Average Error: 29.1 → 29.1
Time: 4.7m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right) + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right) + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r35132610 = x;
        double r35132611 = y;
        double r35132612 = r35132610 * r35132611;
        double r35132613 = z;
        double r35132614 = r35132612 + r35132613;
        double r35132615 = r35132614 * r35132611;
        double r35132616 = 27464.7644705;
        double r35132617 = r35132615 + r35132616;
        double r35132618 = r35132617 * r35132611;
        double r35132619 = 230661.510616;
        double r35132620 = r35132618 + r35132619;
        double r35132621 = r35132620 * r35132611;
        double r35132622 = t;
        double r35132623 = r35132621 + r35132622;
        double r35132624 = a;
        double r35132625 = r35132611 + r35132624;
        double r35132626 = r35132625 * r35132611;
        double r35132627 = b;
        double r35132628 = r35132626 + r35132627;
        double r35132629 = r35132628 * r35132611;
        double r35132630 = c;
        double r35132631 = r35132629 + r35132630;
        double r35132632 = r35132631 * r35132611;
        double r35132633 = i;
        double r35132634 = r35132632 + r35132633;
        double r35132635 = r35132623 / r35132634;
        return r35132635;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r35132636 = y;
        double r35132637 = 27464.7644705;
        double r35132638 = x;
        double r35132639 = r35132638 * r35132636;
        double r35132640 = z;
        double r35132641 = r35132639 + r35132640;
        double r35132642 = r35132636 * r35132641;
        double r35132643 = r35132637 + r35132642;
        double r35132644 = r35132636 * r35132643;
        double r35132645 = 230661.510616;
        double r35132646 = r35132644 + r35132645;
        double r35132647 = r35132646 * r35132636;
        double r35132648 = t;
        double r35132649 = r35132647 + r35132648;
        double r35132650 = c;
        double r35132651 = b;
        double r35132652 = a;
        double r35132653 = r35132636 + r35132652;
        double r35132654 = r35132636 * r35132653;
        double r35132655 = r35132651 + r35132654;
        double r35132656 = r35132636 * r35132655;
        double r35132657 = r35132650 + r35132656;
        double r35132658 = r35132636 * r35132657;
        double r35132659 = i;
        double r35132660 = r35132658 + r35132659;
        double r35132661 = r35132649 / r35132660;
        return r35132661;
}

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 29.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity29.1

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-/l*29.3

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  5. Using strategy rm

  6. Applied div-inv29.4

    \[\leadsto \frac{1}{\color{blue}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  7. Applied associate-/r*29.2

    \[\leadsto \color{blue}{\frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity29.2

    \[\leadsto \frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{1}{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}}}\]

  10. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}}\]

  11. Applied times-frac29.2

    \[\leadsto \frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  12. Applied div-inv29.2

    \[\leadsto \frac{\color{blue}{1 \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\]

  13. Applied times-frac29.2

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1}} \cdot \frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{\sqrt[3]{1}}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  14. Simplified29.2

    \[\leadsto \color{blue}{1} \cdot \frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{\sqrt[3]{1}}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\]

  15. Simplified29.1

    \[\leadsto 1 \cdot \color{blue}{\frac{y \cdot \left(230661.510616 + \left(27464.7644705 + y \cdot \left(z + x \cdot y\right)\right) \cdot y\right) + t}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}}\]

  16. Final simplification29.1

    \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right) + 230661.510616\right) \cdot y + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))