Average Error: 9.4 → 0.4
Time: 28.8s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(\left(\log \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x\right) + z \cdot \left(\left(\log 1 - y \cdot 1\right) - \frac{1}{2} \cdot \left(\frac{y}{1} \cdot \frac{y}{1}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(\left(\log \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x\right) + z \cdot \left(\left(\log 1 - y \cdot 1\right) - \frac{1}{2} \cdot \left(\frac{y}{1} \cdot \frac{y}{1}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r19709912 = x;
        double r19709913 = y;
        double r19709914 = log(r19709913);
        double r19709915 = r19709912 * r19709914;
        double r19709916 = z;
        double r19709917 = 1.0;
        double r19709918 = r19709917 - r19709913;
        double r19709919 = log(r19709918);
        double r19709920 = r19709916 * r19709919;
        double r19709921 = r19709915 + r19709920;
        double r19709922 = t;
        double r19709923 = r19709921 - r19709922;
        return r19709923;
}
↓
double f(double x, double y, double z, double t) {
        double r19709924 = y;
        double r19709925 = cbrt(r19709924);
        double r19709926 = cbrt(r19709925);
        double r19709927 = r19709926 * r19709926;
        double r19709928 = r19709927 * r19709926;
        double r19709929 = log(r19709928);
        double r19709930 = x;
        double r19709931 = r19709929 * r19709930;
        double r19709932 = log(r19709925);
        double r19709933 = r19709932 + r19709932;
        double r19709934 = r19709933 * r19709930;
        double r19709935 = r19709931 + r19709934;
        double r19709936 = z;
        double r19709937 = 1.0;
        double r19709938 = log(r19709937);
        double r19709939 = r19709924 * r19709937;
        double r19709940 = r19709938 - r19709939;
        double r19709941 = 0.5;
        double r19709942 = r19709924 / r19709937;
        double r19709943 = r19709942 * r19709942;
        double r19709944 = r19709941 * r19709943;
        double r19709945 = r19709940 - r19709944;
        double r19709946 = r19709936 * r19709945;
        double r19709947 = r19709935 + r19709946;
        double r19709948 = t;
        double r19709949 = r19709947 - r19709948;
        return r19709949;
}

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

Original9.4
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 9.4

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

  2. Taylor expanded around 0 0.3

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

  3. Simplified0.3

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  10. Applied add-cube-cbrt0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 
(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))