Average Error: 28.6 → 28.7
Time: 37.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y, y + a, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y, y + a, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3654616 = x;
        double r3654617 = y;
        double r3654618 = r3654616 * r3654617;
        double r3654619 = z;
        double r3654620 = r3654618 + r3654619;
        double r3654621 = r3654620 * r3654617;
        double r3654622 = 27464.7644705;
        double r3654623 = r3654621 + r3654622;
        double r3654624 = r3654623 * r3654617;
        double r3654625 = 230661.510616;
        double r3654626 = r3654624 + r3654625;
        double r3654627 = r3654626 * r3654617;
        double r3654628 = t;
        double r3654629 = r3654627 + r3654628;
        double r3654630 = a;
        double r3654631 = r3654617 + r3654630;
        double r3654632 = r3654631 * r3654617;
        double r3654633 = b;
        double r3654634 = r3654632 + r3654633;
        double r3654635 = r3654634 * r3654617;
        double r3654636 = c;
        double r3654637 = r3654635 + r3654636;
        double r3654638 = r3654637 * r3654617;
        double r3654639 = i;
        double r3654640 = r3654638 + r3654639;
        double r3654641 = r3654629 / r3654640;
        return r3654641;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3654642 = t;
        double r3654643 = y;
        double r3654644 = z;
        double r3654645 = x;
        double r3654646 = r3654645 * r3654643;
        double r3654647 = r3654644 + r3654646;
        double r3654648 = r3654643 * r3654647;
        double r3654649 = 27464.7644705;
        double r3654650 = r3654648 + r3654649;
        double r3654651 = r3654643 * r3654650;
        double r3654652 = 230661.510616;
        double r3654653 = r3654651 + r3654652;
        double r3654654 = r3654653 * r3654643;
        double r3654655 = r3654642 + r3654654;
        double r3654656 = i;
        double r3654657 = c;
        double r3654658 = a;
        double r3654659 = r3654643 + r3654658;
        double r3654660 = b;
        double r3654661 = fma(r3654643, r3654659, r3654660);
        double r3654662 = cbrt(r3654643);
        double r3654663 = r3654662 * r3654662;
        double r3654664 = r3654661 * r3654663;
        double r3654665 = r3654664 * r3654662;
        double r3654666 = r3654657 + r3654665;
        double r3654667 = r3654643 * r3654666;
        double r3654668 = r3654656 + r3654667;
        double r3654669 = r3654655 / r3654668;
        return r3654669;
}

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

Derivation

  1. Initial program 28.6

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

  3. Applied add-cube-cbrt28.7

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

  4. Applied associate-*r*28.7

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

  5. Simplified28.7

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

  6. Final simplification28.7

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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)))