Average Error: 1.9 → 0.5
Time: 34.7s
Precision: 64
\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\]
↓
\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\left(\left(\log 1 - 1 \cdot z\right) - \left(\frac{z}{1} \cdot \frac{z}{1}\right) \cdot \frac{1}{2}\right) - b\right)}\]
x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}
↓
x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\left(\left(\log 1 - 1 \cdot z\right) - \left(\frac{z}{1} \cdot \frac{z}{1}\right) \cdot \frac{1}{2}\right) - b\right)}
double f(double x, double y, double z, double t, double a, double b) {
        double r10371243 = x;
        double r10371244 = y;
        double r10371245 = z;
        double r10371246 = log(r10371245);
        double r10371247 = t;
        double r10371248 = r10371246 - r10371247;
        double r10371249 = r10371244 * r10371248;
        double r10371250 = a;
        double r10371251 = 1.0;
        double r10371252 = r10371251 - r10371245;
        double r10371253 = log(r10371252);
        double r10371254 = b;
        double r10371255 = r10371253 - r10371254;
        double r10371256 = r10371250 * r10371255;
        double r10371257 = r10371249 + r10371256;
        double r10371258 = exp(r10371257);
        double r10371259 = r10371243 * r10371258;
        return r10371259;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r10371260 = x;
        double r10371261 = y;
        double r10371262 = z;
        double r10371263 = log(r10371262);
        double r10371264 = t;
        double r10371265 = r10371263 - r10371264;
        double r10371266 = r10371261 * r10371265;
        double r10371267 = a;
        double r10371268 = 1.0;
        double r10371269 = log(r10371268);
        double r10371270 = r10371268 * r10371262;
        double r10371271 = r10371269 - r10371270;
        double r10371272 = r10371262 / r10371268;
        double r10371273 = r10371272 * r10371272;
        double r10371274 = 0.5;
        double r10371275 = r10371273 * r10371274;
        double r10371276 = r10371271 - r10371275;
        double r10371277 = b;
        double r10371278 = r10371276 - r10371277;
        double r10371279 = r10371267 * r10371278;
        double r10371280 = r10371266 + r10371279;
        double r10371281 = exp(r10371280);
        double r10371282 = r10371260 * r10371281;
        return r10371282;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

    \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\]

  2. Taylor expanded around 0 0.5

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

  3. Simplified0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))