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

↓

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

\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)}}

↓

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

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r476789 = x;
        double r476790 = y;
        double r476791 = 2.0;
        double r476792 = z;
        double r476793 = t;
        double r476794 = a;
        double r476795 = r476793 + r476794;
        double r476796 = sqrt(r476795);
        double r476797 = r476792 * r476796;
        double r476798 = r476797 / r476793;
        double r476799 = b;
        double r476800 = c;
        double r476801 = r476799 - r476800;
        double r476802 = 5.0;
        double r476803 = 6.0;
        double r476804 = r476802 / r476803;
        double r476805 = r476794 + r476804;
        double r476806 = 3.0;
        double r476807 = r476793 * r476806;
        double r476808 = r476791 / r476807;
        double r476809 = r476805 - r476808;
        double r476810 = r476801 * r476809;
        double r476811 = r476798 - r476810;
        double r476812 = r476791 * r476811;
        double r476813 = exp(r476812);
        double r476814 = r476790 * r476813;
        double r476815 = r476789 + r476814;
        double r476816 = r476789 / r476815;
        return r476816;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r476817 = x;
        double r476818 = y;
        double r476819 = 2.0;
        double r476820 = z;
        double r476821 = t;
        double r476822 = cbrt(r476821);
        double r476823 = r476822 * r476822;
        double r476824 = r476820 / r476823;
        double r476825 = a;
        double r476826 = r476821 + r476825;
        double r476827 = sqrt(r476826);
        double r476828 = r476827 / r476822;
        double r476829 = r476824 * r476828;
        double r476830 = b;
        double r476831 = c;
        double r476832 = r476830 - r476831;
        double r476833 = 5.0;
        double r476834 = 6.0;
        double r476835 = r476833 / r476834;
        double r476836 = r476825 + r476835;
        double r476837 = 3.0;
        double r476838 = r476821 * r476837;
        double r476839 = r476819 / r476838;
        double r476840 = r476836 - r476839;
        double r476841 = r476832 * r476840;
        double r476842 = r476829 - r476841;
        double r476843 = exp(r476842);
        double r476844 = log(r476843);
        double r476845 = r476819 * r476844;
        double r476846 = exp(r476845);
        double r476847 = r476818 * r476846;
        double r476848 = r476817 + r476847;
        double r476849 = r476817 / r476848;
        return r476849;
}

Target

Original	3.8
Target	3.1
Herbie	2.7

\[\begin{array}{l} \mathbf{if}\;t \lt -2.118326644891581057561884576920117070548 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333333703407674875052180141211 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.196588770651547088010424937268931048836 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 3.8
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt3.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Applied times-frac2.7
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-log-exp7.1
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}\right)}}\]
Applied add-log-exp17.1
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\log \left(e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)\right)}}\]
Applied diff-log17.1
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(\frac{e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}}\right)}}}\]
Simplified2.7
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}}\]
Final simplification2.7
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]

Reproduce

herbie shell --seed 2019350 
(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

Reproduce

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