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

↓

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

\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 r29426139 = x;
        double r29426140 = y;
        double r29426141 = 2.0;
        double r29426142 = z;
        double r29426143 = t;
        double r29426144 = a;
        double r29426145 = r29426143 + r29426144;
        double r29426146 = sqrt(r29426145);
        double r29426147 = r29426142 * r29426146;
        double r29426148 = r29426147 / r29426143;
        double r29426149 = b;
        double r29426150 = c;
        double r29426151 = r29426149 - r29426150;
        double r29426152 = 5.0;
        double r29426153 = 6.0;
        double r29426154 = r29426152 / r29426153;
        double r29426155 = r29426144 + r29426154;
        double r29426156 = 3.0;
        double r29426157 = r29426143 * r29426156;
        double r29426158 = r29426141 / r29426157;
        double r29426159 = r29426155 - r29426158;
        double r29426160 = r29426151 * r29426159;
        double r29426161 = r29426148 - r29426160;
        double r29426162 = r29426141 * r29426161;
        double r29426163 = exp(r29426162);
        double r29426164 = r29426140 * r29426163;
        double r29426165 = r29426139 + r29426164;
        double r29426166 = r29426139 / r29426165;
        return r29426166;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r29426167 = x;
        double r29426168 = y;
        double r29426169 = 2.0;
        double r29426170 = z;
        double r29426171 = t;
        double r29426172 = cbrt(r29426171);
        double r29426173 = r29426172 * r29426172;
        double r29426174 = r29426170 / r29426173;
        double r29426175 = a;
        double r29426176 = r29426171 + r29426175;
        double r29426177 = sqrt(r29426176);
        double r29426178 = r29426177 / r29426172;
        double r29426179 = r29426174 * r29426178;
        double r29426180 = b;
        double r29426181 = c;
        double r29426182 = r29426180 - r29426181;
        double r29426183 = 5.0;
        double r29426184 = 6.0;
        double r29426185 = r29426183 / r29426184;
        double r29426186 = r29426175 + r29426185;
        double r29426187 = 3.0;
        double r29426188 = r29426171 * r29426187;
        double r29426189 = r29426169 / r29426188;
        double r29426190 = r29426186 - r29426189;
        double r29426191 = r29426182 * r29426190;
        double r29426192 = r29426179 - r29426191;
        double r29426193 = r29426169 * r29426192;
        double r29426194 = exp(r29426193);
        double r29426195 = r29426168 * r29426194;
        double r29426196 = r29426167 + r29426195;
        double r29426197 = r29426167 / r29426196;
        return r29426197;
}

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

Reproduce

herbie shell --seed 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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