Average Error: 10.0 → 0.4
Time: 1.5m
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(\left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{y}{1} \cdot \frac{y}{1}}{2}\right) \cdot z + \left(\log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x + \left(x + x\right) \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(\left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{y}{1} \cdot \frac{y}{1}}{2}\right) \cdot z + \left(\log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x + \left(x + x\right) \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r19051167 = x;
        double r19051168 = y;
        double r19051169 = log(r19051168);
        double r19051170 = r19051167 * r19051169;
        double r19051171 = z;
        double r19051172 = 1.0;
        double r19051173 = r19051172 - r19051168;
        double r19051174 = log(r19051173);
        double r19051175 = r19051171 * r19051174;
        double r19051176 = r19051170 + r19051175;
        double r19051177 = t;
        double r19051178 = r19051176 - r19051177;
        return r19051178;
}
↓
double f(double x, double y, double z, double t) {
        double r19051179 = 1.0;
        double r19051180 = log(r19051179);
        double r19051181 = y;
        double r19051182 = r19051179 * r19051181;
        double r19051183 = r19051180 - r19051182;
        double r19051184 = r19051181 / r19051179;
        double r19051185 = r19051184 * r19051184;
        double r19051186 = 2.0;
        double r19051187 = r19051185 / r19051186;
        double r19051188 = r19051183 - r19051187;
        double r19051189 = z;
        double r19051190 = r19051188 * r19051189;
        double r19051191 = cbrt(r19051181);
        double r19051192 = cbrt(r19051191);
        double r19051193 = r19051191 * r19051191;
        double r19051194 = cbrt(r19051193);
        double r19051195 = r19051192 * r19051194;
        double r19051196 = log(r19051195);
        double r19051197 = x;
        double r19051198 = r19051196 * r19051197;
        double r19051199 = r19051197 + r19051197;
        double r19051200 = log(r19051191);
        double r19051201 = r19051199 * r19051200;
        double r19051202 = r19051198 + r19051201;
        double r19051203 = r19051190 + r19051202;
        double r19051204 = t;
        double r19051205 = r19051203 - r19051204;
        return r19051205;
}

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

Original10.0
Target0.2
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 10.0

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

  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

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.4

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

  7. Applied distribute-rgt-in0.4

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

  8. Simplified0.4

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

  10. Applied add-cube-cbrt0.4

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

  11. Applied cbrt-prod0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019200 
(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))