Average Error: 1.9 → 1.3
Time: 1.3m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{x}}}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{x}}}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r7999289 = x;
        double r7999290 = y;
        double r7999291 = z;
        double r7999292 = log(r7999291);
        double r7999293 = r7999290 * r7999292;
        double r7999294 = t;
        double r7999295 = 1.0;
        double r7999296 = r7999294 - r7999295;
        double r7999297 = a;
        double r7999298 = log(r7999297);
        double r7999299 = r7999296 * r7999298;
        double r7999300 = r7999293 + r7999299;
        double r7999301 = b;
        double r7999302 = r7999300 - r7999301;
        double r7999303 = exp(r7999302);
        double r7999304 = r7999289 * r7999303;
        double r7999305 = r7999304 / r7999290;
        return r7999305;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r7999306 = x;
        double r7999307 = cbrt(r7999306);
        double r7999308 = y;
        double r7999309 = cbrt(r7999308);
        double r7999310 = z;
        double r7999311 = log(r7999310);
        double r7999312 = r7999311 * r7999308;
        double r7999313 = t;
        double r7999314 = 1.0;
        double r7999315 = r7999313 - r7999314;
        double r7999316 = a;
        double r7999317 = log(r7999316);
        double r7999318 = r7999315 * r7999317;
        double r7999319 = r7999312 + r7999318;
        double r7999320 = b;
        double r7999321 = r7999319 - r7999320;
        double r7999322 = exp(r7999321);
        double r7999323 = cbrt(r7999322);
        double r7999324 = r7999323 * r7999323;
        double r7999325 = r7999323 * r7999324;
        double r7999326 = r7999309 / r7999325;
        double r7999327 = r7999307 / r7999326;
        double r7999328 = r7999309 / r7999307;
        double r7999329 = r7999307 / r7999328;
        double r7999330 = r7999327 * r7999329;
        double r7999331 = r7999330 / r7999309;
        return r7999331;
}

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 add-cube-cbrt1.9

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

  4. Applied associate-/r*1.9

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

  6. Applied associate-/l*1.6

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

  8. Applied *-un-lft-identity1.6

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

  9. Applied times-frac1.6

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

  10. Applied add-cube-cbrt1.6

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

  11. Applied times-frac1.3

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

  12. Simplified1.3

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

  14. Applied add-cube-cbrt1.3

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

  15. Final simplification1.3

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

Reproduce

herbie shell --seed 2019124 
(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))