Average Error: 29.1 → 29.3
Time: 42.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}}}\]
\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}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), i\right)}}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r87552 = x;
        double r87553 = y;
        double r87554 = r87552 * r87553;
        double r87555 = z;
        double r87556 = r87554 + r87555;
        double r87557 = r87556 * r87553;
        double r87558 = 27464.7644705;
        double r87559 = r87557 + r87558;
        double r87560 = r87559 * r87553;
        double r87561 = 230661.510616;
        double r87562 = r87560 + r87561;
        double r87563 = r87562 * r87553;
        double r87564 = t;
        double r87565 = r87563 + r87564;
        double r87566 = a;
        double r87567 = r87553 + r87566;
        double r87568 = r87567 * r87553;
        double r87569 = b;
        double r87570 = r87568 + r87569;
        double r87571 = r87570 * r87553;
        double r87572 = c;
        double r87573 = r87571 + r87572;
        double r87574 = r87573 * r87553;
        double r87575 = i;
        double r87576 = r87574 + r87575;
        double r87577 = r87565 / r87576;
        return r87577;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r87578 = 1.0;
        double r87579 = x;
        double r87580 = y;
        double r87581 = z;
        double r87582 = fma(r87579, r87580, r87581);
        double r87583 = 27464.7644705;
        double r87584 = fma(r87582, r87580, r87583);
        double r87585 = 230661.510616;
        double r87586 = fma(r87584, r87580, r87585);
        double r87587 = t;
        double r87588 = fma(r87586, r87580, r87587);
        double r87589 = a;
        double r87590 = r87580 + r87589;
        double r87591 = b;
        double r87592 = fma(r87590, r87580, r87591);
        double r87593 = c;
        double r87594 = fma(r87592, r87580, r87593);
        double r87595 = i;
        double r87596 = fma(r87580, r87594, r87595);
        double r87597 = r87588 / r87596;
        double r87598 = r87578 / r87597;
        double r87599 = r87578 / r87598;
        return r87599;
}

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

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

  4. Applied clear-num29.3

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

  6. Applied clear-num29.3

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

  7. Simplified29.3

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

  8. Final simplification29.3

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

Reproduce

herbie shell --seed 2019235 +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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))