Average Error: 0.0 → 0.0
Time: 21.1s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)\right) + \left(y + \left(t - 2\right)\right) \cdot b\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\left(\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)\right) + \left(y + \left(t - 2\right)\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r2700255 = x;
        double r2700256 = y;
        double r2700257 = 1.0;
        double r2700258 = r2700256 - r2700257;
        double r2700259 = z;
        double r2700260 = r2700258 * r2700259;
        double r2700261 = r2700255 - r2700260;
        double r2700262 = t;
        double r2700263 = r2700262 - r2700257;
        double r2700264 = a;
        double r2700265 = r2700263 * r2700264;
        double r2700266 = r2700261 - r2700265;
        double r2700267 = r2700256 + r2700262;
        double r2700268 = 2.0;
        double r2700269 = r2700267 - r2700268;
        double r2700270 = b;
        double r2700271 = r2700269 * r2700270;
        double r2700272 = r2700266 + r2700271;
        return r2700272;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2700273 = x;
        double r2700274 = y;
        double r2700275 = 1.0;
        double r2700276 = r2700274 - r2700275;
        double r2700277 = z;
        double r2700278 = r2700276 * r2700277;
        double r2700279 = r2700273 - r2700278;
        double r2700280 = a;
        double r2700281 = t;
        double r2700282 = r2700281 - r2700275;
        double r2700283 = r2700280 * r2700282;
        double r2700284 = r2700279 - r2700283;
        double r2700285 = 2.0;
        double r2700286 = r2700281 - r2700285;
        double r2700287 = r2700274 + r2700286;
        double r2700288 = b;
        double r2700289 = r2700287 * r2700288;
        double r2700290 = r2700284 + r2700289;
        return r2700290;
}

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 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(t \cdot b + y \cdot b\right) - 2 \cdot b\right)}\]

  3. Simplified0.0

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{b \cdot \left(\left(t - 2\right) + y\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)\right) + \left(y + \left(t - 2\right)\right) \cdot b\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))