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

↓

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

\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 r518420 = x;
        double r518421 = y;
        double r518422 = 2.0;
        double r518423 = z;
        double r518424 = t;
        double r518425 = a;
        double r518426 = r518424 + r518425;
        double r518427 = sqrt(r518426);
        double r518428 = r518423 * r518427;
        double r518429 = r518428 / r518424;
        double r518430 = b;
        double r518431 = c;
        double r518432 = r518430 - r518431;
        double r518433 = 5.0;
        double r518434 = 6.0;
        double r518435 = r518433 / r518434;
        double r518436 = r518425 + r518435;
        double r518437 = 3.0;
        double r518438 = r518424 * r518437;
        double r518439 = r518422 / r518438;
        double r518440 = r518436 - r518439;
        double r518441 = r518432 * r518440;
        double r518442 = r518429 - r518441;
        double r518443 = r518422 * r518442;
        double r518444 = exp(r518443);
        double r518445 = r518421 * r518444;
        double r518446 = r518420 + r518445;
        double r518447 = r518420 / r518446;
        return r518447;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r518448 = x;
        double r518449 = y;
        double r518450 = 2.0;
        double r518451 = z;
        double r518452 = t;
        double r518453 = cbrt(r518452);
        double r518454 = r518453 * r518453;
        double r518455 = r518451 / r518454;
        double r518456 = a;
        double r518457 = r518452 + r518456;
        double r518458 = sqrt(r518457);
        double r518459 = r518458 / r518453;
        double r518460 = r518455 * r518459;
        double r518461 = b;
        double r518462 = c;
        double r518463 = r518461 - r518462;
        double r518464 = 5.0;
        double r518465 = 6.0;
        double r518466 = r518464 / r518465;
        double r518467 = r518456 + r518466;
        double r518468 = 3.0;
        double r518469 = r518452 * r518468;
        double r518470 = r518450 / r518469;
        double r518471 = r518467 - r518470;
        double r518472 = r518463 * r518471;
        double r518473 = r518460 - r518472;
        double r518474 = r518450 * r518473;
        double r518475 = exp(r518474);
        double r518476 = r518449 * r518475;
        double r518477 = r518448 + r518476;
        double r518478 = r518448 / r518477;
        return r518478;
}

Target

Original	4.0
Target	3.1
Herbie	2.7

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

Derivation

Initial program 4.0
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt4.0
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
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
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

Reproduce

herbie shell --seed 2020047 
(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)))))))))))

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

Reproduce

In
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