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

↓

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

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

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r280918 = x;
        double r280919 = y;
        double r280920 = 2.0;
        double r280921 = z;
        double r280922 = t;
        double r280923 = a;
        double r280924 = r280922 + r280923;
        double r280925 = sqrt(r280924);
        double r280926 = r280921 * r280925;
        double r280927 = r280926 / r280922;
        double r280928 = b;
        double r280929 = c;
        double r280930 = r280928 - r280929;
        double r280931 = 5.0;
        double r280932 = 6.0;
        double r280933 = r280931 / r280932;
        double r280934 = r280923 + r280933;
        double r280935 = 3.0;
        double r280936 = r280922 * r280935;
        double r280937 = r280920 / r280936;
        double r280938 = r280934 - r280937;
        double r280939 = r280930 * r280938;
        double r280940 = r280927 - r280939;
        double r280941 = r280920 * r280940;
        double r280942 = exp(r280941);
        double r280943 = r280919 * r280942;
        double r280944 = r280918 + r280943;
        double r280945 = r280918 / r280944;
        return r280945;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r280946 = x;
        double r280947 = y;
        double r280948 = 2.0;
        double r280949 = t;
        double r280950 = a;
        double r280951 = r280949 + r280950;
        double r280952 = sqrt(r280951);
        double r280953 = r280952 / r280949;
        double r280954 = z;
        double r280955 = r280953 * r280954;
        double r280956 = 3.0;
        double r280957 = r280948 / r280956;
        double r280958 = r280957 / r280949;
        double r280959 = r280950 - r280958;
        double r280960 = 5.0;
        double r280961 = 6.0;
        double r280962 = r280960 / r280961;
        double r280963 = r280959 + r280962;
        double r280964 = c;
        double r280965 = b;
        double r280966 = r280964 - r280965;
        double r280967 = r280963 * r280966;
        double r280968 = r280955 + r280967;
        double r280969 = r280948 * r280968;
        double r280970 = exp(r280969);
        double r280971 = r280947 * r280970;
        double r280972 = r280971 + r280946;
        double r280973 = r280946 / r280972;
        return r280973;
}

Target

Original	4.2
Target	3.0
Herbie	3.5

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

Derivation

Initial program 4.2
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Simplified3.5
\[\leadsto \color{blue}{\frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{a + t}}{t} + \left(c - b\right) \cdot \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right)\right)} + x}}\]
Final simplification3.5
\[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(\frac{\sqrt{t + a}}{t} \cdot z + \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right) \cdot \left(c - b\right)\right)} + x}\]

Reproduce

herbie shell --seed 2019196 
(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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