010 = r73008 + r73009;
        double r73011 = b;
        double r73012 = 0.5;
        double r73013 = r73011 - r73012;
        double r73014 = c;
        double r73015 = sqrt(r73014);
        double r73016 = sqrt(r73015);
        double r73017 = sqrt(r73016);
        double r73018 = r73015 * r73017;
        double r73019 = log(r73018);
        double r73020 = log(r73017);
        double r73021 = r73019 + r73020;
        double r73022 = r73013 * r73021;
        double r73023 = r73010 + r73022;
        double r73024 = log(r73016);
        double r73025 = r73013 * r73024;
        double r73026 = r73023 + r73025;
        double r73027 = i;
        double r73028 = r73002 * r73027;
        double r73029 = r73026 + r73028;
        return r73029;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \color{blue}{\left(\sqrt{c} \cdot \sqrt{c}\right)}\right) + y \cdot i\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt{c}\right) + \log \left(\sqrt{c}\right)\right)}\right) + y \cdot i\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(\left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right)}\right) + y \cdot i\]

  6. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right)} + y \cdot i\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\color{blue}{\sqrt{c} \cdot \sqrt{c}}}\right)\right) + y \cdot i\]

  9. Applied sqrt-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right) + \left(b - 0.5\right) \cdot \log \color{blue}{\left(\sqrt{\sqrt{c}} \cdot \sqrt{\sqrt{c}}\right)}\right) + y \cdot i\]

  10. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right) + \left(b - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt{\sqrt{c}}\right) + \log \left(\sqrt{\sqrt{c}}\right)\right)}\right) + y \cdot i\]

  11. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right) + \color{blue}{\left(\left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right)}\right) + y \cdot i\]

  12. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right)} + y \cdot i\]

  13. Simplified0.1

    \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c}\right) + \log \left(\sqrt{\sqrt{c}}\right)\right)\right)} + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]
  14. Using strategy rm

  15. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c}\right) + \log \left(\sqrt{\sqrt{\color{blue}{\sqrt{c} \cdot \sqrt{c}}}}\right)\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]

  16. Applied sqrt-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c}\right) + \log \left(\sqrt{\color{blue}{\sqrt{\sqrt{c}} \cdot \sqrt{\sqrt{c}}}}\right)\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]

  17. Applied sqrt-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c}\right) + \log \color{blue}{\left(\sqrt{\sqrt{\sqrt{c}}} \cdot \sqrt{\sqrt{\sqrt{c}}}\right)}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]

  18. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c}\right) + \color{blue}{\left(\log \left(\sqrt{\sqrt{\sqrt{c}}}\right) + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right)}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]

  19. Applied associate-+r+0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \color{blue}{\left(\left(\log \left(\sqrt{c}\right) + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right) + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right)}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]
  20. Using strategy rm

  21. Applied sum-log0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\color{blue}{\log \left(\sqrt{c} \cdot \sqrt{\sqrt{\sqrt{c}}}\right)} + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]

  22. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \left(\log \left(\sqrt{c} \cdot \sqrt{\sqrt{\sqrt{c}}}\right) + \log \left(\sqrt{\sqrt{\sqrt{c}}}\right)\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt{\sqrt{c}}\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))