\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

↓

\[\begin{array}{l} \mathbf{if}\;a \le 3.45477252400855375 \cdot 10^{233}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}\\ \end{array}\]

\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}

↓

\begin{array}{l}
\mathbf{if}\;a \le 3.45477252400855375 \cdot 10^{233}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r362405 = x;
        double r362406 = y;
        double r362407 = 2.0;
        double r362408 = z;
        double r362409 = t;
        double r362410 = a;
        double r362411 = r362409 + r362410;
        double r362412 = sqrt(r362411);
        double r362413 = r362408 * r362412;
        double r362414 = r362413 / r362409;
        double r362415 = b;
        double r362416 = c;
        double r362417 = r362415 - r362416;
        double r362418 = 5.0;
        double r362419 = 6.0;
        double r362420 = r362418 / r362419;
        double r362421 = r362410 + r362420;
        double r362422 = 3.0;
        double r362423 = r362409 * r362422;
        double r362424 = r362407 / r362423;
        double r362425 = r362421 - r362424;
        double r362426 = r362417 * r362425;
        double r362427 = r362414 - r362426;
        double r362428 = r362407 * r362427;
        double r362429 = exp(r362428);
        double r362430 = r362406 * r362429;
        double r362431 = r362405 + r362430;
        double r362432 = r362405 / r362431;
        return r362432;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r362433 = a;
        double r362434 = 3.4547725240085537e+233;
        bool r362435 = r362433 <= r362434;
        double r362436 = x;
        double r362437 = y;
        double r362438 = 2.0;
        double r362439 = z;
        double r362440 = t;
        double r362441 = r362440 + r362433;
        double r362442 = sqrt(r362441);
        double r362443 = r362439 * r362442;
        double r362444 = r362443 / r362440;
        double r362445 = b;
        double r362446 = c;
        double r362447 = r362445 - r362446;
        double r362448 = 5.0;
        double r362449 = 6.0;
        double r362450 = r362448 / r362449;
        double r362451 = r362433 + r362450;
        double r362452 = 3.0;
        double r362453 = r362440 * r362452;
        double r362454 = r362438 / r362453;
        double r362455 = 3.0;
        double r362456 = pow(r362454, r362455);
        double r362457 = cbrt(r362456);
        double r362458 = r362451 - r362457;
        double r362459 = r362447 * r362458;
        double r362460 = r362444 - r362459;
        double r362461 = r362438 * r362460;
        double r362462 = exp(r362461);
        double r362463 = r362437 * r362462;
        double r362464 = r362436 + r362463;
        double r362465 = r362436 / r362464;
        double r362466 = 0.8333333333333334;
        double r362467 = r362433 + r362466;
        double r362468 = r362446 * r362467;
        double r362469 = r362433 * r362445;
        double r362470 = r362468 - r362469;
        double r362471 = r362438 * r362470;
        double r362472 = exp(r362471);
        double r362473 = r362437 * r362472;
        double r362474 = r362436 + r362473;
        double r362475 = r362436 / r362474;
        double r362476 = r362435 ? r362465 : r362475;
        return r362476;
}

Target

Original	3.8
Target	2.8
Herbie	7.0

\[\begin{array}{l} \mathbf{if}\;t \lt -2.1183266448915811 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.83333333333333337 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.19658877065154709 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

Split input into 2 regimes
if a < 3.4547725240085537e+233
1. Initial program 3.2
  \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
2. Using strategy rm
3. Applied add-cbrt-cube3.2
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot \color{blue}{\sqrt[3]{\left(3 \cdot 3\right) \cdot 3}}}\right)\right)}}\]
4. Applied add-cbrt-cube6.0
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{\color{blue}{\sqrt[3]{\left(t \cdot t\right) \cdot t}} \cdot \sqrt[3]{\left(3 \cdot 3\right) \cdot 3}}\right)\right)}}\]
5. Applied cbrt-unprod6.0
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{\color{blue}{\sqrt[3]{\left(\left(t \cdot t\right) \cdot t\right) \cdot \left(\left(3 \cdot 3\right) \cdot 3\right)}}}\right)\right)}}\]
6. Applied add-cbrt-cube6.0
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{\color{blue}{\sqrt[3]{\left(2 \cdot 2\right) \cdot 2}}}{\sqrt[3]{\left(\left(t \cdot t\right) \cdot t\right) \cdot \left(\left(3 \cdot 3\right) \cdot 3\right)}}\right)\right)}}\]
7. Applied cbrt-undiv6.1
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \color{blue}{\sqrt[3]{\frac{\left(2 \cdot 2\right) \cdot 2}{\left(\left(t \cdot t\right) \cdot t\right) \cdot \left(\left(3 \cdot 3\right) \cdot 3\right)}}}\right)\right)}}\]
8. Simplified6.1
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{\color{blue}{{\left(\frac{2}{t \cdot 3}\right)}^{3}}}\right)\right)}}\]
if 3.4547725240085537e+233 < a
1. Initial program 8.1
  \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
2. Taylor expanded around inf 14.0
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(a \cdot c + 0.83333333333333337 \cdot c\right) - a \cdot b\right)}}}\]
3. Simplified14.0
  \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}}\]
Recombined 2 regimes into one program.
Final simplification7.0
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le 3.45477252400855375 \cdot 10^{233}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3))))))))))))

  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))

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

Error

Try it out

Target

Derivation

`if a < 3.4547725240085537e+233`

`if 3.4547725240085537e+233 < a`

Reproduce

In
Out