Average Error: 2.0 → 2.0
Time: 32.9s
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 r1000437 = x;
        double r1000438 = y;
        double r1000439 = z;
        double r1000440 = log(r1000439);
        double r1000441 = r1000438 * r1000440;
        double r1000442 = t;
        double r1000443 = 1.0;
        double r1000444 = r1000442 - r1000443;
        double r1000445 = a;
        double r1000446 = log(r1000445);
        double r1000447 = r1000444 * r1000446;
        double r1000448 = r1000441 + r1000447;
        double r1000449 = b;
        double r1000450 = r1000448 - r1000449;
        double r1000451 = exp(r1000450);
        double r1000452 = r1000437 * r1000451;
        double r1000453 = r1000452 / r1000438;
        return r1000453;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1000454 = x;
        double r1000455 = y;
        double r1000456 = z;
        double r1000457 = log(r1000456);
        double r1000458 = r1000455 * r1000457;
        double r1000459 = t;
        double r1000460 = 1.0;
        double r1000461 = r1000459 - r1000460;
        double r1000462 = a;
        double r1000463 = log(r1000462);
        double r1000464 = r1000461 * r1000463;
        double r1000465 = r1000458 + r1000464;
        double r1000466 = b;
        double r1000467 = r1000465 - r1000466;
        double r1000468 = exp(r1000467);
        double r1000469 = r1000454 * r1000468;
        double r1000470 = r1000469 / r1000455;
        return r1000470;
}

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

Original2.0
Target11.2
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  2. Final simplification2.0

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

Reproduce

herbie shell --seed 2019303 
(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))