Average Error: 2.1 → 2.1
Time: 39.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r371216 = x;
        double r371217 = y;
        double r371218 = z;
        double r371219 = log(r371218);
        double r371220 = r371217 * r371219;
        double r371221 = t;
        double r371222 = 1.0;
        double r371223 = r371221 - r371222;
        double r371224 = a;
        double r371225 = log(r371224);
        double r371226 = r371223 * r371225;
        double r371227 = r371220 + r371226;
        double r371228 = b;
        double r371229 = r371227 - r371228;
        double r371230 = exp(r371229);
        double r371231 = r371216 * r371230;
        double r371232 = r371231 / r371217;
        return r371232;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r371233 = x;
        double r371234 = a;
        double r371235 = log(r371234);
        double r371236 = t;
        double r371237 = 1.0;
        double r371238 = r371236 - r371237;
        double r371239 = r371235 * r371238;
        double r371240 = z;
        double r371241 = log(r371240);
        double r371242 = y;
        double r371243 = r371241 * r371242;
        double r371244 = r371239 + r371243;
        double r371245 = b;
        double r371246 = r371244 - r371245;
        double r371247 = exp(r371246);
        double r371248 = r371233 * r371247;
        double r371249 = r371248 / r371242;
        return r371249;
}

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

Original2.1
Target10.9
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  2. Final simplification2.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))