Average Error: 29.6 → 29.6
Time: 7.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r72965 = x;
        double r72966 = y;
        double r72967 = r72965 * r72966;
        double r72968 = z;
        double r72969 = r72967 + r72968;
        double r72970 = r72969 * r72966;
        double r72971 = 27464.7644705;
        double r72972 = r72970 + r72971;
        double r72973 = r72972 * r72966;
        double r72974 = 230661.510616;
        double r72975 = r72973 + r72974;
        double r72976 = r72975 * r72966;
        double r72977 = t;
        double r72978 = r72976 + r72977;
        double r72979 = a;
        double r72980 = r72966 + r72979;
        double r72981 = r72980 * r72966;
        double r72982 = b;
        double r72983 = r72981 + r72982;
        double r72984 = r72983 * r72966;
        double r72985 = c;
        double r72986 = r72984 + r72985;
        double r72987 = r72986 * r72966;
        double r72988 = i;
        double r72989 = r72987 + r72988;
        double r72990 = r72978 / r72989;
        return r72990;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r72991 = x;
        double r72992 = y;
        double r72993 = r72991 * r72992;
        double r72994 = z;
        double r72995 = r72993 + r72994;
        double r72996 = r72995 * r72992;
        double r72997 = 27464.7644705;
        double r72998 = r72996 + r72997;
        double r72999 = r72998 * r72992;
        double r73000 = 230661.510616;
        double r73001 = r72999 + r73000;
        double r73002 = r73001 * r72992;
        double r73003 = t;
        double r73004 = r73002 + r73003;
        double r73005 = a;
        double r73006 = r72992 + r73005;
        double r73007 = r73006 * r72992;
        double r73008 = b;
        double r73009 = r73007 + r73008;
        double r73010 = r73009 * r72992;
        double r73011 = c;
        double r73012 = r73010 + r73011;
        double r73013 = r73012 * r72992;
        double r73014 = i;
        double r73015 = r73013 + r73014;
        double r73016 = r73004 / r73015;
        return r73016;
}

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 29.6

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied clear-num29.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity29.8

    \[\leadsto \frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right)}}}\]

  6. Applied *-un-lft-identity29.8

    \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right)}}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right)}}\]

  7. Applied times-frac29.8

    \[\leadsto \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  8. Applied add-cube-cbrt29.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]

  9. Applied times-frac29.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  10. Simplified29.8

    \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]

  11. Simplified29.6

    \[\leadsto 1 \cdot \color{blue}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  12. Final simplification29.6

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))