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

↓

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

\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 r20803507 = x;
        double r20803508 = y;
        double r20803509 = 2.0;
        double r20803510 = z;
        double r20803511 = t;
        double r20803512 = a;
        double r20803513 = r20803511 + r20803512;
        double r20803514 = sqrt(r20803513);
        double r20803515 = r20803510 * r20803514;
        double r20803516 = r20803515 / r20803511;
        double r20803517 = b;
        double r20803518 = c;
        double r20803519 = r20803517 - r20803518;
        double r20803520 = 5.0;
        double r20803521 = 6.0;
        double r20803522 = r20803520 / r20803521;
        double r20803523 = r20803512 + r20803522;
        double r20803524 = 3.0;
        double r20803525 = r20803511 * r20803524;
        double r20803526 = r20803509 / r20803525;
        double r20803527 = r20803523 - r20803526;
        double r20803528 = r20803519 * r20803527;
        double r20803529 = r20803516 - r20803528;
        double r20803530 = r20803509 * r20803529;
        double r20803531 = exp(r20803530);
        double r20803532 = r20803508 * r20803531;
        double r20803533 = r20803507 + r20803532;
        double r20803534 = r20803507 / r20803533;
        return r20803534;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r20803535 = x;
        double r20803536 = y;
        double r20803537 = a;
        double r20803538 = t;
        double r20803539 = r20803537 + r20803538;
        double r20803540 = sqrt(r20803539);
        double r20803541 = cbrt(r20803538);
        double r20803542 = r20803540 / r20803541;
        double r20803543 = z;
        double r20803544 = r20803541 * r20803541;
        double r20803545 = r20803543 / r20803544;
        double r20803546 = r20803542 * r20803545;
        double r20803547 = 5.0;
        double r20803548 = 6.0;
        double r20803549 = r20803547 / r20803548;
        double r20803550 = r20803537 + r20803549;
        double r20803551 = 2.0;
        double r20803552 = 3.0;
        double r20803553 = r20803538 * r20803552;
        double r20803554 = r20803551 / r20803553;
        double r20803555 = r20803550 - r20803554;
        double r20803556 = b;
        double r20803557 = c;
        double r20803558 = r20803556 - r20803557;
        double r20803559 = r20803555 * r20803558;
        double r20803560 = r20803546 - r20803559;
        double r20803561 = r20803560 * r20803551;
        double r20803562 = exp(r20803561);
        double r20803563 = r20803536 * r20803562;
        double r20803564 = r20803535 + r20803563;
        double r20803565 = r20803535 / r20803564;
        return r20803565;
}

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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