Average Error: 29.0 → 29.1
Time: 43.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, a + y, b\right), c\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y\right)\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, a + y, b\right), c\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3071577 = x;
        double r3071578 = y;
        double r3071579 = r3071577 * r3071578;
        double r3071580 = z;
        double r3071581 = r3071579 + r3071580;
        double r3071582 = r3071581 * r3071578;
        double r3071583 = 27464.7644705;
        double r3071584 = r3071582 + r3071583;
        double r3071585 = r3071584 * r3071578;
        double r3071586 = 230661.510616;
        double r3071587 = r3071585 + r3071586;
        double r3071588 = r3071587 * r3071578;
        double r3071589 = t;
        double r3071590 = r3071588 + r3071589;
        double r3071591 = a;
        double r3071592 = r3071578 + r3071591;
        double r3071593 = r3071592 * r3071578;
        double r3071594 = b;
        double r3071595 = r3071593 + r3071594;
        double r3071596 = r3071595 * r3071578;
        double r3071597 = c;
        double r3071598 = r3071596 + r3071597;
        double r3071599 = r3071598 * r3071578;
        double r3071600 = i;
        double r3071601 = r3071599 + r3071600;
        double r3071602 = r3071590 / r3071601;
        return r3071602;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3071603 = 1.0;
        double r3071604 = y;
        double r3071605 = a;
        double r3071606 = r3071605 + r3071604;
        double r3071607 = b;
        double r3071608 = fma(r3071604, r3071606, r3071607);
        double r3071609 = c;
        double r3071610 = fma(r3071604, r3071608, r3071609);
        double r3071611 = i;
        double r3071612 = fma(r3071610, r3071604, r3071611);
        double r3071613 = r3071603 / r3071612;
        double r3071614 = t;
        double r3071615 = z;
        double r3071616 = x;
        double r3071617 = r3071616 * r3071604;
        double r3071618 = r3071615 + r3071617;
        double r3071619 = r3071604 * r3071618;
        double r3071620 = 27464.7644705;
        double r3071621 = r3071619 + r3071620;
        double r3071622 = r3071604 * r3071621;
        double r3071623 = 230661.510616;
        double r3071624 = r3071622 + r3071623;
        double r3071625 = r3071624 * r3071604;
        double r3071626 = r3071614 + r3071625;
        double r3071627 = r3071613 * r3071626;
        return r3071627;
}

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 29.0

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv29.1

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Simplified29.1

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, y + a, b\right), c\right), y, i\right)}}\]

  5. Final simplification29.1

    \[\leadsto \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, a + y, b\right), c\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y\right)\]

Reproduce

herbie shell --seed 2019169 +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)))