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

↓

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

\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 r32123167 = x;
        double r32123168 = y;
        double r32123169 = 2.0;
        double r32123170 = z;
        double r32123171 = t;
        double r32123172 = a;
        double r32123173 = r32123171 + r32123172;
        double r32123174 = sqrt(r32123173);
        double r32123175 = r32123170 * r32123174;
        double r32123176 = r32123175 / r32123171;
        double r32123177 = b;
        double r32123178 = c;
        double r32123179 = r32123177 - r32123178;
        double r32123180 = 5.0;
        double r32123181 = 6.0;
        double r32123182 = r32123180 / r32123181;
        double r32123183 = r32123172 + r32123182;
        double r32123184 = 3.0;
        double r32123185 = r32123171 * r32123184;
        double r32123186 = r32123169 / r32123185;
        double r32123187 = r32123183 - r32123186;
        double r32123188 = r32123179 * r32123187;
        double r32123189 = r32123176 - r32123188;
        double r32123190 = r32123169 * r32123189;
        double r32123191 = exp(r32123190);
        double r32123192 = r32123168 * r32123191;
        double r32123193 = r32123167 + r32123192;
        double r32123194 = r32123167 / r32123193;
        return r32123194;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r32123195 = x;
        double r32123196 = y;
        double r32123197 = a;
        double r32123198 = t;
        double r32123199 = r32123197 + r32123198;
        double r32123200 = sqrt(r32123199);
        double r32123201 = cbrt(r32123198);
        double r32123202 = r32123200 / r32123201;
        double r32123203 = z;
        double r32123204 = r32123201 * r32123201;
        double r32123205 = r32123203 / r32123204;
        double r32123206 = r32123202 * r32123205;
        double r32123207 = 5.0;
        double r32123208 = 6.0;
        double r32123209 = r32123207 / r32123208;
        double r32123210 = r32123197 + r32123209;
        double r32123211 = 2.0;
        double r32123212 = 3.0;
        double r32123213 = r32123198 * r32123212;
        double r32123214 = r32123211 / r32123213;
        double r32123215 = r32123210 - r32123214;
        double r32123216 = b;
        double r32123217 = c;
        double r32123218 = r32123216 - r32123217;
        double r32123219 = r32123215 * r32123218;
        double r32123220 = r32123206 - r32123219;
        double r32123221 = r32123220 * r32123211;
        double r32123222 = exp(r32123221);
        double r32123223 = r32123196 * r32123222;
        double r32123224 = r32123195 + r32123223;
        double r32123225 = r32123195 / r32123224;
        return r32123225;
}

Target

Original	3.9
Target	3.0
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 3.9
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
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-frac2.7
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Final simplification2.7
\[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]

Reproduce

herbie shell --seed 2019171 
(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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