Average Error: 1.9 → 2.0
Time: 1.3m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{\sqrt[3]{y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)\right)\right)}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{\sqrt[3]{y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)\right)\right)}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r10537334 = x;
        double r10537335 = y;
        double r10537336 = z;
        double r10537337 = log(r10537336);
        double r10537338 = r10537335 * r10537337;
        double r10537339 = t;
        double r10537340 = 1.0;
        double r10537341 = r10537339 - r10537340;
        double r10537342 = a;
        double r10537343 = log(r10537342);
        double r10537344 = r10537341 * r10537343;
        double r10537345 = r10537338 + r10537344;
        double r10537346 = b;
        double r10537347 = r10537345 - r10537346;
        double r10537348 = exp(r10537347);
        double r10537349 = r10537334 * r10537348;
        double r10537350 = r10537349 / r10537335;
        return r10537350;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r10537351 = exp(1.0);
        double r10537352 = z;
        double r10537353 = log(r10537352);
        double r10537354 = y;
        double r10537355 = r10537353 * r10537354;
        double r10537356 = t;
        double r10537357 = 1.0;
        double r10537358 = r10537356 - r10537357;
        double r10537359 = a;
        double r10537360 = log(r10537359);
        double r10537361 = r10537358 * r10537360;
        double r10537362 = r10537355 + r10537361;
        double r10537363 = b;
        double r10537364 = r10537362 - r10537363;
        double r10537365 = pow(r10537351, r10537364);
        double r10537366 = x;
        double r10537367 = r10537365 * r10537366;
        double r10537368 = cbrt(r10537354);
        double r10537369 = cbrt(r10537368);
        double r10537370 = r10537369 * r10537369;
        double r10537371 = cbrt(r10537369);
        double r10537372 = r10537371 * r10537371;
        double r10537373 = r10537371 * r10537372;
        double r10537374 = r10537370 * r10537373;
        double r10537375 = r10537368 * r10537374;
        double r10537376 = r10537367 / r10537375;
        double r10537377 = r10537376 / r10537368;
        return r10537377;
}

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

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity1.9

    \[\leadsto \frac{x \cdot e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}\]

  4. Applied exp-prod2.0

    \[\leadsto \frac{x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}\]

  5. Simplified2.0

    \[\leadsto \frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.0

    \[\leadsto \frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  8. Applied associate-/r*2.0

    \[\leadsto \color{blue}{\frac{\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt2.0

    \[\leadsto \frac{\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{\sqrt[3]{y} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}\right)}}}{\sqrt[3]{y}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt2.0

    \[\leadsto \frac{\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{\sqrt[3]{y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)}\right)}}{\sqrt[3]{y}}\]

  13. Final simplification2.0

    \[\leadsto \frac{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{\sqrt[3]{y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)\right)\right)}}{\sqrt[3]{y}}\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))