Average Error: 28.6 → 28.7
Time: 36.2s
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 r2510433 = x;
        double r2510434 = y;
        double r2510435 = r2510433 * r2510434;
        double r2510436 = z;
        double r2510437 = r2510435 + r2510436;
        double r2510438 = r2510437 * r2510434;
        double r2510439 = 27464.7644705;
        double r2510440 = r2510438 + r2510439;
        double r2510441 = r2510440 * r2510434;
        double r2510442 = 230661.510616;
        double r2510443 = r2510441 + r2510442;
        double r2510444 = r2510443 * r2510434;
        double r2510445 = t;
        double r2510446 = r2510444 + r2510445;
        double r2510447 = a;
        double r2510448 = r2510434 + r2510447;
        double r2510449 = r2510448 * r2510434;
        double r2510450 = b;
        double r2510451 = r2510449 + r2510450;
        double r2510452 = r2510451 * r2510434;
        double r2510453 = c;
        double r2510454 = r2510452 + r2510453;
        double r2510455 = r2510454 * r2510434;
        double r2510456 = i;
        double r2510457 = r2510455 + r2510456;
        double r2510458 = r2510446 / r2510457;
        return r2510458;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2510459 = t;
        double r2510460 = y;
        double r2510461 = z;
        double r2510462 = x;
        double r2510463 = r2510462 * r2510460;
        double r2510464 = r2510461 + r2510463;
        double r2510465 = r2510460 * r2510464;
        double r2510466 = 27464.7644705;
        double r2510467 = r2510465 + r2510466;
        double r2510468 = r2510460 * r2510467;
        double r2510469 = 230661.510616;
        double r2510470 = r2510468 + r2510469;
        double r2510471 = r2510470 * r2510460;
        double r2510472 = r2510459 + r2510471;
        double r2510473 = i;
        double r2510474 = c;
        double r2510475 = a;
        double r2510476 = r2510460 + r2510475;
        double r2510477 = b;
        double r2510478 = fma(r2510460, r2510476, r2510477);
        double r2510479 = cbrt(r2510460);
        double r2510480 = r2510479 * r2510479;
        double r2510481 = r2510478 * r2510480;
        double r2510482 = r2510481 * r2510479;
        double r2510483 = r2510474 + r2510482;
        double r2510484 = r2510460 * r2510483;
        double r2510485 = r2510473 + r2510484;
        double r2510486 = r2510472 / r2510485;
        return r2510486;
}

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)))