Average Error: 1.9 → 25.1
Time: 1.1m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{\frac{\frac{y}{{z}^{y}}}{x}}}{\frac{e^{b}}{{a}^{t}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{\frac{\frac{y}{{z}^{y}}}{x}}}{\frac{e^{b}}{{a}^{t}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r186516 = x;
        double r186517 = y;
        double r186518 = z;
        double r186519 = log(r186518);
        double r186520 = r186517 * r186519;
        double r186521 = t;
        double r186522 = 1.0;
        double r186523 = r186521 - r186522;
        double r186524 = a;
        double r186525 = log(r186524);
        double r186526 = r186523 * r186525;
        double r186527 = r186520 + r186526;
        double r186528 = b;
        double r186529 = r186527 - r186528;
        double r186530 = exp(r186529);
        double r186531 = r186516 * r186530;
        double r186532 = r186531 / r186517;
        return r186532;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r186533 = 1.0;
        double r186534 = a;
        double r186535 = r186533 / r186534;
        double r186536 = 1.0;
        double r186537 = pow(r186535, r186536);
        double r186538 = y;
        double r186539 = z;
        double r186540 = pow(r186539, r186538);
        double r186541 = r186538 / r186540;
        double r186542 = x;
        double r186543 = r186541 / r186542;
        double r186544 = r186537 / r186543;
        double r186545 = b;
        double r186546 = exp(r186545);
        double r186547 = t;
        double r186548 = pow(r186534, r186547);
        double r186549 = r186546 / r186548;
        double r186550 = r186544 / r186549;
        return r186550;
}

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. Using strategy rm

  3. Applied add-cube-cbrt1.9

    \[\leadsto \frac{x \cdot \color{blue}{\left(\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right)}}{y}\]

  4. Taylor expanded around inf 1.9

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

  5. Simplified6.5

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

  7. Applied div-inv6.5

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

  8. Applied associate-/r*1.4

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

  9. Final simplification25.1

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

Reproduce

herbie shell --seed 2019304 
(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))