\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

↓

\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]

\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\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{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r23728167 = x;
        double r23728168 = y;
        double r23728169 = 2.0;
        double r23728170 = z;
        double r23728171 = t;
        double r23728172 = a;
        double r23728173 = r23728171 + r23728172;
        double r23728174 = sqrt(r23728173);
        double r23728175 = r23728170 * r23728174;
        double r23728176 = r23728175 / r23728171;
        double r23728177 = b;
        double r23728178 = c;
        double r23728179 = r23728177 - r23728178;
        double r23728180 = 5.0;
        double r23728181 = 6.0;
        double r23728182 = r23728180 / r23728181;
        double r23728183 = r23728172 + r23728182;
        double r23728184 = 3.0;
        double r23728185 = r23728171 * r23728184;
        double r23728186 = r23728169 / r23728185;
        double r23728187 = r23728183 - r23728186;
        double r23728188 = r23728179 * r23728187;
        double r23728189 = r23728176 - r23728188;
        double r23728190 = r23728169 * r23728189;
        double r23728191 = exp(r23728190);
        double r23728192 = r23728168 * r23728191;
        double r23728193 = r23728167 + r23728192;
        double r23728194 = r23728167 / r23728193;
        return r23728194;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r23728195 = x;
        double r23728196 = y;
        double r23728197 = a;
        double r23728198 = t;
        double r23728199 = r23728197 + r23728198;
        double r23728200 = sqrt(r23728199);
        double r23728201 = cbrt(r23728198);
        double r23728202 = r23728200 / r23728201;
        double r23728203 = z;
        double r23728204 = r23728201 * r23728201;
        double r23728205 = r23728203 / r23728204;
        double r23728206 = r23728202 * r23728205;
        double r23728207 = 5.0;
        double r23728208 = 6.0;
        double r23728209 = r23728207 / r23728208;
        double r23728210 = r23728197 + r23728209;
        double r23728211 = 2.0;
        double r23728212 = 3.0;
        double r23728213 = r23728198 * r23728212;
        double r23728214 = r23728211 / r23728213;
        double r23728215 = r23728210 - r23728214;
        double r23728216 = b;
        double r23728217 = c;
        double r23728218 = r23728216 - r23728217;
        double r23728219 = r23728215 * r23728218;
        double r23728220 = r23728206 - r23728219;
        double r23728221 = r23728220 * r23728211;
        double r23728222 = exp(r23728221);
        double r23728223 = r23728196 * r23728222;
        double r23728224 = r23728195 + r23728223;
        double r23728225 = r23728195 / r23728224;
        return r23728225;
}

Target

Original	3.6
Target	3.1
Herbie	2.4

\[\begin{array}{l} \mathbf{if}\;t \lt -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) - \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(3.0 \cdot t\right) - 2.0\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 3.6
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt3.6
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Applied times-frac2.4
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Final simplification2.4
\[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]

Reproduce

herbie shell --seed 2019163 
(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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