Average Error: 9.1 → 0.4
Time: 34.5s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t\]
↓
\[\left(z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right) + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t
↓
\left(z \cdot \left(\left(\log 1.0 - 1.0 \cdot y\right) - \frac{\frac{\frac{1}{2}}{\frac{1.0}{y}}}{\frac{1.0}{y}}\right) + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r22651768 = x;
        double r22651769 = y;
        double r22651770 = log(r22651769);
        double r22651771 = r22651768 * r22651770;
        double r22651772 = z;
        double r22651773 = 1.0;
        double r22651774 = r22651773 - r22651769;
        double r22651775 = log(r22651774);
        double r22651776 = r22651772 * r22651775;
        double r22651777 = r22651771 + r22651776;
        double r22651778 = t;
        double r22651779 = r22651777 - r22651778;
        return r22651779;
}
↓
double f(double x, double y, double z, double t) {
        double r22651780 = z;
        double r22651781 = 1.0;
        double r22651782 = log(r22651781);
        double r22651783 = y;
        double r22651784 = r22651781 * r22651783;
        double r22651785 = r22651782 - r22651784;
        double r22651786 = 0.5;
        double r22651787 = r22651781 / r22651783;
        double r22651788 = r22651786 / r22651787;
        double r22651789 = r22651788 / r22651787;
        double r22651790 = r22651785 - r22651789;
        double r22651791 = r22651780 * r22651790;
        double r22651792 = cbrt(r22651783);
        double r22651793 = log(r22651792);
        double r22651794 = r22651793 + r22651793;
        double r22651795 = x;
        double r22651796 = r22651794 * r22651795;
        double r22651797 = 0.3333333333333333;
        double r22651798 = pow(r22651783, r22651797);
        double r22651799 = log(r22651798);
        double r22651800 = r22651795 * r22651799;
        double r22651801 = r22651796 + r22651800;
        double r22651802 = r22651791 + r22651801;
        double r22651803 = t;
        double r22651804 = r22651802 - r22651803;
        return r22651804;
}

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

Original9.1
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 9.1

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

  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-cbrt0.3

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

  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

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

  10. Applied pow1/30.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019162 
(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))