Average Error: 2.1 → 2.1
Time: 55.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}\right)}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}\right)}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r3929249 = x;
        double r3929250 = y;
        double r3929251 = z;
        double r3929252 = log(r3929251);
        double r3929253 = r3929250 * r3929252;
        double r3929254 = t;
        double r3929255 = 1.0;
        double r3929256 = r3929254 - r3929255;
        double r3929257 = a;
        double r3929258 = log(r3929257);
        double r3929259 = r3929256 * r3929258;
        double r3929260 = r3929253 + r3929259;
        double r3929261 = b;
        double r3929262 = r3929260 - r3929261;
        double r3929263 = exp(r3929262);
        double r3929264 = r3929249 * r3929263;
        double r3929265 = r3929264 / r3929250;
        return r3929265;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3929266 = x;
        double r3929267 = a;
        double r3929268 = log(r3929267);
        double r3929269 = t;
        double r3929270 = 1.0;
        double r3929271 = r3929269 - r3929270;
        double r3929272 = r3929268 * r3929271;
        double r3929273 = z;
        double r3929274 = log(r3929273);
        double r3929275 = y;
        double r3929276 = r3929274 * r3929275;
        double r3929277 = r3929272 + r3929276;
        double r3929278 = b;
        double r3929279 = r3929277 - r3929278;
        double r3929280 = exp(r3929279);
        double r3929281 = cbrt(r3929280);
        double r3929282 = r3929281 * r3929281;
        double r3929283 = exp(1.0);
        double r3929284 = sqrt(r3929283);
        double r3929285 = pow(r3929284, r3929279);
        double r3929286 = r3929285 * r3929285;
        double r3929287 = cbrt(r3929286);
        double r3929288 = r3929282 * r3929287;
        double r3929289 = r3929266 * r3929288;
        double r3929290 = r3929289 / r3929275;
        return r3929290;
}

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 2.1

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

  3. Applied add-cube-cbrt2.1

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

  5. Applied *-un-lft-identity2.1

    \[\leadsto \frac{x \cdot \left(\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}\right)}{y}\]

  6. Applied exp-prod2.1

    \[\leadsto \frac{x \cdot \left(\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}\right)}{y}\]

  7. Simplified2.1

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

  9. Applied add-sqr-sqrt2.2

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

  10. Applied unpow-prod-down2.1

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

  11. Final simplification2.1

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

Reproduce

herbie shell --seed 2019149 
(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))