\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -42825168323351446000 \lor \neg \left(z \le 1662749332887347460\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{1}{z} \cdot \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}

↓

\begin{array}{l}
\mathbf{if}\;z \le -42825168323351446000 \lor \neg \left(z \le 1662749332887347460\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{1}{z} \cdot \frac{t}{z}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r352588 = x;
        double r352589 = y;
        double r352590 = z;
        double r352591 = 3.13060547623;
        double r352592 = r352590 * r352591;
        double r352593 = 11.1667541262;
        double r352594 = r352592 + r352593;
        double r352595 = r352594 * r352590;
        double r352596 = t;
        double r352597 = r352595 + r352596;
        double r352598 = r352597 * r352590;
        double r352599 = a;
        double r352600 = r352598 + r352599;
        double r352601 = r352600 * r352590;
        double r352602 = b;
        double r352603 = r352601 + r352602;
        double r352604 = r352589 * r352603;
        double r352605 = 15.234687407;
        double r352606 = r352590 + r352605;
        double r352607 = r352606 * r352590;
        double r352608 = 31.4690115749;
        double r352609 = r352607 + r352608;
        double r352610 = r352609 * r352590;
        double r352611 = 11.9400905721;
        double r352612 = r352610 + r352611;
        double r352613 = r352612 * r352590;
        double r352614 = 0.607771387771;
        double r352615 = r352613 + r352614;
        double r352616 = r352604 / r352615;
        double r352617 = r352588 + r352616;
        return r352617;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r352618 = z;
        double r352619 = -4.2825168323351446e+19;
        bool r352620 = r352618 <= r352619;
        double r352621 = 1.6627493328873475e+18;
        bool r352622 = r352618 <= r352621;
        double r352623 = !r352622;
        bool r352624 = r352620 || r352623;
        double r352625 = y;
        double r352626 = 3.13060547623;
        double r352627 = 1.0;
        double r352628 = r352627 / r352618;
        double r352629 = t;
        double r352630 = r352629 / r352618;
        double r352631 = r352628 * r352630;
        double r352632 = r352626 + r352631;
        double r352633 = x;
        double r352634 = fma(r352625, r352632, r352633);
        double r352635 = 15.234687407;
        double r352636 = r352618 + r352635;
        double r352637 = 31.4690115749;
        double r352638 = fma(r352636, r352618, r352637);
        double r352639 = 11.9400905721;
        double r352640 = fma(r352638, r352618, r352639);
        double r352641 = 0.607771387771;
        double r352642 = fma(r352640, r352618, r352641);
        double r352643 = r352625 / r352642;
        double r352644 = 11.1667541262;
        double r352645 = fma(r352618, r352626, r352644);
        double r352646 = fma(r352645, r352618, r352629);
        double r352647 = a;
        double r352648 = fma(r352646, r352618, r352647);
        double r352649 = b;
        double r352650 = fma(r352648, r352618, r352649);
        double r352651 = fma(r352643, r352650, r352633);
        double r352652 = r352624 ? r352634 : r352651;
        return r352652;
}

Original	29.7
Target	1.0
Herbie	1.1

Derivation

Split input into 2 regimes
if z < -4.2825168323351446e+19 or 1.6627493328873475e+18 < z
1. Initial program 57.9
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified55.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.0
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.9
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
5. Using strategy rm
6. Applied add-sqr-sqrt33.0
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}}^{2}}, x\right)\]
7. Applied unpow-prod-down33.0
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{\color{blue}{{\left(\sqrt{z}\right)}^{2} \cdot {\left(\sqrt{z}\right)}^{2}}}, x\right)\]
8. Applied *-un-lft-identity33.0
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \frac{\color{blue}{1 \cdot t}}{{\left(\sqrt{z}\right)}^{2} \cdot {\left(\sqrt{z}\right)}^{2}}, x\right)\]
9. Applied times-frac33.0
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \color{blue}{\frac{1}{{\left(\sqrt{z}\right)}^{2}} \cdot \frac{t}{{\left(\sqrt{z}\right)}^{2}}}, x\right)\]
10. Simplified32.9
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \color{blue}{\frac{1}{z}} \cdot \frac{t}{{\left(\sqrt{z}\right)}^{2}}, x\right)\]
11. Simplified1.9
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \frac{1}{z} \cdot \color{blue}{\frac{t}{z}}, x\right)\]
if -4.2825168323351446e+19 < z < 1.6627493328873475e+18
1. Initial program 0.4
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified0.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
Recombined 2 regimes into one program.
Final simplification1.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -42825168323351446000 \lor \neg \left(z \le 1662749332887347460\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{1}{z} \cdot \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))

Error

Target

Derivation

`if z < -4.2825168323351446e+19 or 1.6627493328873475e+18 < z`

`if -4.2825168323351446e+19 < z < 1.6627493328873475e+18`

Reproduce