Average Error: 28.7 → 28.8
Time: 8.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73571 = x;
        double r73572 = y;
        double r73573 = r73571 * r73572;
        double r73574 = z;
        double r73575 = r73573 + r73574;
        double r73576 = r73575 * r73572;
        double r73577 = 27464.7644705;
        double r73578 = r73576 + r73577;
        double r73579 = r73578 * r73572;
        double r73580 = 230661.510616;
        double r73581 = r73579 + r73580;
        double r73582 = r73581 * r73572;
        double r73583 = t;
        double r73584 = r73582 + r73583;
        double r73585 = a;
        double r73586 = r73572 + r73585;
        double r73587 = r73586 * r73572;
        double r73588 = b;
        double r73589 = r73587 + r73588;
        double r73590 = r73589 * r73572;
        double r73591 = c;
        double r73592 = r73590 + r73591;
        double r73593 = r73592 * r73572;
        double r73594 = i;
        double r73595 = r73593 + r73594;
        double r73596 = r73584 / r73595;
        return r73596;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73597 = x;
        double r73598 = y;
        double r73599 = r73597 * r73598;
        double r73600 = z;
        double r73601 = r73599 + r73600;
        double r73602 = r73601 * r73598;
        double r73603 = 27464.7644705;
        double r73604 = r73602 + r73603;
        double r73605 = r73604 * r73598;
        double r73606 = 230661.510616;
        double r73607 = r73605 + r73606;
        double r73608 = r73607 * r73598;
        double r73609 = t;
        double r73610 = r73608 + r73609;
        double r73611 = 1.0;
        double r73612 = a;
        double r73613 = r73598 + r73612;
        double r73614 = b;
        double r73615 = fma(r73613, r73598, r73614);
        double r73616 = c;
        double r73617 = fma(r73615, r73598, r73616);
        double r73618 = i;
        double r73619 = fma(r73617, r73598, r73618);
        double r73620 = r73619 * r73611;
        double r73621 = r73611 / r73620;
        double r73622 = r73610 * r73621;
        return r73622;
}

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 28.7

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Simplified28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]

Reproduce

herbie shell --seed 2020065 +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) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))