Average Error: 0.0 → 0.0
Time: 16.4s
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 r1418429 = x;
        double r1418430 = y;
        double r1418431 = 1.0;
        double r1418432 = r1418430 - r1418431;
        double r1418433 = z;
        double r1418434 = r1418432 * r1418433;
        double r1418435 = r1418429 - r1418434;
        double r1418436 = t;
        double r1418437 = r1418436 - r1418431;
        double r1418438 = a;
        double r1418439 = r1418437 * r1418438;
        double r1418440 = r1418435 - r1418439;
        double r1418441 = r1418430 + r1418436;
        double r1418442 = 2.0;
        double r1418443 = r1418441 - r1418442;
        double r1418444 = b;
        double r1418445 = r1418443 * r1418444;
        double r1418446 = r1418440 + r1418445;
        return r1418446;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1418447 = a;
        double r1418448 = 1.0;
        double r1418449 = t;
        double r1418450 = r1418448 - r1418449;
        double r1418451 = y;
        double r1418452 = r1418448 - r1418451;
        double r1418453 = z;
        double r1418454 = b;
        double r1418455 = r1418449 + r1418451;
        double r1418456 = 2.0;
        double r1418457 = r1418455 - r1418456;
        double r1418458 = x;
        double r1418459 = fma(r1418454, r1418457, r1418458);
        double r1418460 = fma(r1418452, r1418453, r1418459);
        double r1418461 = fma(r1418447, r1418450, r1418460);
        return r1418461;
}

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 2019192 +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)))