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

↓

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

\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 r22861103 = x;
        double r22861104 = y;
        double r22861105 = 2.0;
        double r22861106 = z;
        double r22861107 = t;
        double r22861108 = a;
        double r22861109 = r22861107 + r22861108;
        double r22861110 = sqrt(r22861109);
        double r22861111 = r22861106 * r22861110;
        double r22861112 = r22861111 / r22861107;
        double r22861113 = b;
        double r22861114 = c;
        double r22861115 = r22861113 - r22861114;
        double r22861116 = 5.0;
        double r22861117 = 6.0;
        double r22861118 = r22861116 / r22861117;
        double r22861119 = r22861108 + r22861118;
        double r22861120 = 3.0;
        double r22861121 = r22861107 * r22861120;
        double r22861122 = r22861105 / r22861121;
        double r22861123 = r22861119 - r22861122;
        double r22861124 = r22861115 * r22861123;
        double r22861125 = r22861112 - r22861124;
        double r22861126 = r22861105 * r22861125;
        double r22861127 = exp(r22861126);
        double r22861128 = r22861104 * r22861127;
        double r22861129 = r22861103 + r22861128;
        double r22861130 = r22861103 / r22861129;
        return r22861130;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r22861131 = x;
        double r22861132 = y;
        double r22861133 = a;
        double r22861134 = t;
        double r22861135 = r22861133 + r22861134;
        double r22861136 = sqrt(r22861135);
        double r22861137 = cbrt(r22861134);
        double r22861138 = r22861136 / r22861137;
        double r22861139 = z;
        double r22861140 = r22861137 * r22861137;
        double r22861141 = r22861139 / r22861140;
        double r22861142 = r22861138 * r22861141;
        double r22861143 = 5.0;
        double r22861144 = 6.0;
        double r22861145 = r22861143 / r22861144;
        double r22861146 = r22861133 + r22861145;
        double r22861147 = 2.0;
        double r22861148 = 3.0;
        double r22861149 = r22861134 * r22861148;
        double r22861150 = r22861147 / r22861149;
        double r22861151 = r22861146 - r22861150;
        double r22861152 = b;
        double r22861153 = c;
        double r22861154 = r22861152 - r22861153;
        double r22861155 = r22861151 * r22861154;
        double r22861156 = r22861142 - r22861155;
        double r22861157 = r22861156 * r22861147;
        double r22861158 = exp(r22861157);
        double r22861159 = r22861132 * r22861158;
        double r22861160 = r22861131 + r22861159;
        double r22861161 = r22861131 / r22861160;
        return r22861161;
}

Target

Original	3.9
Target	2.9
Herbie	2.6

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

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

Reproduce

herbie shell --seed 2019174 
(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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