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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -505680.708675332775 \lor \neg \left(z \le 0.442681492773434881\right):\\ \;\;\;\;x + \left(0.0692910599291888946 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.404622038699921249}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

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 -505680.708675332775 \lor \neg \left(z \le 0.442681492773434881\right):\\
\;\;\;\;x + \left(0.0692910599291888946 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.404622038699921249}{z}\right)\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 r424966 = x;
        double r424967 = y;
        double r424968 = z;
        double r424969 = 0.0692910599291889;
        double r424970 = r424968 * r424969;
        double r424971 = 0.4917317610505968;
        double r424972 = r424970 + r424971;
        double r424973 = r424972 * r424968;
        double r424974 = 0.279195317918525;
        double r424975 = r424973 + r424974;
        double r424976 = r424967 * r424975;
        double r424977 = 6.012459259764103;
        double r424978 = r424968 + r424977;
        double r424979 = r424978 * r424968;
        double r424980 = 3.350343815022304;
        double r424981 = r424979 + r424980;
        double r424982 = r424976 / r424981;
        double r424983 = r424966 + r424982;
        return r424983;
}

↓

double f(double x, double y, double z) {
        double r424984 = z;
        double r424985 = -505680.7086753328;
        bool r424986 = r424984 <= r424985;
        double r424987 = 0.4426814927734349;
        bool r424988 = r424984 <= r424987;
        double r424989 = !r424988;
        bool r424990 = r424986 || r424989;
        double r424991 = x;
        double r424992 = 0.0692910599291889;
        double r424993 = y;
        double r424994 = r424992 * r424993;
        double r424995 = r424993 / r424984;
        double r424996 = 0.07512208616047561;
        double r424997 = 0.40462203869992125;
        double r424998 = r424997 / r424984;
        double r424999 = r424996 - r424998;
        double r425000 = r424995 * r424999;
        double r425001 = r424994 + r425000;
        double r425002 = r424991 + r425001;
        double r425003 = r424984 * r424992;
        double r425004 = 0.4917317610505968;
        double r425005 = r425003 + r425004;
        double r425006 = r425005 * r424984;
        double r425007 = 0.279195317918525;
        double r425008 = r425006 + r425007;
        double r425009 = 6.012459259764103;
        double r425010 = r424984 + r425009;
        double r425011 = r425010 * r424984;
        double r425012 = 3.350343815022304;
        double r425013 = r425011 + r425012;
        double r425014 = r425008 / r425013;
        double r425015 = r424993 * r425014;
        double r425016 = r424991 + r425015;
        double r425017 = r424990 ? r425002 : r425016;
        return r425017;
}

Original	20.3
Target	0.2
Herbie	0.2

Derivation

Split input into 2 regimes
if z < -505680.7086753328 or 0.4426814927734349 < z
1. Initial program 40.3
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied *-un-lft-identity40.3
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]
4. Applied times-frac32.8
  \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\]
5. Simplified32.8
  \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
6. Taylor expanded around inf 0.2
  \[\leadsto x + \color{blue}{\left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)}\]
7. Simplified0.2
  \[\leadsto x + \color{blue}{\left(0.0692910599291888946 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.404622038699921249}{z}\right)\right)}\]
if -505680.7086753328 < z < 0.4426814927734349
1. Initial program 0.1
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.1
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]
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
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -505680.708675332775 \lor \neg \left(z \le 0.442681492773434881\right):\\ \;\;\;\;x + \left(0.0692910599291888946 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.404622038699921249}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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 < -505680.7086753328 or 0.4426814927734349 < z`

`if -505680.7086753328 < z < 0.4426814927734349`

Reproduce

In
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