Average Error: 0.0 → 0.0
Time: 22.0s
Precision: 64
\[\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)\]
\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b
↓
\mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r2142473 = x;
        double r2142474 = y;
        double r2142475 = 1.0;
        double r2142476 = r2142474 - r2142475;
        double r2142477 = z;
        double r2142478 = r2142476 * r2142477;
        double r2142479 = r2142473 - r2142478;
        double r2142480 = t;
        double r2142481 = r2142480 - r2142475;
        double r2142482 = a;
        double r2142483 = r2142481 * r2142482;
        double r2142484 = r2142479 - r2142483;
        double r2142485 = r2142474 + r2142480;
        double r2142486 = 2.0;
        double r2142487 = r2142485 - r2142486;
        double r2142488 = b;
        double r2142489 = r2142487 * r2142488;
        double r2142490 = r2142484 + r2142489;
        return r2142490;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2142491 = y;
        double r2142492 = t;
        double r2142493 = r2142491 + r2142492;
        double r2142494 = 2.0;
        double r2142495 = r2142493 - r2142494;
        double r2142496 = b;
        double r2142497 = a;
        double r2142498 = 1.0;
        double r2142499 = r2142498 - r2142492;
        double r2142500 = z;
        double r2142501 = r2142498 - r2142491;
        double r2142502 = x;
        double r2142503 = fma(r2142500, r2142501, r2142502);
        double r2142504 = fma(r2142497, r2142499, r2142503);
        double r2142505 = fma(r2142495, r2142496, r2142504);
        return r2142505;
}

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

    \[\left(\left(x - \left(y - 1.0\right) \cdot z\right) - \left(t - 1.0\right) \cdot a\right) + \left(\left(y + t\right) - 2.0\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2.0, b, \mathsf{fma}\left(a, 1.0 - t, \mathsf{fma}\left(z, 1.0 - y, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019168 +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)))