Average Error: 9.6 → 0.4
Time: 35.1s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t\]
↓
\[\left(z \cdot \left(\left(\log 1.0 - y \cdot 1.0\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right) + \left(\left(\log \left({y}^{\frac{1}{3}}\right) + \log \left({y}^{\frac{1}{3}}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t
↓
\left(z \cdot \left(\left(\log 1.0 - y \cdot 1.0\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right) + \left(\left(\log \left({y}^{\frac{1}{3}}\right) + \log \left({y}^{\frac{1}{3}}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r10493624 = x;
        double r10493625 = y;
        double r10493626 = log(r10493625);
        double r10493627 = r10493624 * r10493626;
        double r10493628 = z;
        double r10493629 = 1.0;
        double r10493630 = r10493629 - r10493625;
        double r10493631 = log(r10493630);
        double r10493632 = r10493628 * r10493631;
        double r10493633 = r10493627 + r10493632;
        double r10493634 = t;
        double r10493635 = r10493633 - r10493634;
        return r10493635;
}
↓
double f(double x, double y, double z, double t) {
        double r10493636 = z;
        double r10493637 = 1.0;
        double r10493638 = log(r10493637);
        double r10493639 = y;
        double r10493640 = r10493639 * r10493637;
        double r10493641 = r10493638 - r10493640;
        double r10493642 = 0.5;
        double r10493643 = r10493637 / r10493639;
        double r10493644 = r10493642 / r10493643;
        double r10493645 = r10493644 / r10493643;
        double r10493646 = r10493641 - r10493645;
        double r10493647 = r10493636 * r10493646;
        double r10493648 = 0.3333333333333333;
        double r10493649 = pow(r10493639, r10493648);
        double r10493650 = log(r10493649);
        double r10493651 = r10493650 + r10493650;
        double r10493652 = x;
        double r10493653 = r10493651 * r10493652;
        double r10493654 = cbrt(r10493639);
        double r10493655 = log(r10493654);
        double r10493656 = r10493652 * r10493655;
        double r10493657 = r10493653 + r10493656;
        double r10493658 = r10493647 + r10493657;
        double r10493659 = t;
        double r10493660 = r10493658 - r10493659;
        return r10493660;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.6
Target0.3
Herbie0.4
\[\left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{\frac{1}{3}}{1.0 \cdot \left(1.0 \cdot 1.0\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right)\]

Derivation

  1. Initial program 9.6

    \[\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t\]

  2. Taylor expanded around 0 0.3

    \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\log 1.0 - \left(1.0 \cdot y + \frac{1}{2} \cdot \frac{{y}^{2}}{{1.0}^{2}}\right)\right)}\right) - t\]

  3. Simplified0.3

    \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)}\right) - t\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.4

    \[\leadsto \left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)\right) - t\]

  6. Applied log-prod0.4

    \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)\right) - t\]

  7. Applied distribute-rgt-in0.4

    \[\leadsto \left(\color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)} + z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)\right) - t\]

  8. Simplified0.4

    \[\leadsto \left(\left(\color{blue}{x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)\right) - t\]
  9. Using strategy rm

  10. Applied pow1/30.4

    \[\leadsto \left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \color{blue}{\left({y}^{\frac{1}{3}}\right)}\right) + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)\right) - t\]
  11. Using strategy rm

  12. Applied pow1/30.4

    \[\leadsto \left(\left(x \cdot \left(\log \color{blue}{\left({y}^{\frac{1}{3}}\right)} + \log \left({y}^{\frac{1}{3}}\right)\right) + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right)\right) - t\]

  13. Final simplification0.4

    \[\leadsto \left(z \cdot \left(\left(\log 1.0 - y \cdot 1.0\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right) + \left(\left(\log \left({y}^{\frac{1}{3}}\right) + \log \left({y}^{\frac{1}{3}}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - t\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"

  :herbie-target
  (- (* (- z) (+ (+ (* 0.5 (* y y)) y) (* (/ 1/3 (* 1.0 (* 1.0 1.0))) (* y (* y y))))) (- t (* x (log y))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))