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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.30119042405714593 \cdot 10^{53} \lor \neg \left(z \le 2.9457931334716344 \cdot 10^{36}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -1.30119042405714593 \cdot 10^{53} \lor \neg \left(z \le 2.9457931334716344 \cdot 10^{36}\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, 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 r384933 = x;
        double r384934 = y;
        double r384935 = z;
        double r384936 = 3.13060547623;
        double r384937 = r384935 * r384936;
        double r384938 = 11.1667541262;
        double r384939 = r384937 + r384938;
        double r384940 = r384939 * r384935;
        double r384941 = t;
        double r384942 = r384940 + r384941;
        double r384943 = r384942 * r384935;
        double r384944 = a;
        double r384945 = r384943 + r384944;
        double r384946 = r384945 * r384935;
        double r384947 = b;
        double r384948 = r384946 + r384947;
        double r384949 = r384934 * r384948;
        double r384950 = 15.234687407;
        double r384951 = r384935 + r384950;
        double r384952 = r384951 * r384935;
        double r384953 = 31.4690115749;
        double r384954 = r384952 + r384953;
        double r384955 = r384954 * r384935;
        double r384956 = 11.9400905721;
        double r384957 = r384955 + r384956;
        double r384958 = r384957 * r384935;
        double r384959 = 0.607771387771;
        double r384960 = r384958 + r384959;
        double r384961 = r384949 / r384960;
        double r384962 = r384933 + r384961;
        return r384962;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r384963 = z;
        double r384964 = -1.301190424057146e+53;
        bool r384965 = r384963 <= r384964;
        double r384966 = 2.9457931334716344e+36;
        bool r384967 = r384963 <= r384966;
        double r384968 = !r384967;
        bool r384969 = r384965 || r384968;
        double r384970 = y;
        double r384971 = 3.13060547623;
        double r384972 = t;
        double r384973 = 2.0;
        double r384974 = pow(r384963, r384973);
        double r384975 = r384972 / r384974;
        double r384976 = r384971 + r384975;
        double r384977 = x;
        double r384978 = fma(r384970, r384976, r384977);
        double r384979 = 15.234687407;
        double r384980 = r384963 + r384979;
        double r384981 = 31.4690115749;
        double r384982 = fma(r384980, r384963, r384981);
        double r384983 = 11.9400905721;
        double r384984 = fma(r384982, r384963, r384983);
        double r384985 = 0.607771387771;
        double r384986 = fma(r384984, r384963, r384985);
        double r384987 = r384970 / r384986;
        double r384988 = 11.1667541262;
        double r384989 = fma(r384963, r384971, r384988);
        double r384990 = fma(r384989, r384963, r384972);
        double r384991 = a;
        double r384992 = fma(r384990, r384963, r384991);
        double r384993 = b;
        double r384994 = fma(r384992, r384963, r384993);
        double r384995 = fma(r384987, r384994, r384977);
        double r384996 = r384969 ? r384978 : r384995;
        return r384996;
}

Original	29.0
Target	1.1
Herbie	1.1

Derivation

Split input into 2 regimes
if z < -1.301190424057146e+53 or 2.9457931334716344e+36 < z
1. Initial program 60.4
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified58.9
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.8
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -1.301190424057146e+53 < z < 2.9457931334716344e+36
1. Initial program 2.3
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified1.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
Recombined 2 regimes into one program.
Final simplification1.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.30119042405714593 \cdot 10^{53} \lor \neg \left(z \le 2.9457931334716344 \cdot 10^{36}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 +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 < -1.301190424057146e+53 or 2.9457931334716344e+36 < z`

`if -1.301190424057146e+53 < z < 2.9457931334716344e+36`

Reproduce