Average Error: 2.0 → 1.3
Time: 21.1s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{\left(b - \log z \cdot y\right) - \log a \cdot t}}\right) \cdot \frac{1}{y}\]
\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^{\left(b - \log z \cdot y\right) - \log a \cdot t}}\right) \cdot \frac{1}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r102591 = x;
        double r102592 = y;
        double r102593 = z;
        double r102594 = log(r102593);
        double r102595 = r102592 * r102594;
        double r102596 = t;
        double r102597 = 1.0;
        double r102598 = r102596 - r102597;
        double r102599 = a;
        double r102600 = log(r102599);
        double r102601 = r102598 * r102600;
        double r102602 = r102595 + r102601;
        double r102603 = b;
        double r102604 = r102602 - r102603;
        double r102605 = exp(r102604);
        double r102606 = r102591 * r102605;
        double r102607 = r102606 / r102592;
        return r102607;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r102608 = x;
        double r102609 = 1.0;
        double r102610 = a;
        double r102611 = r102609 / r102610;
        double r102612 = 1.0;
        double r102613 = pow(r102611, r102612);
        double r102614 = b;
        double r102615 = z;
        double r102616 = log(r102615);
        double r102617 = y;
        double r102618 = r102616 * r102617;
        double r102619 = r102614 - r102618;
        double r102620 = log(r102610);
        double r102621 = t;
        double r102622 = r102620 * r102621;
        double r102623 = r102619 - r102622;
        double r102624 = exp(r102623);
        double r102625 = r102613 / r102624;
        double r102626 = r102608 * r102625;
        double r102627 = r102609 / r102617;
        double r102628 = r102626 * r102627;
        return r102628;
}

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 2.0

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

  2. Taylor expanded around inf 2.0

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

  3. Simplified1.3

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

  5. Applied div-inv1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020047 
(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))