Average Error: 0.0 → 0.0
Time: 35.2s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)\]
\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
↓
\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r46255 = x;
        double r46256 = y;
        double r46257 = 1.0;
        double r46258 = r46256 - r46257;
        double r46259 = z;
        double r46260 = r46258 * r46259;
        double r46261 = r46255 - r46260;
        double r46262 = t;
        double r46263 = r46262 - r46257;
        double r46264 = a;
        double r46265 = r46263 * r46264;
        double r46266 = r46261 - r46265;
        double r46267 = r46256 + r46262;
        double r46268 = 2.0;
        double r46269 = r46267 - r46268;
        double r46270 = b;
        double r46271 = r46269 * r46270;
        double r46272 = r46266 + r46271;
        return r46272;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r46273 = a;
        double r46274 = 1.0;
        double r46275 = t;
        double r46276 = r46274 - r46275;
        double r46277 = y;
        double r46278 = r46274 - r46277;
        double r46279 = z;
        double r46280 = b;
        double r46281 = r46275 + r46277;
        double r46282 = 2.0;
        double r46283 = r46281 - r46282;
        double r46284 = x;
        double r46285 = fma(r46280, r46283, r46284);
        double r46286 = fma(r46278, r46279, r46285);
        double r46287 = fma(r46273, r46276, r46286);
        return r46287;
}

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

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. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))