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

↓

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

\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 r20455458 = x;
        double r20455459 = y;
        double r20455460 = 2.0;
        double r20455461 = z;
        double r20455462 = t;
        double r20455463 = a;
        double r20455464 = r20455462 + r20455463;
        double r20455465 = sqrt(r20455464);
        double r20455466 = r20455461 * r20455465;
        double r20455467 = r20455466 / r20455462;
        double r20455468 = b;
        double r20455469 = c;
        double r20455470 = r20455468 - r20455469;
        double r20455471 = 5.0;
        double r20455472 = 6.0;
        double r20455473 = r20455471 / r20455472;
        double r20455474 = r20455463 + r20455473;
        double r20455475 = 3.0;
        double r20455476 = r20455462 * r20455475;
        double r20455477 = r20455460 / r20455476;
        double r20455478 = r20455474 - r20455477;
        double r20455479 = r20455470 * r20455478;
        double r20455480 = r20455467 - r20455479;
        double r20455481 = r20455460 * r20455480;
        double r20455482 = exp(r20455481);
        double r20455483 = r20455459 * r20455482;
        double r20455484 = r20455458 + r20455483;
        double r20455485 = r20455458 / r20455484;
        return r20455485;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r20455486 = x;
        double r20455487 = y;
        double r20455488 = a;
        double r20455489 = t;
        double r20455490 = r20455488 + r20455489;
        double r20455491 = sqrt(r20455490);
        double r20455492 = cbrt(r20455489);
        double r20455493 = r20455491 / r20455492;
        double r20455494 = z;
        double r20455495 = r20455492 * r20455492;
        double r20455496 = r20455494 / r20455495;
        double r20455497 = r20455493 * r20455496;
        double r20455498 = 5.0;
        double r20455499 = 6.0;
        double r20455500 = r20455498 / r20455499;
        double r20455501 = r20455488 + r20455500;
        double r20455502 = 2.0;
        double r20455503 = 3.0;
        double r20455504 = r20455489 * r20455503;
        double r20455505 = r20455502 / r20455504;
        double r20455506 = r20455501 - r20455505;
        double r20455507 = b;
        double r20455508 = c;
        double r20455509 = r20455507 - r20455508;
        double r20455510 = r20455506 * r20455509;
        double r20455511 = r20455497 - r20455510;
        double r20455512 = r20455511 * r20455502;
        double r20455513 = exp(r20455512);
        double r20455514 = r20455487 * r20455513;
        double r20455515 = r20455486 + r20455514;
        double r20455516 = r20455486 / r20455515;
        return r20455516;
}

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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