Average Error: 1.9 → 1.9
Time: 36.7s
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 r356275 = x;
        double r356276 = y;
        double r356277 = z;
        double r356278 = log(r356277);
        double r356279 = r356276 * r356278;
        double r356280 = t;
        double r356281 = 1.0;
        double r356282 = r356280 - r356281;
        double r356283 = a;
        double r356284 = log(r356283);
        double r356285 = r356282 * r356284;
        double r356286 = r356279 + r356285;
        double r356287 = b;
        double r356288 = r356286 - r356287;
        double r356289 = exp(r356288);
        double r356290 = r356275 * r356289;
        double r356291 = r356290 / r356276;
        return r356291;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r356292 = x;
        double r356293 = a;
        double r356294 = log(r356293);
        double r356295 = t;
        double r356296 = 1.0;
        double r356297 = r356295 - r356296;
        double r356298 = r356294 * r356297;
        double r356299 = z;
        double r356300 = log(r356299);
        double r356301 = y;
        double r356302 = r356300 * r356301;
        double r356303 = r356298 + r356302;
        double r356304 = b;
        double r356305 = r356303 - r356304;
        double r356306 = exp(r356305);
        double r356307 = r356292 * r356306;
        double r356308 = r356307 / r356301;
        return r356308;
}

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

Original1.9
Target11.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  2. Final simplification1.9

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

Reproduce

herbie shell --seed 2019195 
(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))