Average Error: 2.1 → 2.0
Time: 1.2m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}\right)}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \left(\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}\right) \cdot \sqrt[3]{{\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log a \cdot \left(t - 1\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 r21997430 = x;
        double r21997431 = y;
        double r21997432 = z;
        double r21997433 = log(r21997432);
        double r21997434 = r21997431 * r21997433;
        double r21997435 = t;
        double r21997436 = 1.0;
        double r21997437 = r21997435 - r21997436;
        double r21997438 = a;
        double r21997439 = log(r21997438);
        double r21997440 = r21997437 * r21997439;
        double r21997441 = r21997434 + r21997440;
        double r21997442 = b;
        double r21997443 = r21997441 - r21997442;
        double r21997444 = exp(r21997443);
        double r21997445 = r21997430 * r21997444;
        double r21997446 = r21997445 / r21997431;
        return r21997446;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21997447 = x;
        double r21997448 = a;
        double r21997449 = log(r21997448);
        double r21997450 = t;
        double r21997451 = 1.0;
        double r21997452 = r21997450 - r21997451;
        double r21997453 = r21997449 * r21997452;
        double r21997454 = z;
        double r21997455 = log(r21997454);
        double r21997456 = y;
        double r21997457 = r21997455 * r21997456;
        double r21997458 = r21997453 + r21997457;
        double r21997459 = b;
        double r21997460 = r21997458 - r21997459;
        double r21997461 = exp(r21997460);
        double r21997462 = cbrt(r21997461);
        double r21997463 = r21997462 * r21997462;
        double r21997464 = exp(1.0);
        double r21997465 = sqrt(r21997464);
        double r21997466 = pow(r21997465, r21997460);
        double r21997467 = r21997466 * r21997466;
        double r21997468 = cbrt(r21997467);
        double r21997469 = r21997463 * r21997468;
        double r21997470 = cbrt(r21997469);
        double r21997471 = r21997463 * r21997470;
        double r21997472 = r21997447 * r21997471;
        double r21997473 = r21997472 / r21997456;
        return r21997473;
}

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

Target

Original2.1
Target10.9
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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. Using strategy rm

  3. Applied add-cube-cbrt2.1

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

  5. Applied add-cube-cbrt2.1

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

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

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

  8. Applied exp-prod2.1

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

  9. Simplified2.1

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

  11. Applied add-sqr-sqrt2.0

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

  12. Applied unpow-prod-down2.0

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

  13. Final simplification2.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))