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

↓

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

\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 r23020697 = x;
        double r23020698 = y;
        double r23020699 = 2.0;
        double r23020700 = z;
        double r23020701 = t;
        double r23020702 = a;
        double r23020703 = r23020701 + r23020702;
        double r23020704 = sqrt(r23020703);
        double r23020705 = r23020700 * r23020704;
        double r23020706 = r23020705 / r23020701;
        double r23020707 = b;
        double r23020708 = c;
        double r23020709 = r23020707 - r23020708;
        double r23020710 = 5.0;
        double r23020711 = 6.0;
        double r23020712 = r23020710 / r23020711;
        double r23020713 = r23020702 + r23020712;
        double r23020714 = 3.0;
        double r23020715 = r23020701 * r23020714;
        double r23020716 = r23020699 / r23020715;
        double r23020717 = r23020713 - r23020716;
        double r23020718 = r23020709 * r23020717;
        double r23020719 = r23020706 - r23020718;
        double r23020720 = r23020699 * r23020719;
        double r23020721 = exp(r23020720);
        double r23020722 = r23020698 * r23020721;
        double r23020723 = r23020697 + r23020722;
        double r23020724 = r23020697 / r23020723;
        return r23020724;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r23020725 = x;
        double r23020726 = y;
        double r23020727 = a;
        double r23020728 = t;
        double r23020729 = r23020727 + r23020728;
        double r23020730 = sqrt(r23020729);
        double r23020731 = cbrt(r23020728);
        double r23020732 = r23020730 / r23020731;
        double r23020733 = z;
        double r23020734 = r23020731 * r23020731;
        double r23020735 = r23020733 / r23020734;
        double r23020736 = r23020732 * r23020735;
        double r23020737 = 5.0;
        double r23020738 = 6.0;
        double r23020739 = r23020737 / r23020738;
        double r23020740 = r23020727 + r23020739;
        double r23020741 = 2.0;
        double r23020742 = 3.0;
        double r23020743 = r23020728 * r23020742;
        double r23020744 = r23020741 / r23020743;
        double r23020745 = r23020740 - r23020744;
        double r23020746 = b;
        double r23020747 = c;
        double r23020748 = r23020746 - r23020747;
        double r23020749 = r23020745 * r23020748;
        double r23020750 = r23020736 - r23020749;
        double r23020751 = r23020750 * r23020741;
        double r23020752 = exp(r23020751);
        double r23020753 = r23020726 * r23020752;
        double r23020754 = r23020725 + r23020753;
        double r23020755 = r23020725 / r23020754;
        return r23020755;
}

Target

Original	4.0
Target	3.0
Herbie	2.8

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

Derivation

Initial program 4.0
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
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-frac2.8
\[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
Final simplification2.8
\[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]

Reproduce

herbie shell --seed 2019172 
(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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