Average Error: 9.0 → 0.5
Time: 7.4s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(\left(z \cdot \log 1 + \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right)\right) - 1 \cdot \left(z \cdot y\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(\left(z \cdot \log 1 + \left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right)\right) - 1 \cdot \left(z \cdot y\right)\right) - t
double f(double x, double y, double z, double t) {
        double r435578 = x;
        double r435579 = y;
        double r435580 = log(r435579);
        double r435581 = r435578 * r435580;
        double r435582 = z;
        double r435583 = 1.0;
        double r435584 = r435583 - r435579;
        double r435585 = log(r435584);
        double r435586 = r435582 * r435585;
        double r435587 = r435581 + r435586;
        double r435588 = t;
        double r435589 = r435587 - r435588;
        return r435589;
}
↓
double f(double x, double y, double z, double t) {
        double r435590 = z;
        double r435591 = 1.0;
        double r435592 = log(r435591);
        double r435593 = r435590 * r435592;
        double r435594 = x;
        double r435595 = 2.0;
        double r435596 = y;
        double r435597 = cbrt(r435596);
        double r435598 = log(r435597);
        double r435599 = r435595 * r435598;
        double r435600 = r435594 * r435599;
        double r435601 = 1.0;
        double r435602 = 0.3333333333333333;
        double r435603 = pow(r435596, r435602);
        double r435604 = r435601 * r435603;
        double r435605 = log(r435604);
        double r435606 = r435594 * r435605;
        double r435607 = r435600 + r435606;
        double r435608 = r435593 + r435607;
        double r435609 = r435590 * r435596;
        double r435610 = r435591 * r435609;
        double r435611 = r435608 - r435610;
        double r435612 = t;
        double r435613 = r435611 - r435612;
        return r435613;
}

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

Original9.0
Target0.2
Herbie0.5
\[\left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.333333333333333315}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right)\]

Derivation

  1. Initial program 9.0

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

  2. Taylor expanded around 0 0.5

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

  4. Applied add-cube-cbrt0.5

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

  5. Applied log-prod0.5

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

  6. Applied distribute-lft-in0.5

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

  7. Simplified0.5

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

  9. Applied *-un-lft-identity0.5

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

  10. Applied cbrt-prod0.5

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

  11. Simplified0.5

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

  12. Simplified0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (- (* (- z) (+ (+ (* 0.5 (* y y)) y) (* (/ 0.3333333333333333 (* 1 (* 1 1))) (* y (* y y))))) (- t (* x (log y))))

  (- (+ (* x (log y)) (* z (log (- 1 y)))) t))