\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -5.03697642486000799 \cdot 10^{32} \lor \neg \left(\left(t - 1\right) \cdot \log a \le 65.394405318574371\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}\\ \end{array}\]

\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}

↓

\begin{array}{l}
\mathbf{if}\;\left(t - 1\right) \cdot \log a \le -5.03697642486000799 \cdot 10^{32} \lor \neg \left(\left(t - 1\right) \cdot \log a \le 65.394405318574371\right):\\
\;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r607658 = x;
        double r607659 = y;
        double r607660 = z;
        double r607661 = log(r607660);
        double r607662 = r607659 * r607661;
        double r607663 = t;
        double r607664 = 1.0;
        double r607665 = r607663 - r607664;
        double r607666 = a;
        double r607667 = log(r607666);
        double r607668 = r607665 * r607667;
        double r607669 = r607662 + r607668;
        double r607670 = b;
        double r607671 = r607669 - r607670;
        double r607672 = exp(r607671);
        double r607673 = r607658 * r607672;
        double r607674 = r607673 / r607659;
        return r607674;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r607675 = t;
        double r607676 = 1.0;
        double r607677 = r607675 - r607676;
        double r607678 = a;
        double r607679 = log(r607678);
        double r607680 = r607677 * r607679;
        double r607681 = -5.036976424860008e+32;
        bool r607682 = r607680 <= r607681;
        double r607683 = 65.39440531857437;
        bool r607684 = r607680 <= r607683;
        double r607685 = !r607684;
        bool r607686 = r607682 || r607685;
        double r607687 = x;
        double r607688 = y;
        double r607689 = z;
        double r607690 = log(r607689);
        double r607691 = r607688 * r607690;
        double r607692 = r607691 + r607680;
        double r607693 = b;
        double r607694 = r607692 - r607693;
        double r607695 = exp(r607694);
        double r607696 = r607687 * r607695;
        double r607697 = r607696 / r607688;
        double r607698 = r607693 - r607691;
        double r607699 = exp(r607698);
        double r607700 = pow(r607678, r607675);
        double r607701 = r607699 / r607700;
        double r607702 = 1.0;
        double r607703 = r607702 / r607688;
        double r607704 = pow(r607678, r607676);
        double r607705 = r607703 / r607704;
        double r607706 = r607701 / r607705;
        double r607707 = r607687 / r607706;
        double r607708 = r607686 ? r607697 : r607707;
        return r607708;
}

Original	1.9
Target	11.7
Herbie	0.6

Derivation

Split input into 2 regimes
if (* (- t 1.0) (log a)) < -5.036976424860008e+32 or 65.39440531857437 < (* (- t 1.0) (log a))
1. Initial program 0.5
  \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
if -5.036976424860008e+32 < (* (- t 1.0) (log a)) < 65.39440531857437
1. Initial program 4.7
  \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
2. Taylor expanded around inf 4.7
  \[\leadsto \color{blue}{\frac{x \cdot e^{1 \cdot \log \left(\frac{1}{a}\right) - \left(y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)\right)}}{y}}\]
3. Simplified8.5
  \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{{a}^{1}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity8.5
  \[\leadsto \frac{\frac{\frac{x}{y}}{\color{blue}{1 \cdot {a}^{1}}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
6. Applied div-inv8.5
  \[\leadsto \frac{\frac{\color{blue}{x \cdot \frac{1}{y}}}{1 \cdot {a}^{1}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
7. Applied times-frac2.6
  \[\leadsto \frac{\color{blue}{\frac{x}{1} \cdot \frac{\frac{1}{y}}{{a}^{1}}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
8. Applied associate-/l*0.9
  \[\leadsto \color{blue}{\frac{\frac{x}{1}}{\frac{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}{\frac{\frac{1}{y}}{{a}^{1}}}}}\]
9. Simplified0.9
  \[\leadsto \frac{\frac{x}{1}}{\color{blue}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}}\]
Recombined 2 regimes into one program.
Final simplification0.6
\[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -5.03697642486000799 \cdot 10^{32} \lor \neg \left(\left(t - 1\right) \cdot \log a \le 65.394405318574371\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))

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

Error

Try it out

Target

Derivation

`if (* (- t 1.0) (log a)) < -5.036976424860008e+32 or 65.39440531857437 < (* (- t 1.0) (log a))`

`if -5.036976424860008e+32 < (* (- t 1.0) (log a)) < 65.39440531857437`

Reproduce

In
Out