Average Error: 28.7 → 28.8
Time: 8.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{y}\right) + c\right) \cdot y + i}\]
\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(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{y}\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59553 = x;
        double r59554 = y;
        double r59555 = r59553 * r59554;
        double r59556 = z;
        double r59557 = r59555 + r59556;
        double r59558 = r59557 * r59554;
        double r59559 = 27464.7644705;
        double r59560 = r59558 + r59559;
        double r59561 = r59560 * r59554;
        double r59562 = 230661.510616;
        double r59563 = r59561 + r59562;
        double r59564 = r59563 * r59554;
        double r59565 = t;
        double r59566 = r59564 + r59565;
        double r59567 = a;
        double r59568 = r59554 + r59567;
        double r59569 = r59568 * r59554;
        double r59570 = b;
        double r59571 = r59569 + r59570;
        double r59572 = r59571 * r59554;
        double r59573 = c;
        double r59574 = r59572 + r59573;
        double r59575 = r59574 * r59554;
        double r59576 = i;
        double r59577 = r59575 + r59576;
        double r59578 = r59566 / r59577;
        return r59578;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59579 = x;
        double r59580 = y;
        double r59581 = r59579 * r59580;
        double r59582 = z;
        double r59583 = r59581 + r59582;
        double r59584 = r59583 * r59580;
        double r59585 = 27464.7644705;
        double r59586 = r59584 + r59585;
        double r59587 = r59586 * r59580;
        double r59588 = 230661.510616;
        double r59589 = r59587 + r59588;
        double r59590 = r59589 * r59580;
        double r59591 = t;
        double r59592 = r59590 + r59591;
        double r59593 = a;
        double r59594 = r59580 + r59593;
        double r59595 = r59594 * r59580;
        double r59596 = b;
        double r59597 = r59595 + r59596;
        double r59598 = r59597 * r59580;
        double r59599 = cbrt(r59598);
        double r59600 = r59599 * r59599;
        double r59601 = cbrt(r59597);
        double r59602 = cbrt(r59580);
        double r59603 = r59601 * r59602;
        double r59604 = r59600 * r59603;
        double r59605 = c;
        double r59606 = r59604 + r59605;
        double r59607 = r59606 * r59580;
        double r59608 = i;
        double r59609 = r59607 + r59608;
        double r59610 = r59592 / r59609;
        return r59610;
}

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 28.7

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

  3. Applied add-cube-cbrt28.8

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

  5. Applied cbrt-prod28.8

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

  6. Final simplification28.8

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))