\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.6182939126081175 \cdot 10^{49} \lor \neg \left(z \le 698981194.60847616\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z}, y, \mathsf{fma}\left(y, 0.0692910599291888946, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291888946, 0.49173176105059679\right), z, 0.279195317918524977\right) \cdot 1}{\mathsf{fma}\left(z + 6.0124592597641033, z, 3.35034381502230394\right)}\\ \end{array}\]

x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}

↓

\begin{array}{l}
\mathbf{if}\;z \le -1.6182939126081175 \cdot 10^{49} \lor \neg \left(z \le 698981194.60847616\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z}, y, \mathsf{fma}\left(y, 0.0692910599291888946, x\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291888946, 0.49173176105059679\right), z, 0.279195317918524977\right) \cdot 1}{\mathsf{fma}\left(z + 6.0124592597641033, z, 3.35034381502230394\right)}\\

\end{array}

double f(double x, double y, double z) {
        double r380985 = x;
        double r380986 = y;
        double r380987 = z;
        double r380988 = 0.0692910599291889;
        double r380989 = r380987 * r380988;
        double r380990 = 0.4917317610505968;
        double r380991 = r380989 + r380990;
        double r380992 = r380991 * r380987;
        double r380993 = 0.279195317918525;
        double r380994 = r380992 + r380993;
        double r380995 = r380986 * r380994;
        double r380996 = 6.012459259764103;
        double r380997 = r380987 + r380996;
        double r380998 = r380997 * r380987;
        double r380999 = 3.350343815022304;
        double r381000 = r380998 + r380999;
        double r381001 = r380995 / r381000;
        double r381002 = r380985 + r381001;
        return r381002;
}

↓

double f(double x, double y, double z) {
        double r381003 = z;
        double r381004 = -1.6182939126081175e+49;
        bool r381005 = r381003 <= r381004;
        double r381006 = 698981194.6084762;
        bool r381007 = r381003 <= r381006;
        double r381008 = !r381007;
        bool r381009 = r381005 || r381008;
        double r381010 = 0.07512208616047561;
        double r381011 = r381010 / r381003;
        double r381012 = y;
        double r381013 = 0.0692910599291889;
        double r381014 = x;
        double r381015 = fma(r381012, r381013, r381014);
        double r381016 = fma(r381011, r381012, r381015);
        double r381017 = 0.4917317610505968;
        double r381018 = fma(r381003, r381013, r381017);
        double r381019 = 0.279195317918525;
        double r381020 = fma(r381018, r381003, r381019);
        double r381021 = 1.0;
        double r381022 = r381020 * r381021;
        double r381023 = 6.012459259764103;
        double r381024 = r381003 + r381023;
        double r381025 = 3.350343815022304;
        double r381026 = fma(r381024, r381003, r381025);
        double r381027 = r381022 / r381026;
        double r381028 = r381012 * r381027;
        double r381029 = r381014 + r381028;
        double r381030 = r381009 ? r381016 : r381029;
        return r381030;
}

Original	20.1
Target	0.1
Herbie	0.1

Derivation

Split input into 2 regimes
if z < -1.6182939126081175e+49 or 698981194.6084762 < z
1. Initial program 44.3
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Simplified37.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(z + 6.0124592597641033, z, 3.35034381502230394\right)}, \mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291888946, 0.49173176105059679\right), z, 0.279195317918524977\right), x\right)}\]
3. Taylor expanded around inf 0.0
  \[\leadsto \color{blue}{x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)}\]
4. Simplified0.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0.07512208616047561}{z}, y, \mathsf{fma}\left(y, 0.0692910599291888946, x\right)\right)}\]
if -1.6182939126081175e+49 < z < 698981194.6084762
1. Initial program 0.6
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.6
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]
4. Applied times-frac0.1
  \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\]
5. Simplified0.1
  \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
6. Simplified0.1
  \[\leadsto x + y \cdot \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291888946, 0.49173176105059679\right), z, 0.279195317918524977\right) \cdot 1}{\mathsf{fma}\left(z + 6.0124592597641033, z, 3.35034381502230394\right)}}\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.6182939126081175 \cdot 10^{49} \lor \neg \left(z \le 698981194.60847616\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z}, y, \mathsf{fma}\left(y, 0.0692910599291888946, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(z, 0.0692910599291888946, 0.49173176105059679\right), z, 0.279195317918524977\right) \cdot 1}{\mathsf{fma}\left(z + 6.0124592597641033, z, 3.35034381502230394\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 657611897278737680000) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

Error

Target

Derivation

`if z < -1.6182939126081175e+49 or 698981194.6084762 < z`

`if -1.6182939126081175e+49 < z < 698981194.6084762`

Reproduce