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

↓

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

\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)}}

↓

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

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r22688977 = x;
        double r22688978 = y;
        double r22688979 = 2.0;
        double r22688980 = z;
        double r22688981 = t;
        double r22688982 = a;
        double r22688983 = r22688981 + r22688982;
        double r22688984 = sqrt(r22688983);
        double r22688985 = r22688980 * r22688984;
        double r22688986 = r22688985 / r22688981;
        double r22688987 = b;
        double r22688988 = c;
        double r22688989 = r22688987 - r22688988;
        double r22688990 = 5.0;
        double r22688991 = 6.0;
        double r22688992 = r22688990 / r22688991;
        double r22688993 = r22688982 + r22688992;
        double r22688994 = 3.0;
        double r22688995 = r22688981 * r22688994;
        double r22688996 = r22688979 / r22688995;
        double r22688997 = r22688993 - r22688996;
        double r22688998 = r22688989 * r22688997;
        double r22688999 = r22688986 - r22688998;
        double r22689000 = r22688979 * r22688999;
        double r22689001 = exp(r22689000);
        double r22689002 = r22688978 * r22689001;
        double r22689003 = r22688977 + r22689002;
        double r22689004 = r22688977 / r22689003;
        return r22689004;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r22689005 = x;
        double r22689006 = y;
        double r22689007 = a;
        double r22689008 = t;
        double r22689009 = r22689007 + r22689008;
        double r22689010 = sqrt(r22689009);
        double r22689011 = cbrt(r22689008);
        double r22689012 = r22689010 / r22689011;
        double r22689013 = z;
        double r22689014 = r22689011 * r22689011;
        double r22689015 = r22689013 / r22689014;
        double r22689016 = r22689012 * r22689015;
        double r22689017 = 5.0;
        double r22689018 = 6.0;
        double r22689019 = r22689017 / r22689018;
        double r22689020 = r22689007 + r22689019;
        double r22689021 = 2.0;
        double r22689022 = 3.0;
        double r22689023 = r22689008 * r22689022;
        double r22689024 = r22689021 / r22689023;
        double r22689025 = r22689020 - r22689024;
        double r22689026 = b;
        double r22689027 = c;
        double r22689028 = r22689026 - r22689027;
        double r22689029 = r22689025 * r22689028;
        double r22689030 = r22689016 - r22689029;
        double r22689031 = r22689030 * r22689021;
        double r22689032 = exp(r22689031);
        double r22689033 = r22689006 * r22689032;
        double r22689034 = r22689005 + r22689033;
        double r22689035 = r22689005 / r22689034;
        return r22689035;
}

Target

Original	3.9
Target	2.9
Herbie	2.8

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

Derivation

Initial program 3.9
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt3.9
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Applied times-frac2.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Final simplification2.8
\[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

Error

Try it out

Target

Derivation

Reproduce

In
Out