Average Error: 9.6 → 0.3
Time: 23.1s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(x \cdot \log y + z \cdot \left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{1}{2}}{\frac{1}{y} \cdot \frac{1}{y}}\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(x \cdot \log y + z \cdot \left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{1}{2}}{\frac{1}{y} \cdot \frac{1}{y}}\right)\right) - t
double f(double x, double y, double z, double t) {
        double r29212173 = x;
        double r29212174 = y;
        double r29212175 = log(r29212174);
        double r29212176 = r29212173 * r29212175;
        double r29212177 = z;
        double r29212178 = 1.0;
        double r29212179 = r29212178 - r29212174;
        double r29212180 = log(r29212179);
        double r29212181 = r29212177 * r29212180;
        double r29212182 = r29212176 + r29212181;
        double r29212183 = t;
        double r29212184 = r29212182 - r29212183;
        return r29212184;
}
↓
double f(double x, double y, double z, double t) {
        double r29212185 = x;
        double r29212186 = y;
        double r29212187 = log(r29212186);
        double r29212188 = r29212185 * r29212187;
        double r29212189 = z;
        double r29212190 = 1.0;
        double r29212191 = log(r29212190);
        double r29212192 = r29212190 * r29212186;
        double r29212193 = r29212191 - r29212192;
        double r29212194 = 0.5;
        double r29212195 = r29212190 / r29212186;
        double r29212196 = r29212195 * r29212195;
        double r29212197 = r29212194 / r29212196;
        double r29212198 = r29212193 - r29212197;
        double r29212199 = r29212189 * r29212198;
        double r29212200 = r29212188 + r29212199;
        double r29212201 = t;
        double r29212202 = r29212200 - r29212201;
        return r29212202;
}

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

Original9.6
Target0.2
Herbie0.3
\[\left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.3333333333333333148296162562473909929395}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right)\]

Derivation

  1. Initial program 9.6

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

  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

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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))