\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

↓

\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]

\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\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{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r19905090 = x;
        double r19905091 = y;
        double r19905092 = 2.0;
        double r19905093 = z;
        double r19905094 = t;
        double r19905095 = a;
        double r19905096 = r19905094 + r19905095;
        double r19905097 = sqrt(r19905096);
        double r19905098 = r19905093 * r19905097;
        double r19905099 = r19905098 / r19905094;
        double r19905100 = b;
        double r19905101 = c;
        double r19905102 = r19905100 - r19905101;
        double r19905103 = 5.0;
        double r19905104 = 6.0;
        double r19905105 = r19905103 / r19905104;
        double r19905106 = r19905095 + r19905105;
        double r19905107 = 3.0;
        double r19905108 = r19905094 * r19905107;
        double r19905109 = r19905092 / r19905108;
        double r19905110 = r19905106 - r19905109;
        double r19905111 = r19905102 * r19905110;
        double r19905112 = r19905099 - r19905111;
        double r19905113 = r19905092 * r19905112;
        double r19905114 = exp(r19905113);
        double r19905115 = r19905091 * r19905114;
        double r19905116 = r19905090 + r19905115;
        double r19905117 = r19905090 / r19905116;
        return r19905117;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c) {
        double r19905118 = x;
        double r19905119 = y;
        double r19905120 = a;
        double r19905121 = t;
        double r19905122 = r19905120 + r19905121;
        double r19905123 = sqrt(r19905122);
        double r19905124 = cbrt(r19905121);
        double r19905125 = r19905123 / r19905124;
        double r19905126 = z;
        double r19905127 = r19905124 * r19905124;
        double r19905128 = r19905126 / r19905127;
        double r19905129 = r19905125 * r19905128;
        double r19905130 = 5.0;
        double r19905131 = 6.0;
        double r19905132 = r19905130 / r19905131;
        double r19905133 = r19905120 + r19905132;
        double r19905134 = 2.0;
        double r19905135 = 3.0;
        double r19905136 = r19905121 * r19905135;
        double r19905137 = r19905134 / r19905136;
        double r19905138 = r19905133 - r19905137;
        double r19905139 = b;
        double r19905140 = c;
        double r19905141 = r19905139 - r19905140;
        double r19905142 = r19905138 * r19905141;
        double r19905143 = r19905129 - r19905142;
        double r19905144 = r19905143 * r19905134;
        double r19905145 = exp(r19905144);
        double r19905146 = r19905119 * r19905145;
        double r19905147 = r19905118 + r19905146;
        double r19905148 = r19905118 / r19905147;
        return r19905148;
}

Target

Original	3.6
Target	3.1
Herbie	2.4

\[\begin{array}{l} \mathbf{if}\;t \lt -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t \lt 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) - \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(3.0 \cdot t\right) - 2.0\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\\ \end{array}\]

Derivation

Initial program 3.6
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Using strategy rm
Applied add-cube-cbrt3.6
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Applied times-frac2.4
\[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Final simplification2.4
\[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]

Reproduce

herbie shell --seed 2019163 
(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

In
Out