Average Error: 4.1 → 2.2
Time: 1.1m
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.499850531274005 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{elif}\;t \le 1.230296909173772 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(\left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot z\right) \cdot \sqrt{t + a} - \left(b - c\right) \cdot \left(t \cdot \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) - 2.0 \cdot \left(a - \frac{5.0}{6.0}\right)\right)\right)}{\left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot t} \cdot 2.0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \end{array}\]
\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)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.499850531274005 \cdot 10^{-14}:\\
\;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\

\mathbf{elif}\;t \le 1.230296909173772 \cdot 10^{-287}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(\left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot z\right) \cdot \sqrt{t + a} - \left(b - c\right) \cdot \left(t \cdot \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) - 2.0 \cdot \left(a - \frac{5.0}{6.0}\right)\right)\right)}{\left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot t} \cdot 2.0}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4944223 = x;
        double r4944224 = y;
        double r4944225 = 2.0;
        double r4944226 = z;
        double r4944227 = t;
        double r4944228 = a;
        double r4944229 = r4944227 + r4944228;
        double r4944230 = sqrt(r4944229);
        double r4944231 = r4944226 * r4944230;
        double r4944232 = r4944231 / r4944227;
        double r4944233 = b;
        double r4944234 = c;
        double r4944235 = r4944233 - r4944234;
        double r4944236 = 5.0;
        double r4944237 = 6.0;
        double r4944238 = r4944236 / r4944237;
        double r4944239 = r4944228 + r4944238;
        double r4944240 = 3.0;
        double r4944241 = r4944227 * r4944240;
        double r4944242 = r4944225 / r4944241;
        double r4944243 = r4944239 - r4944242;
        double r4944244 = r4944235 * r4944243;
        double r4944245 = r4944232 - r4944244;
        double r4944246 = r4944225 * r4944245;
        double r4944247 = exp(r4944246);
        double r4944248 = r4944224 * r4944247;
        double r4944249 = r4944223 + r4944248;
        double r4944250 = r4944223 / r4944249;
        return r4944250;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4944251 = t;
        double r4944252 = -9.499850531274005e-14;
        bool r4944253 = r4944251 <= r4944252;
        double r4944254 = x;
        double r4944255 = z;
        double r4944256 = cbrt(r4944251);
        double r4944257 = r4944256 * r4944256;
        double r4944258 = r4944255 / r4944257;
        double r4944259 = a;
        double r4944260 = r4944251 + r4944259;
        double r4944261 = sqrt(r4944260);
        double r4944262 = r4944261 / r4944256;
        double r4944263 = r4944258 * r4944262;
        double r4944264 = 5.0;
        double r4944265 = 6.0;
        double r4944266 = r4944264 / r4944265;
        double r4944267 = r4944266 + r4944259;
        double r4944268 = 2.0;
        double r4944269 = 3.0;
        double r4944270 = r4944251 * r4944269;
        double r4944271 = r4944268 / r4944270;
        double r4944272 = r4944267 - r4944271;
        double r4944273 = b;
        double r4944274 = c;
        double r4944275 = r4944273 - r4944274;
        double r4944276 = r4944272 * r4944275;
        double r4944277 = r4944263 - r4944276;
        double r4944278 = r4944277 * r4944268;
        double r4944279 = exp(r4944278);
        double r4944280 = y;
        double r4944281 = r4944279 * r4944280;
        double r4944282 = r4944281 + r4944254;
        double r4944283 = r4944254 / r4944282;
        double r4944284 = 1.230296909173772e-287;
        bool r4944285 = r4944251 <= r4944284;
        double r4944286 = r4944259 - r4944266;
        double r4944287 = r4944270 * r4944286;
        double r4944288 = r4944287 * r4944255;
        double r4944289 = r4944288 * r4944261;
        double r4944290 = r4944267 * r4944287;
        double r4944291 = r4944268 * r4944286;
        double r4944292 = r4944290 - r4944291;
        double r4944293 = r4944251 * r4944292;
        double r4944294 = r4944275 * r4944293;
        double r4944295 = r4944289 - r4944294;
        double r4944296 = r4944287 * r4944251;
        double r4944297 = r4944295 / r4944296;
        double r4944298 = r4944297 * r4944268;
        double r4944299 = exp(r4944298);
        double r4944300 = r4944280 * r4944299;
        double r4944301 = r4944254 + r4944300;
        double r4944302 = r4944254 / r4944301;
        double r4944303 = r4944285 ? r4944302 : r4944283;
        double r4944304 = r4944253 ? r4944283 : r4944303;
        return r4944304;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -9.499850531274005e-14 or 1.230296909173772e-287 < t

    1. Initial program 3.1

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

    3. Applied add-cube-cbrt3.1

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

    4. Applied times-frac1.6

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

    if -9.499850531274005e-14 < t < 1.230296909173772e-287

    1. Initial program 7.8

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

    3. Applied flip-+10.0

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

    4. Applied frac-sub10.0

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

    5. Applied associate-*r/10.1

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

    6. Applied frac-sub7.0

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

    7. Simplified4.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\sqrt{a + t} \cdot \left(z \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)\right) - \left(b - c\right) \cdot \left(\left(\left(a + \frac{5.0}{6.0}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - 2.0 \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot t\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.499850531274005 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{elif}\;t \le 1.230296909173772 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(\left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot z\right) \cdot \sqrt{t + a} - \left(b - c\right) \cdot \left(t \cdot \left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) - 2.0 \cdot \left(a - \frac{5.0}{6.0}\right)\right)\right)}{\left(\left(t \cdot 3.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot t} \cdot 2.0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))