Average Error: 2.1 → 1.4
Time: 40.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y} \cdot \frac{{\left(\frac{\sqrt{1}}{\sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot x\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(\frac{\frac{{\left(\frac{\sqrt{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y} \cdot \frac{{\left(\frac{\sqrt{1}}{\sqrt[3]{a}}\right)}^{1}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot x
double f(double x, double y, double z, double t, double a, double b) {
        double r99323 = x;
        double r99324 = y;
        double r99325 = z;
        double r99326 = log(r99325);
        double r99327 = r99324 * r99326;
        double r99328 = t;
        double r99329 = 1.0;
        double r99330 = r99328 - r99329;
        double r99331 = a;
        double r99332 = log(r99331);
        double r99333 = r99330 * r99332;
        double r99334 = r99327 + r99333;
        double r99335 = b;
        double r99336 = r99334 - r99335;
        double r99337 = exp(r99336);
        double r99338 = r99323 * r99337;
        double r99339 = r99338 / r99324;
        return r99339;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r99340 = 1.0;
        double r99341 = sqrt(r99340);
        double r99342 = a;
        double r99343 = cbrt(r99342);
        double r99344 = r99343 * r99343;
        double r99345 = r99341 / r99344;
        double r99346 = 1.0;
        double r99347 = pow(r99345, r99346);
        double r99348 = y;
        double r99349 = z;
        double r99350 = r99340 / r99349;
        double r99351 = log(r99350);
        double r99352 = r99348 * r99351;
        double r99353 = r99340 / r99342;
        double r99354 = log(r99353);
        double r99355 = t;
        double r99356 = r99354 * r99355;
        double r99357 = b;
        double r99358 = r99356 + r99357;
        double r99359 = r99352 + r99358;
        double r99360 = exp(r99359);
        double r99361 = sqrt(r99360);
        double r99362 = r99347 / r99361;
        double r99363 = r99362 / r99348;
        double r99364 = r99341 / r99343;
        double r99365 = pow(r99364, r99346);
        double r99366 = r99365 / r99361;
        double r99367 = r99363 * r99366;
        double r99368 = x;
        double r99369 = r99367 * r99368;
        return r99369;
}

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

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

  2. Taylor expanded around inf 2.1

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

  3. Simplified6.2

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

  5. Applied div-inv6.2

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

  6. Applied add-sqr-sqrt6.2

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

  7. Applied add-cube-cbrt6.4

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

  8. Applied add-sqr-sqrt6.4

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

  9. Applied times-frac6.4

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

  10. Applied unpow-prod-down6.4

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

  11. Applied times-frac6.4

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

  12. Applied times-frac1.2

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

  13. Final simplification1.4

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

Reproduce

herbie shell --seed 2019298 
(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))