Average Error: 2.0 → 2.0
Time: 1.8m
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 r786294 = x;
        double r786295 = y;
        double r786296 = z;
        double r786297 = log(r786296);
        double r786298 = r786295 * r786297;
        double r786299 = t;
        double r786300 = 1.0;
        double r786301 = r786299 - r786300;
        double r786302 = a;
        double r786303 = log(r786302);
        double r786304 = r786301 * r786303;
        double r786305 = r786298 + r786304;
        double r786306 = b;
        double r786307 = r786305 - r786306;
        double r786308 = exp(r786307);
        double r786309 = r786294 * r786308;
        double r786310 = r786309 / r786295;
        return r786310;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r786311 = x;
        double r786312 = y;
        double r786313 = z;
        double r786314 = log(r786313);
        double r786315 = r786312 * r786314;
        double r786316 = t;
        double r786317 = 1.0;
        double r786318 = r786316 - r786317;
        double r786319 = a;
        double r786320 = log(r786319);
        double r786321 = r786318 * r786320;
        double r786322 = r786315 + r786321;
        double r786323 = b;
        double r786324 = r786322 - r786323;
        double r786325 = exp(r786324);
        double r786326 = r786311 * r786325;
        double r786327 = r786326 / r786312;
        return r786327;
}

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
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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 2020047 
(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))