Average Error: 2.1 → 2.1
Time: 37.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}\right) \cdot \frac{1}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r61403 = x;
        double r61404 = y;
        double r61405 = z;
        double r61406 = log(r61405);
        double r61407 = r61404 * r61406;
        double r61408 = t;
        double r61409 = 1.0;
        double r61410 = r61408 - r61409;
        double r61411 = a;
        double r61412 = log(r61411);
        double r61413 = r61410 * r61412;
        double r61414 = r61407 + r61413;
        double r61415 = b;
        double r61416 = r61414 - r61415;
        double r61417 = exp(r61416);
        double r61418 = r61403 * r61417;
        double r61419 = r61418 / r61404;
        return r61419;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r61420 = x;
        double r61421 = y;
        double r61422 = z;
        double r61423 = log(r61422);
        double r61424 = r61421 * r61423;
        double r61425 = t;
        double r61426 = 1.0;
        double r61427 = r61425 - r61426;
        double r61428 = a;
        double r61429 = log(r61428);
        double r61430 = r61427 * r61429;
        double r61431 = r61424 + r61430;
        double r61432 = b;
        double r61433 = r61431 - r61432;
        double r61434 = exp(r61433);
        double r61435 = r61420 * r61434;
        double r61436 = 1.0;
        double r61437 = r61436 / r61421;
        double r61438 = r61435 * r61437;
        return r61438;
}

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 2.1

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

  3. Applied div-inv2.1

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

  4. Final simplification2.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))