Average Error: 9.1 → 0.3
Time: 17.6s
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t\]
↓
\[\left(\left(\left(\log 1.0 \cdot z - \frac{z \cdot \frac{1}{2}}{\frac{1.0}{y} \cdot \frac{1.0}{y}}\right) - \left(y \cdot 1.0\right) \cdot z\right) + x \cdot \log y\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t
↓
\left(\left(\left(\log 1.0 \cdot z - \frac{z \cdot \frac{1}{2}}{\frac{1.0}{y} \cdot \frac{1.0}{y}}\right) - \left(y \cdot 1.0\right) \cdot z\right) + x \cdot \log y\right) - t
double f(double x, double y, double z, double t) {
        double r9942585 = x;
        double r9942586 = y;
        double r9942587 = log(r9942586);
        double r9942588 = r9942585 * r9942587;
        double r9942589 = z;
        double r9942590 = 1.0;
        double r9942591 = r9942590 - r9942586;
        double r9942592 = log(r9942591);
        double r9942593 = r9942589 * r9942592;
        double r9942594 = r9942588 + r9942593;
        double r9942595 = t;
        double r9942596 = r9942594 - r9942595;
        return r9942596;
}
↓
double f(double x, double y, double z, double t) {
        double r9942597 = 1.0;
        double r9942598 = log(r9942597);
        double r9942599 = z;
        double r9942600 = r9942598 * r9942599;
        double r9942601 = 0.5;
        double r9942602 = r9942599 * r9942601;
        double r9942603 = y;
        double r9942604 = r9942597 / r9942603;
        double r9942605 = r9942604 * r9942604;
        double r9942606 = r9942602 / r9942605;
        double r9942607 = r9942600 - r9942606;
        double r9942608 = r9942603 * r9942597;
        double r9942609 = r9942608 * r9942599;
        double r9942610 = r9942607 - r9942609;
        double r9942611 = x;
        double r9942612 = log(r9942603);
        double r9942613 = r9942611 * r9942612;
        double r9942614 = r9942610 + r9942613;
        double r9942615 = t;
        double r9942616 = r9942614 - r9942615;
        return r9942616;
}

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

Original9.1
Target0.3
Herbie0.3
\[\left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{\frac{1}{3}}{1.0 \cdot \left(1.0 \cdot 1.0\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right)\]

Derivation

  1. Initial program 9.1

    \[\left(x \cdot \log y + z \cdot \log \left(1.0 - y\right)\right) - t\]

  2. Taylor expanded around 0 0.3

    \[\leadsto \left(x \cdot \log y + \color{blue}{\left(\log 1.0 \cdot z - \left(\frac{1}{2} \cdot \frac{z \cdot {y}^{2}}{{1.0}^{2}} + 1.0 \cdot \left(z \cdot y\right)\right)\right)}\right) - t\]

  3. Simplified0.3

    \[\leadsto \left(x \cdot \log y + \color{blue}{\left(\left(\log 1.0 \cdot z - \frac{z \cdot \frac{1}{2}}{\frac{1.0}{y} \cdot \frac{1.0}{y}}\right) - \left(1.0 \cdot y\right) \cdot z\right)}\right) - t\]

  4. Final simplification0.3

    \[\leadsto \left(\left(\left(\log 1.0 \cdot z - \frac{z \cdot \frac{1}{2}}{\frac{1.0}{y} \cdot \frac{1.0}{y}}\right) - \left(y \cdot 1.0\right) \cdot z\right) + x \cdot \log y\right) - t\]

Reproduce

herbie shell --seed 2019156 
(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) (* (/ 1/3 (* 1.0 (* 1.0 1.0))) (* y (* y y))))) (- t (* x (log y))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))