Average Error: 9.4 → 0.4
Time: 24.0s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(z \cdot \left(\frac{-1}{2} \cdot \left(\frac{y}{1} \cdot \frac{y}{1}\right) + \left(\log 1 - y \cdot 1\right)\right) + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(z \cdot \left(\frac{-1}{2} \cdot \left(\frac{y}{1} \cdot \frac{y}{1}\right) + \left(\log 1 - y \cdot 1\right)\right) + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r26438437 = x;
        double r26438438 = y;
        double r26438439 = log(r26438438);
        double r26438440 = r26438437 * r26438439;
        double r26438441 = z;
        double r26438442 = 1.0;
        double r26438443 = r26438442 - r26438438;
        double r26438444 = log(r26438443);
        double r26438445 = r26438441 * r26438444;
        double r26438446 = r26438440 + r26438445;
        double r26438447 = t;
        double r26438448 = r26438446 - r26438447;
        return r26438448;
}
↓
double f(double x, double y, double z, double t) {
        double r26438449 = z;
        double r26438450 = -0.5;
        double r26438451 = y;
        double r26438452 = 1.0;
        double r26438453 = r26438451 / r26438452;
        double r26438454 = r26438453 * r26438453;
        double r26438455 = r26438450 * r26438454;
        double r26438456 = log(r26438452);
        double r26438457 = r26438451 * r26438452;
        double r26438458 = r26438456 - r26438457;
        double r26438459 = r26438455 + r26438458;
        double r26438460 = r26438449 * r26438459;
        double r26438461 = cbrt(r26438451);
        double r26438462 = log(r26438461);
        double r26438463 = x;
        double r26438464 = r26438462 * r26438463;
        double r26438465 = r26438464 + r26438464;
        double r26438466 = 0.3333333333333333;
        double r26438467 = pow(r26438451, r26438466);
        double r26438468 = log(r26438467);
        double r26438469 = r26438463 * r26438468;
        double r26438470 = r26438465 + r26438469;
        double r26438471 = r26438460 + r26438470;
        double r26438472 = t;
        double r26438473 = r26438471 - r26438472;
        return r26438473;
}

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

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  10. Applied pow1/30.4

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

  11. Final simplification0.4

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

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))