Average Error: 2.0 → 1.3
Time: 33.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\left(\sqrt{\frac{{a}^{\left(-1\right)}}{e^{\left(b - \log a \cdot t\right) - \log z \cdot y}}} \cdot x\right) \cdot \sqrt{\frac{{a}^{\left(-1\right)}}{e^{\left(-\left(\log z \cdot y + \log a \cdot t\right)\right) + b}}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\left(\sqrt{\frac{{a}^{\left(-1\right)}}{e^{\left(b - \log a \cdot t\right) - \log z \cdot y}}} \cdot x\right) \cdot \sqrt{\frac{{a}^{\left(-1\right)}}{e^{\left(-\left(\log z \cdot y + \log a \cdot t\right)\right) + b}}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r76440 = x;
        double r76441 = y;
        double r76442 = z;
        double r76443 = log(r76442);
        double r76444 = r76441 * r76443;
        double r76445 = t;
        double r76446 = 1.0;
        double r76447 = r76445 - r76446;
        double r76448 = a;
        double r76449 = log(r76448);
        double r76450 = r76447 * r76449;
        double r76451 = r76444 + r76450;
        double r76452 = b;
        double r76453 = r76451 - r76452;
        double r76454 = exp(r76453);
        double r76455 = r76440 * r76454;
        double r76456 = r76455 / r76441;
        return r76456;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r76457 = a;
        double r76458 = 1.0;
        double r76459 = -r76458;
        double r76460 = pow(r76457, r76459);
        double r76461 = b;
        double r76462 = log(r76457);
        double r76463 = t;
        double r76464 = r76462 * r76463;
        double r76465 = r76461 - r76464;
        double r76466 = z;
        double r76467 = log(r76466);
        double r76468 = y;
        double r76469 = r76467 * r76468;
        double r76470 = r76465 - r76469;
        double r76471 = exp(r76470);
        double r76472 = r76460 / r76471;
        double r76473 = sqrt(r76472);
        double r76474 = x;
        double r76475 = r76473 * r76474;
        double r76476 = r76469 + r76464;
        double r76477 = -r76476;
        double r76478 = r76477 + r76461;
        double r76479 = exp(r76478);
        double r76480 = r76460 / r76479;
        double r76481 = sqrt(r76480);
        double r76482 = r76475 * r76481;
        double r76483 = r76482 / r76468;
        return r76483;
}

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

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

  5. Applied add-sqr-sqrt1.3

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

  6. Applied associate-*r*1.3

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2019235 
(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))