Average Error: 9.4 → 0.4
Time: 32.7s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(z \cdot \left(\left(\frac{-1}{2} \cdot \left(\frac{y}{1} \cdot \frac{y}{1}\right) + \log 1\right) - 1 \cdot y\right) + \left(\left(x + x\right) \cdot \log \left(\sqrt[3]{y}\right) + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(z \cdot \left(\left(\frac{-1}{2} \cdot \left(\frac{y}{1} \cdot \frac{y}{1}\right) + \log 1\right) - 1 \cdot y\right) + \left(\left(x + x\right) \cdot \log \left(\sqrt[3]{y}\right) + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right)\right) - t
double f(double x, double y, double z, double t) {
        double r21481126 = x;
        double r21481127 = y;
        double r21481128 = log(r21481127);
        double r21481129 = r21481126 * r21481128;
        double r21481130 = z;
        double r21481131 = 1.0;
        double r21481132 = r21481131 - r21481127;
        double r21481133 = log(r21481132);
        double r21481134 = r21481130 * r21481133;
        double r21481135 = r21481129 + r21481134;
        double r21481136 = t;
        double r21481137 = r21481135 - r21481136;
        return r21481137;
}
↓
double f(double x, double y, double z, double t) {
        double r21481138 = z;
        double r21481139 = -0.5;
        double r21481140 = y;
        double r21481141 = 1.0;
        double r21481142 = r21481140 / r21481141;
        double r21481143 = r21481142 * r21481142;
        double r21481144 = r21481139 * r21481143;
        double r21481145 = log(r21481141);
        double r21481146 = r21481144 + r21481145;
        double r21481147 = r21481141 * r21481140;
        double r21481148 = r21481146 - r21481147;
        double r21481149 = r21481138 * r21481148;
        double r21481150 = x;
        double r21481151 = r21481150 + r21481150;
        double r21481152 = cbrt(r21481140);
        double r21481153 = log(r21481152);
        double r21481154 = r21481151 * r21481153;
        double r21481155 = 0.3333333333333333;
        double r21481156 = pow(r21481140, r21481155);
        double r21481157 = log(r21481156);
        double r21481158 = r21481157 * r21481150;
        double r21481159 = r21481154 + r21481158;
        double r21481160 = r21481149 + r21481159;
        double r21481161 = t;
        double r21481162 = r21481160 - r21481161;
        return r21481162;
}

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

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  10. Applied pow1/30.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 
(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))