Average Error: 1.9 → 1.9
Time: 1.6m
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 r479620 = x;
        double r479621 = y;
        double r479622 = z;
        double r479623 = log(r479622);
        double r479624 = r479621 * r479623;
        double r479625 = t;
        double r479626 = 1.0;
        double r479627 = r479625 - r479626;
        double r479628 = a;
        double r479629 = log(r479628);
        double r479630 = r479627 * r479629;
        double r479631 = r479624 + r479630;
        double r479632 = b;
        double r479633 = r479631 - r479632;
        double r479634 = exp(r479633);
        double r479635 = r479620 * r479634;
        double r479636 = r479635 / r479621;
        return r479636;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r479637 = x;
        double r479638 = y;
        double r479639 = z;
        double r479640 = log(r479639);
        double r479641 = r479638 * r479640;
        double r479642 = t;
        double r479643 = 1.0;
        double r479644 = r479642 - r479643;
        double r479645 = a;
        double r479646 = log(r479645);
        double r479647 = r479644 * r479646;
        double r479648 = r479641 + r479647;
        double r479649 = b;
        double r479650 = r479648 - r479649;
        double r479651 = exp(r479650);
        double r479652 = r479637 * r479651;
        double r479653 = r479652 / r479638;
        return r479653;
}

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
Target10.9
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 2019304 +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 -0.88458485041274715) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.22883740731) (/ (* (/ 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))