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

↓

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

\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 r22236960 = x;
        double r22236961 = y;
        double r22236962 = 2.0;
        double r22236963 = z;
        double r22236964 = t;
        double r22236965 = a;
        double r22236966 = r22236964 + r22236965;
        double r22236967 = sqrt(r22236966);
        double r22236968 = r22236963 * r22236967;
        double r22236969 = r22236968 / r22236964;
        double r22236970 = b;
        double r22236971 = c;
        double r22236972 = r22236970 - r22236971;
        double r22236973 = 5.0;
        double r22236974 = 6.0;
        double r22236975 = r22236973 / r22236974;
        double r22236976 = r22236965 + r22236975;
        double r22236977 = 3.0;
        double r22236978 = r22236964 * r22236977;
        double r22236979 = r22236962 / r22236978;
        double r22236980 = r22236976 - r22236979;
        double r22236981 = r22236972 * r22236980;
        double r22236982 = r22236969 - r22236981;
        double r22236983 = r22236962 * r22236982;
        double r22236984 = exp(r22236983);
        double r22236985 = r22236961 * r22236984;
        double r22236986 = r22236960 + r22236985;
        double r22236987 = r22236960 / r22236986;
        return r22236987;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r22236988 = x;
        double r22236989 = y;
        double r22236990 = a;
        double r22236991 = t;
        double r22236992 = r22236990 + r22236991;
        double r22236993 = sqrt(r22236992);
        double r22236994 = cbrt(r22236991);
        double r22236995 = r22236993 / r22236994;
        double r22236996 = z;
        double r22236997 = r22236994 * r22236994;
        double r22236998 = r22236996 / r22236997;
        double r22236999 = r22236995 * r22236998;
        double r22237000 = 5.0;
        double r22237001 = 6.0;
        double r22237002 = r22237000 / r22237001;
        double r22237003 = r22236990 + r22237002;
        double r22237004 = 2.0;
        double r22237005 = 3.0;
        double r22237006 = r22236991 * r22237005;
        double r22237007 = r22237004 / r22237006;
        double r22237008 = r22237003 - r22237007;
        double r22237009 = b;
        double r22237010 = c;
        double r22237011 = r22237009 - r22237010;
        double r22237012 = r22237008 * r22237011;
        double r22237013 = r22236999 - r22237012;
        double r22237014 = r22237013 * r22237004;
        double r22237015 = exp(r22237014);
        double r22237016 = r22236989 * r22237015;
        double r22237017 = r22236988 + r22237016;
        double r22237018 = r22236988 / r22237017;
        return r22237018;
}

Target

Original	4.0
Target	3.0
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 4.0
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt4.0
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
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 2019172 
(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

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