Average Error: 1.9 → 1.9
Time: 36.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r289411 = x;
        double r289412 = y;
        double r289413 = z;
        double r289414 = log(r289413);
        double r289415 = r289412 * r289414;
        double r289416 = t;
        double r289417 = 1.0;
        double r289418 = r289416 - r289417;
        double r289419 = a;
        double r289420 = log(r289419);
        double r289421 = r289418 * r289420;
        double r289422 = r289415 + r289421;
        double r289423 = b;
        double r289424 = r289422 - r289423;
        double r289425 = exp(r289424);
        double r289426 = r289411 * r289425;
        double r289427 = r289426 / r289412;
        return r289427;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r289428 = x;
        double r289429 = y;
        double r289430 = z;
        double r289431 = log(r289430);
        double r289432 = r289429 * r289431;
        double r289433 = t;
        double r289434 = 1.0;
        double r289435 = r289433 - r289434;
        double r289436 = a;
        double r289437 = log(r289436);
        double r289438 = r289435 * r289437;
        double r289439 = r289432 + r289438;
        double r289440 = b;
        double r289441 = r289439 - r289440;
        double r289442 = exp(r289441);
        double r289443 = r289428 * r289442;
        double r289444 = r289443 / r289429;
        return r289444;
}

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
Target11.3
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

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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))