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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -879834.049726674915 \lor \neg \left(z \le 758422.16501321143\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

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 -879834.049726674915 \lor \neg \left(z \le 758422.16501321143\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 r483657 = x;
        double r483658 = y;
        double r483659 = z;
        double r483660 = 0.0692910599291889;
        double r483661 = r483659 * r483660;
        double r483662 = 0.4917317610505968;
        double r483663 = r483661 + r483662;
        double r483664 = r483663 * r483659;
        double r483665 = 0.279195317918525;
        double r483666 = r483664 + r483665;
        double r483667 = r483658 * r483666;
        double r483668 = 6.012459259764103;
        double r483669 = r483659 + r483668;
        double r483670 = r483669 * r483659;
        double r483671 = 3.350343815022304;
        double r483672 = r483670 + r483671;
        double r483673 = r483667 / r483672;
        double r483674 = r483657 + r483673;
        return r483674;
}

↓

double f(double x, double y, double z) {
        double r483675 = z;
        double r483676 = -879834.0497266749;
        bool r483677 = r483675 <= r483676;
        double r483678 = 758422.1650132114;
        bool r483679 = r483675 <= r483678;
        double r483680 = !r483679;
        bool r483681 = r483677 || r483680;
        double r483682 = x;
        double r483683 = 0.07512208616047561;
        double r483684 = y;
        double r483685 = r483684 / r483675;
        double r483686 = r483683 * r483685;
        double r483687 = 0.0692910599291889;
        double r483688 = r483687 * r483684;
        double r483689 = r483686 + r483688;
        double r483690 = 0.40462203869992125;
        double r483691 = 2.0;
        double r483692 = pow(r483675, r483691);
        double r483693 = r483684 / r483692;
        double r483694 = r483690 * r483693;
        double r483695 = r483689 - r483694;
        double r483696 = r483682 + r483695;
        double r483697 = r483675 * r483687;
        double r483698 = 0.4917317610505968;
        double r483699 = r483697 + r483698;
        double r483700 = r483699 * r483675;
        double r483701 = 0.279195317918525;
        double r483702 = r483700 + r483701;
        double r483703 = 6.012459259764103;
        double r483704 = r483675 + r483703;
        double r483705 = r483704 * r483675;
        double r483706 = 3.350343815022304;
        double r483707 = r483705 + r483706;
        double r483708 = r483702 / r483707;
        double r483709 = r483684 * r483708;
        double r483710 = r483682 + r483709;
        double r483711 = r483681 ? r483696 : r483710;
        return r483711;
}

Original	20.1
Target	0.2
Herbie	0.1

Derivation

Split input into 2 regimes
if z < -879834.0497266749 or 758422.1650132114 < z
1. Initial program 40.9
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied add-sqr-sqrt40.9
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394} \cdot \sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}}\]
4. Applied times-frac32.9
  \[\leadsto x + \color{blue}{\frac{y}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}}\]
5. Taylor expanded around inf 0.0
  \[\leadsto x + \color{blue}{\left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)}\]
if -879834.0497266749 < z < 758422.1650132114
1. Initial program 0.2
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.2
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]
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 simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -879834.049726674915 \lor \neg \left(z \le 758422.16501321143\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(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

Try it out

Target

Derivation

`if z < -879834.0497266749 or 758422.1650132114 < z`

`if -879834.0497266749 < z < 758422.1650132114`

Reproduce

In
Out