Average Error: 1.9 → 1.1
Time: 38.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\left(x \cdot \frac{\sqrt{{a}^{\left(-1\right)}}}{\sqrt{e^{\left(t \cdot \left(-\log a\right) + b\right) + \left(-\log z\right) \cdot y}}}\right) \cdot \frac{\left|\sqrt[3]{{a}^{\left(-1\right)}}\right|}{\sqrt{\sqrt{e^{\left(t \cdot \left(-\log a\right) + b\right) + \left(-\log z\right) \cdot y}}}}\right) \cdot \frac{\frac{\sqrt{\sqrt[3]{{a}^{\left(-1\right)}}}}{\sqrt{\sqrt{e^{\left(t \cdot \left(-\log a\right) + b\right) + \left(-\log z\right) \cdot y}}}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(\left(x \cdot \frac{\sqrt{{a}^{\left(-1\right)}}}{\sqrt{e^{\left(t \cdot \left(-\log a\right) + b\right) + \left(-\log z\right) \cdot y}}}\right) \cdot \frac{\left|\sqrt[3]{{a}^{\left(-1\right)}}\right|}{\sqrt{\sqrt{e^{\left(t \cdot \left(-\log a\right) + b\right) + \left(-\log z\right) \cdot y}}}}\right) \cdot \frac{\frac{\sqrt{\sqrt[3]{{a}^{\left(-1\right)}}}}{\sqrt{\sqrt{e^{\left(t \cdot \left(-\log a\right) + b\right) + \left(-\log z\right) \cdot y}}}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r87362 = x;
        double r87363 = y;
        double r87364 = z;
        double r87365 = log(r87364);
        double r87366 = r87363 * r87365;
        double r87367 = t;
        double r87368 = 1.0;
        double r87369 = r87367 - r87368;
        double r87370 = a;
        double r87371 = log(r87370);
        double r87372 = r87369 * r87371;
        double r87373 = r87366 + r87372;
        double r87374 = b;
        double r87375 = r87373 - r87374;
        double r87376 = exp(r87375);
        double r87377 = r87362 * r87376;
        double r87378 = r87377 / r87363;
        return r87378;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r87379 = x;
        double r87380 = a;
        double r87381 = 1.0;
        double r87382 = -r87381;
        double r87383 = pow(r87380, r87382);
        double r87384 = sqrt(r87383);
        double r87385 = t;
        double r87386 = log(r87380);
        double r87387 = -r87386;
        double r87388 = r87385 * r87387;
        double r87389 = b;
        double r87390 = r87388 + r87389;
        double r87391 = z;
        double r87392 = log(r87391);
        double r87393 = -r87392;
        double r87394 = y;
        double r87395 = r87393 * r87394;
        double r87396 = r87390 + r87395;
        double r87397 = exp(r87396);
        double r87398 = sqrt(r87397);
        double r87399 = r87384 / r87398;
        double r87400 = r87379 * r87399;
        double r87401 = cbrt(r87383);
        double r87402 = fabs(r87401);
        double r87403 = sqrt(r87398);
        double r87404 = r87402 / r87403;
        double r87405 = r87400 * r87404;
        double r87406 = sqrt(r87401);
        double r87407 = r87406 / r87403;
        double r87408 = r87407 / r87394;
        double r87409 = r87405 * r87408;
        return r87409;
}

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

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

  2. Taylor expanded around inf 1.9

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

  3. Simplified6.9

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

  5. Applied div-inv6.9

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

  6. Applied associate-*l*1.4

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

  7. Simplified1.4

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

  9. Applied *-un-lft-identity1.4

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

  10. Applied add-sqr-sqrt1.4

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

  11. Applied add-sqr-sqrt1.5

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

  12. Applied times-frac1.5

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

  13. Applied times-frac1.4

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

  14. Applied associate-*r*1.0

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

  15. Simplified1.0

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

  17. Applied *-un-lft-identity1.0

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

  18. Applied add-sqr-sqrt1.0

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

  19. Applied sqrt-prod1.0

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

  20. Applied add-cube-cbrt1.0

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

  21. Applied sqrt-prod1.0

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

  22. Applied times-frac1.0

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

  23. Applied times-frac1.0

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

  24. Applied associate-*r*1.1

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

  25. Simplified1.1

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

  26. Final simplification1.1

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

Reproduce

herbie shell --seed 2019195 
(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))