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

↓

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

\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 r516742 = x;
        double r516743 = y;
        double r516744 = 2.0;
        double r516745 = z;
        double r516746 = t;
        double r516747 = a;
        double r516748 = r516746 + r516747;
        double r516749 = sqrt(r516748);
        double r516750 = r516745 * r516749;
        double r516751 = r516750 / r516746;
        double r516752 = b;
        double r516753 = c;
        double r516754 = r516752 - r516753;
        double r516755 = 5.0;
        double r516756 = 6.0;
        double r516757 = r516755 / r516756;
        double r516758 = r516747 + r516757;
        double r516759 = 3.0;
        double r516760 = r516746 * r516759;
        double r516761 = r516744 / r516760;
        double r516762 = r516758 - r516761;
        double r516763 = r516754 * r516762;
        double r516764 = r516751 - r516763;
        double r516765 = r516744 * r516764;
        double r516766 = exp(r516765);
        double r516767 = r516743 * r516766;
        double r516768 = r516742 + r516767;
        double r516769 = r516742 / r516768;
        return r516769;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r516770 = a;
        double r516771 = 3.4547725240085537e+233;
        bool r516772 = r516770 <= r516771;
        double r516773 = x;
        double r516774 = y;
        double r516775 = 2.0;
        double r516776 = z;
        double r516777 = t;
        double r516778 = r516777 + r516770;
        double r516779 = sqrt(r516778);
        double r516780 = r516776 * r516779;
        double r516781 = r516780 / r516777;
        double r516782 = b;
        double r516783 = c;
        double r516784 = r516782 - r516783;
        double r516785 = 5.0;
        double r516786 = 6.0;
        double r516787 = r516785 / r516786;
        double r516788 = r516770 + r516787;
        double r516789 = 3.0;
        double r516790 = r516777 * r516789;
        double r516791 = r516775 / r516790;
        double r516792 = 3.0;
        double r516793 = pow(r516791, r516792);
        double r516794 = cbrt(r516793);
        double r516795 = r516788 - r516794;
        double r516796 = r516784 * r516795;
        double r516797 = r516781 - r516796;
        double r516798 = r516775 * r516797;
        double r516799 = exp(r516798);
        double r516800 = r516774 * r516799;
        double r516801 = r516773 + r516800;
        double r516802 = r516773 / r516801;
        double r516803 = 0.8333333333333334;
        double r516804 = r516770 + r516803;
        double r516805 = r516783 * r516804;
        double r516806 = r516770 * r516782;
        double r516807 = r516805 - r516806;
        double r516808 = r516775 * r516807;
        double r516809 = exp(r516808);
        double r516810 = r516774 * r516809;
        double r516811 = r516773 + r516810;
        double r516812 = r516773 / r516811;
        double r516813 = r516772 ? r516802 : r516812;
        return r516813;
}

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