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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2.6139341557841157 \cdot 10^{33} \lor \neg \left(z \le 0.200318100483606681\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

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 -2.6139341557841157 \cdot 10^{33} \lor \neg \left(z \le 0.200318100483606681\right):\\
\;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\

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

\end{array}

double f(double x, double y, double z) {
        double r388942 = x;
        double r388943 = y;
        double r388944 = z;
        double r388945 = 0.0692910599291889;
        double r388946 = r388944 * r388945;
        double r388947 = 0.4917317610505968;
        double r388948 = r388946 + r388947;
        double r388949 = r388948 * r388944;
        double r388950 = 0.279195317918525;
        double r388951 = r388949 + r388950;
        double r388952 = r388943 * r388951;
        double r388953 = 6.012459259764103;
        double r388954 = r388944 + r388953;
        double r388955 = r388954 * r388944;
        double r388956 = 3.350343815022304;
        double r388957 = r388955 + r388956;
        double r388958 = r388952 / r388957;
        double r388959 = r388942 + r388958;
        return r388959;
}

↓

double f(double x, double y, double z) {
        double r388960 = z;
        double r388961 = -2.613934155784116e+33;
        bool r388962 = r388960 <= r388961;
        double r388963 = 0.20031810048360668;
        bool r388964 = r388960 <= r388963;
        double r388965 = !r388964;
        bool r388966 = r388962 || r388965;
        double r388967 = x;
        double r388968 = 0.07512208616047561;
        double r388969 = y;
        double r388970 = r388969 / r388960;
        double r388971 = r388968 * r388970;
        double r388972 = 0.0692910599291889;
        double r388973 = r388972 * r388969;
        double r388974 = r388971 + r388973;
        double r388975 = 0.40462203869992125;
        double r388976 = 2.0;
        double r388977 = pow(r388960, r388976);
        double r388978 = r388969 / r388977;
        double r388979 = r388975 * r388978;
        double r388980 = r388974 - r388979;
        double r388981 = r388967 + r388980;
        double r388982 = r388960 * r388972;
        double r388983 = 0.4917317610505968;
        double r388984 = r388982 + r388983;
        double r388985 = r388984 * r388960;
        double r388986 = 0.279195317918525;
        double r388987 = r388985 + r388986;
        double r388988 = 6.012459259764103;
        double r388989 = r388960 + r388988;
        double r388990 = r388989 * r388960;
        double r388991 = 3.350343815022304;
        double r388992 = r388990 + r388991;
        double r388993 = r388987 / r388992;
        double r388994 = r388969 * r388993;
        double r388995 = r388967 + r388994;
        double r388996 = r388966 ? r388981 : r388995;
        return r388996;
}

Original	19.8
Target	0.2
Herbie	0.2

Derivation

Split input into 2 regimes
if z < -2.613934155784116e+33 or 0.20031810048360668 < z
1. Initial program 42.0
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Taylor expanded around inf 0.2
  \[\leadsto x + \color{blue}{\left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)}\]
if -2.613934155784116e+33 < z < 0.20031810048360668
1. Initial program 0.3
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.3
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]
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
  \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.6139341557841157 \cdot 10^{33} \lor \neg \left(z \le 0.200318100483606681\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(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))))

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if z < -2.613934155784116e+33 or 0.20031810048360668 < z`

`if -2.613934155784116e+33 < z < 0.20031810048360668`

Reproduce

In
Out