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

↓

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

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

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r304298 = x;
        double r304299 = y;
        double r304300 = 2.0;
        double r304301 = z;
        double r304302 = t;
        double r304303 = a;
        double r304304 = r304302 + r304303;
        double r304305 = sqrt(r304304);
        double r304306 = r304301 * r304305;
        double r304307 = r304306 / r304302;
        double r304308 = b;
        double r304309 = c;
        double r304310 = r304308 - r304309;
        double r304311 = 5.0;
        double r304312 = 6.0;
        double r304313 = r304311 / r304312;
        double r304314 = r304303 + r304313;
        double r304315 = 3.0;
        double r304316 = r304302 * r304315;
        double r304317 = r304300 / r304316;
        double r304318 = r304314 - r304317;
        double r304319 = r304310 * r304318;
        double r304320 = r304307 - r304319;
        double r304321 = r304300 * r304320;
        double r304322 = exp(r304321);
        double r304323 = r304299 * r304322;
        double r304324 = r304298 + r304323;
        double r304325 = r304298 / r304324;
        return r304325;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r304326 = x;
        double r304327 = y;
        double r304328 = 2.0;
        double r304329 = z;
        double r304330 = t;
        double r304331 = a;
        double r304332 = r304330 + r304331;
        double r304333 = sqrt(r304332);
        double r304334 = r304333 / r304330;
        double r304335 = r304329 * r304334;
        double r304336 = b;
        double r304337 = c;
        double r304338 = r304336 - r304337;
        double r304339 = 5.0;
        double r304340 = 6.0;
        double r304341 = r304339 / r304340;
        double r304342 = r304331 + r304341;
        double r304343 = 3.0;
        double r304344 = r304330 * r304343;
        double r304345 = r304328 / r304344;
        double r304346 = r304342 - r304345;
        double r304347 = r304338 * r304346;
        double r304348 = r304335 - r304347;
        double r304349 = r304328 * r304348;
        double r304350 = exp(r304349);
        double r304351 = r304327 * r304350;
        double r304352 = r304326 + r304351;
        double r304353 = r304326 / r304352;
        return r304353;
}

Target

Original	4.2
Target	3.1
Herbie	3.6

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

Derivation

Initial program 4.2
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied *-un-lft-identity4.2
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{1 \cdot t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Applied times-frac3.6
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{1} \cdot \frac{\sqrt{t + a}}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Simplified3.6
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{z} \cdot \frac{\sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Final simplification3.6
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3))))))))))))

  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))

Error

Try it out

Target

Derivation

Reproduce

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