Average Error: 29.1 → 29.2
Time: 31.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)\]
\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(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61572 = x;
        double r61573 = y;
        double r61574 = r61572 * r61573;
        double r61575 = z;
        double r61576 = r61574 + r61575;
        double r61577 = r61576 * r61573;
        double r61578 = 27464.7644705;
        double r61579 = r61577 + r61578;
        double r61580 = r61579 * r61573;
        double r61581 = 230661.510616;
        double r61582 = r61580 + r61581;
        double r61583 = r61582 * r61573;
        double r61584 = t;
        double r61585 = r61583 + r61584;
        double r61586 = a;
        double r61587 = r61573 + r61586;
        double r61588 = r61587 * r61573;
        double r61589 = b;
        double r61590 = r61588 + r61589;
        double r61591 = r61590 * r61573;
        double r61592 = c;
        double r61593 = r61591 + r61592;
        double r61594 = r61593 * r61573;
        double r61595 = i;
        double r61596 = r61594 + r61595;
        double r61597 = r61585 / r61596;
        return r61597;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61598 = 1.0;
        double r61599 = y;
        double r61600 = a;
        double r61601 = r61599 + r61600;
        double r61602 = b;
        double r61603 = fma(r61601, r61599, r61602);
        double r61604 = c;
        double r61605 = fma(r61599, r61603, r61604);
        double r61606 = i;
        double r61607 = fma(r61599, r61605, r61606);
        double r61608 = r61598 / r61607;
        double r61609 = x;
        double r61610 = z;
        double r61611 = fma(r61599, r61609, r61610);
        double r61612 = 27464.7644705;
        double r61613 = fma(r61599, r61611, r61612);
        double r61614 = 230661.510616;
        double r61615 = fma(r61599, r61613, r61614);
        double r61616 = t;
        double r61617 = fma(r61615, r61599, r61616);
        double r61618 = r61608 * r61617;
        return r61618;
}

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 29.1

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

  2. Simplified29.1

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied div-inv29.2

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

  5. Simplified29.2

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

  6. Final simplification29.2

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

Reproduce

herbie shell --seed 2019194 +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)))