Average Error: 1.8 → 1.2
Time: 16.4s
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 r89314 = x;
        double r89315 = y;
        double r89316 = z;
        double r89317 = log(r89316);
        double r89318 = r89315 * r89317;
        double r89319 = t;
        double r89320 = 1.0;
        double r89321 = r89319 - r89320;
        double r89322 = a;
        double r89323 = log(r89322);
        double r89324 = r89321 * r89323;
        double r89325 = r89318 + r89324;
        double r89326 = b;
        double r89327 = r89325 - r89326;
        double r89328 = exp(r89327);
        double r89329 = r89314 * r89328;
        double r89330 = r89329 / r89315;
        return r89330;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r89331 = x;
        double r89332 = 1.0;
        double r89333 = a;
        double r89334 = r89332 / r89333;
        double r89335 = 1.0;
        double r89336 = pow(r89334, r89335);
        double r89337 = y;
        double r89338 = z;
        double r89339 = r89332 / r89338;
        double r89340 = log(r89339);
        double r89341 = r89337 * r89340;
        double r89342 = log(r89334);
        double r89343 = t;
        double r89344 = r89342 * r89343;
        double r89345 = b;
        double r89346 = r89344 + r89345;
        double r89347 = r89341 + r89346;
        double r89348 = exp(r89347);
        double r89349 = r89336 / r89348;
        double r89350 = r89331 * r89349;
        double r89351 = r89332 / r89337;
        double r89352 = r89350 * r89351;
        return r89352;
}

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 1.8

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

  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. Simplified1.1

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

  5. Applied div-inv1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020100 
(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))