Average Error: 1.9 → 1.3
Time: 12.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right) \cdot \frac{1}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right) \cdot \frac{1}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r72283 = x;
        double r72284 = y;
        double r72285 = z;
        double r72286 = log(r72285);
        double r72287 = r72284 * r72286;
        double r72288 = t;
        double r72289 = 1.0;
        double r72290 = r72288 - r72289;
        double r72291 = a;
        double r72292 = log(r72291);
        double r72293 = r72290 * r72292;
        double r72294 = r72287 + r72293;
        double r72295 = b;
        double r72296 = r72294 - r72295;
        double r72297 = exp(r72296);
        double r72298 = r72283 * r72297;
        double r72299 = r72298 / r72284;
        return r72299;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r72300 = x;
        double r72301 = 1.0;
        double r72302 = a;
        double r72303 = r72301 / r72302;
        double r72304 = 1.0;
        double r72305 = pow(r72303, r72304);
        double r72306 = y;
        double r72307 = z;
        double r72308 = r72301 / r72307;
        double r72309 = log(r72308);
        double r72310 = r72306 * r72309;
        double r72311 = log(r72303);
        double r72312 = t;
        double r72313 = r72311 * r72312;
        double r72314 = b;
        double r72315 = r72313 + r72314;
        double r72316 = r72310 + r72315;
        double r72317 = exp(r72316);
        double r72318 = r72305 / r72317;
        double r72319 = r72300 * r72318;
        double r72320 = r72301 / r72306;
        double r72321 = r72319 * r72320;
        return r72321;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

  2. Taylor expanded around inf 1.9

    \[\leadsto \frac{x \cdot \color{blue}{e^{1 \cdot \log \left(\frac{1}{a}\right) - \left(y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)\right)}}}{y}\]

  3. Simplified1.2

    \[\leadsto \frac{x \cdot \color{blue}{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]
  4. Using strategy rm

  5. Applied div-inv1.3

    \[\leadsto \color{blue}{\left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right) \cdot \frac{1}{y}}\]

  6. Final simplification1.3

    \[\leadsto \left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right) \cdot \frac{1}{y}\]

Reproduce

herbie shell --seed 2020059 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))