Average Error: 9.5 → 0.4
Time: 29.3s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(z \cdot \left(\left(\left(\frac{y}{1} \cdot \frac{y}{1}\right) \cdot \frac{-1}{2} + \log 1\right) - 1 \cdot y\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right) + \left(\left(x + x\right) \cdot \log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(z \cdot \left(\left(\left(\frac{y}{1} \cdot \frac{y}{1}\right) \cdot \frac{-1}{2} + \log 1\right) - 1 \cdot y\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right) + \left(\left(x + x\right) \cdot \log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r21543686 = x;
        double r21543687 = y;
        double r21543688 = log(r21543687);
        double r21543689 = r21543686 * r21543688;
        double r21543690 = z;
        double r21543691 = 1.0;
        double r21543692 = r21543691 - r21543687;
        double r21543693 = log(r21543692);
        double r21543694 = r21543690 * r21543693;
        double r21543695 = r21543689 + r21543694;
        double r21543696 = t;
        double r21543697 = r21543695 - r21543696;
        return r21543697;
}
↓
double f(double x, double y, double z, double t) {
        double r21543698 = z;
        double r21543699 = y;
        double r21543700 = 1.0;
        double r21543701 = r21543699 / r21543700;
        double r21543702 = r21543701 * r21543701;
        double r21543703 = -0.5;
        double r21543704 = r21543702 * r21543703;
        double r21543705 = log(r21543700);
        double r21543706 = r21543704 + r21543705;
        double r21543707 = r21543700 * r21543699;
        double r21543708 = r21543706 - r21543707;
        double r21543709 = r21543698 * r21543708;
        double r21543710 = x;
        double r21543711 = cbrt(r21543699);
        double r21543712 = cbrt(r21543711);
        double r21543713 = log(r21543712);
        double r21543714 = r21543710 * r21543713;
        double r21543715 = r21543710 + r21543710;
        double r21543716 = log(r21543711);
        double r21543717 = r21543715 * r21543716;
        double r21543718 = r21543712 * r21543712;
        double r21543719 = log(r21543718);
        double r21543720 = r21543719 * r21543710;
        double r21543721 = r21543717 + r21543720;
        double r21543722 = r21543714 + r21543721;
        double r21543723 = r21543709 + r21543722;
        double r21543724 = t;
        double r21543725 = r21543723 - r21543724;
        return r21543725;
}

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

Original9.5
Target0.3
Herbie0.4
\[\left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.3333333333333333148296162562473909929395}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right)\]

Derivation

  1. Initial program 9.5

    \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]

  2. Taylor expanded around 0 0.4

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

  3. Simplified0.4

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

  5. Applied add-cube-cbrt0.4

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

  6. Applied log-prod0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  10. Applied add-cube-cbrt0.4

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

  11. Applied log-prod0.4

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

  12. Applied distribute-rgt-in0.4

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

  13. Applied associate-+r+0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019169 
(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) (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y))))) (- t (* x (log y))))

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