Average Error: 2.0 → 1.3
Time: 19.1s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{e^{\log z \cdot y - \left(b - t \cdot \log a\right)}}{{a}^{1}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \frac{e^{\log z \cdot y - \left(b - t \cdot \log a\right)}}{{a}^{1}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r500218 = x;
        double r500219 = y;
        double r500220 = z;
        double r500221 = log(r500220);
        double r500222 = r500219 * r500221;
        double r500223 = t;
        double r500224 = 1.0;
        double r500225 = r500223 - r500224;
        double r500226 = a;
        double r500227 = log(r500226);
        double r500228 = r500225 * r500227;
        double r500229 = r500222 + r500228;
        double r500230 = b;
        double r500231 = r500229 - r500230;
        double r500232 = exp(r500231);
        double r500233 = r500218 * r500232;
        double r500234 = r500233 / r500219;
        return r500234;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r500235 = x;
        double r500236 = z;
        double r500237 = log(r500236);
        double r500238 = y;
        double r500239 = r500237 * r500238;
        double r500240 = b;
        double r500241 = t;
        double r500242 = a;
        double r500243 = log(r500242);
        double r500244 = r500241 * r500243;
        double r500245 = r500240 - r500244;
        double r500246 = r500239 - r500245;
        double r500247 = exp(r500246);
        double r500248 = 1.0;
        double r500249 = pow(r500242, r500248);
        double r500250 = r500247 / r500249;
        double r500251 = r500235 * r500250;
        double r500252 = r500251 / r500238;
        return r500252;
}

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

Target

Original2.0
Target11.2
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  2. Taylor expanded around inf 2.0

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

  3. Simplified1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))