Average Error: 1.8 → 0.9
Time: 42.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}} \cdot x\right)\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}} \cdot x\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r4162295 = x;
        double r4162296 = y;
        double r4162297 = z;
        double r4162298 = log(r4162297);
        double r4162299 = r4162296 * r4162298;
        double r4162300 = t;
        double r4162301 = 1.0;
        double r4162302 = r4162300 - r4162301;
        double r4162303 = a;
        double r4162304 = log(r4162303);
        double r4162305 = r4162302 * r4162304;
        double r4162306 = r4162299 + r4162305;
        double r4162307 = b;
        double r4162308 = r4162306 - r4162307;
        double r4162309 = exp(r4162308);
        double r4162310 = r4162295 * r4162309;
        double r4162311 = r4162310 / r4162296;
        return r4162311;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4162312 = y;
        double r4162313 = z;
        double r4162314 = log(r4162313);
        double r4162315 = r4162312 * r4162314;
        double r4162316 = t;
        double r4162317 = 1.0;
        double r4162318 = r4162316 - r4162317;
        double r4162319 = a;
        double r4162320 = log(r4162319);
        double r4162321 = r4162318 * r4162320;
        double r4162322 = r4162315 + r4162321;
        double r4162323 = b;
        double r4162324 = r4162322 - r4162323;
        double r4162325 = exp(r4162324);
        double r4162326 = cbrt(r4162325);
        double r4162327 = cbrt(r4162312);
        double r4162328 = r4162326 / r4162327;
        double r4162329 = x;
        double r4162330 = r4162328 * r4162329;
        double r4162331 = r4162328 * r4162330;
        double r4162332 = r4162328 * r4162331;
        return r4162332;
}

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 1.8

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

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

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

  4. Applied times-frac2.2

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

  5. Simplified2.2

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

  7. Applied add-cube-cbrt2.2

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

  8. Applied add-cube-cbrt2.2

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

  9. Applied times-frac2.2

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

  10. Applied associate-*r*1.1

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

  11. Simplified0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2019170 
(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))