Average Error: 9.2 → 0.4
Time: 19.3s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(\left(3 \cdot x\right) \cdot \log \left(\sqrt[3]{-y} \cdot \sqrt[3]{-1}\right) + z \cdot \left(\log 1 - \left(1 \cdot y + \frac{1}{2} \cdot \frac{{y}^{2}}{{1}^{2}}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(\left(3 \cdot x\right) \cdot \log \left(\sqrt[3]{-y} \cdot \sqrt[3]{-1}\right) + z \cdot \left(\log 1 - \left(1 \cdot y + \frac{1}{2} \cdot \frac{{y}^{2}}{{1}^{2}}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r271985 = x;
        double r271986 = y;
        double r271987 = log(r271986);
        double r271988 = r271985 * r271987;
        double r271989 = z;
        double r271990 = 1.0;
        double r271991 = r271990 - r271986;
        double r271992 = log(r271991);
        double r271993 = r271989 * r271992;
        double r271994 = r271988 + r271993;
        double r271995 = t;
        double r271996 = r271994 - r271995;
        return r271996;
}
↓
double f(double x, double y, double z, double t) {
        double r271997 = 3.0;
        double r271998 = x;
        double r271999 = r271997 * r271998;
        double r272000 = y;
        double r272001 = -r272000;
        double r272002 = cbrt(r272001);
        double r272003 = -1.0;
        double r272004 = cbrt(r272003);
        double r272005 = r272002 * r272004;
        double r272006 = log(r272005);
        double r272007 = r271999 * r272006;
        double r272008 = z;
        double r272009 = 1.0;
        double r272010 = log(r272009);
        double r272011 = r272009 * r272000;
        double r272012 = 0.5;
        double r272013 = 2.0;
        double r272014 = pow(r272000, r272013);
        double r272015 = pow(r272009, r272013);
        double r272016 = r272014 / r272015;
        double r272017 = r272012 * r272016;
        double r272018 = r272011 + r272017;
        double r272019 = r272010 - r272018;
        double r272020 = r272008 * r272019;
        double r272021 = r272007 + r272020;
        double r272022 = t;
        double r272023 = r272021 - r272022;
        return r272023;
}

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

Original9.2
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 9.2

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

  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. Using strategy rm

  4. Applied add-cube-cbrt0.3

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

  5. Applied log-prod0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Simplified0.4

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

  8. Taylor expanded around -inf 64.0

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(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) (* (/ 0.333333333333333315 (* 1 (* 1 1))) (* y (* y y))))) (- t (* x (log y))))

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