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

↓

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

\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(\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)}}

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r484416 = x;
        double r484417 = y;
        double r484418 = 2.0;
        double r484419 = z;
        double r484420 = t;
        double r484421 = a;
        double r484422 = r484420 + r484421;
        double r484423 = sqrt(r484422);
        double r484424 = r484419 * r484423;
        double r484425 = r484424 / r484420;
        double r484426 = b;
        double r484427 = c;
        double r484428 = r484426 - r484427;
        double r484429 = 5.0;
        double r484430 = 6.0;
        double r484431 = r484429 / r484430;
        double r484432 = r484421 + r484431;
        double r484433 = 3.0;
        double r484434 = r484420 * r484433;
        double r484435 = r484418 / r484434;
        double r484436 = r484432 - r484435;
        double r484437 = r484428 * r484436;
        double r484438 = r484425 - r484437;
        double r484439 = r484418 * r484438;
        double r484440 = exp(r484439);
        double r484441 = r484417 * r484440;
        double r484442 = r484416 + r484441;
        double r484443 = r484416 / r484442;
        return r484443;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r484444 = x;
        double r484445 = y;
        double r484446 = 2.0;
        double r484447 = z;
        double r484448 = t;
        double r484449 = cbrt(r484448);
        double r484450 = r484449 * r484449;
        double r484451 = r484447 / r484450;
        double r484452 = a;
        double r484453 = r484448 + r484452;
        double r484454 = sqrt(r484453);
        double r484455 = r484454 / r484449;
        double r484456 = r484451 * r484455;
        double r484457 = b;
        double r484458 = c;
        double r484459 = r484457 - r484458;
        double r484460 = 5.0;
        double r484461 = 6.0;
        double r484462 = r484460 / r484461;
        double r484463 = r484452 + r484462;
        double r484464 = 3.0;
        double r484465 = r484448 * r484464;
        double r484466 = r484446 / r484465;
        double r484467 = r484463 - r484466;
        double r484468 = r484459 * r484467;
        double r484469 = r484456 - r484468;
        double r484470 = r484446 * r484469;
        double r484471 = exp(r484470);
        double r484472 = r484445 * r484471;
        double r484473 = r484444 + r484472;
        double r484474 = r484444 / r484473;
        return r484474;
}

Target

Original	3.8
Target	3.1
Herbie	2.6

\[\begin{array}{l} \mathbf{if}\;t \lt -2.1183266448915811 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.83333333333333337 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.19658877065154709 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 3.8
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt3.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Applied times-frac2.6
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Final simplification2.6
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

Reproduce

herbie shell --seed 2020060 
(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

In
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