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

↓

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

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 r634607 = x;
        double r634608 = y;
        double r634609 = z;
        double r634610 = 0.0692910599291889;
        double r634611 = r634609 * r634610;
        double r634612 = 0.4917317610505968;
        double r634613 = r634611 + r634612;
        double r634614 = r634613 * r634609;
        double r634615 = 0.279195317918525;
        double r634616 = r634614 + r634615;
        double r634617 = r634608 * r634616;
        double r634618 = 6.012459259764103;
        double r634619 = r634609 + r634618;
        double r634620 = r634619 * r634609;
        double r634621 = 3.350343815022304;
        double r634622 = r634620 + r634621;
        double r634623 = r634617 / r634622;
        double r634624 = r634607 + r634623;
        return r634624;
}

↓

double f(double x, double y, double z) {
        double r634625 = z;
        double r634626 = -505680.7086753328;
        bool r634627 = r634625 <= r634626;
        double r634628 = 0.4426814927734349;
        bool r634629 = r634625 <= r634628;
        double r634630 = !r634629;
        bool r634631 = r634627 || r634630;
        double r634632 = x;
        double r634633 = 0.0692910599291889;
        double r634634 = y;
        double r634635 = r634633 * r634634;
        double r634636 = r634634 / r634625;
        double r634637 = 0.07512208616047561;
        double r634638 = 0.40462203869992125;
        double r634639 = r634638 / r634625;
        double r634640 = r634637 - r634639;
        double r634641 = r634636 * r634640;
        double r634642 = r634635 + r634641;
        double r634643 = r634632 + r634642;
        double r634644 = r634625 * r634633;
        double r634645 = 0.4917317610505968;
        double r634646 = r634644 + r634645;
        double r634647 = r634646 * r634625;
        double r634648 = 0.279195317918525;
        double r634649 = r634647 + r634648;
        double r634650 = 6.012459259764103;
        double r634651 = r634625 + r634650;
        double r634652 = r634651 * r634625;
        double r634653 = 3.350343815022304;
        double r634654 = r634652 + r634653;
        double r634655 = r634649 / r634654;
        double r634656 = r634634 * r634655;
        double r634657 = r634632 + r634656;
        double r634658 = r634631 ? r634643 : r634657;
        return r634658;
}

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

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