Average Error: 0.0 → 0.0
Time: 14.3s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)\]
\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(\left(y + t\right) - 2, b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r4030384 = x;
        double r4030385 = y;
        double r4030386 = 1.0;
        double r4030387 = r4030385 - r4030386;
        double r4030388 = z;
        double r4030389 = r4030387 * r4030388;
        double r4030390 = r4030384 - r4030389;
        double r4030391 = t;
        double r4030392 = r4030391 - r4030386;
        double r4030393 = a;
        double r4030394 = r4030392 * r4030393;
        double r4030395 = r4030390 - r4030394;
        double r4030396 = r4030385 + r4030391;
        double r4030397 = 2.0;
        double r4030398 = r4030396 - r4030397;
        double r4030399 = b;
        double r4030400 = r4030398 * r4030399;
        double r4030401 = r4030395 + r4030400;
        return r4030401;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4030402 = y;
        double r4030403 = t;
        double r4030404 = r4030402 + r4030403;
        double r4030405 = 2.0;
        double r4030406 = r4030404 - r4030405;
        double r4030407 = b;
        double r4030408 = a;
        double r4030409 = 1.0;
        double r4030410 = r4030409 - r4030403;
        double r4030411 = z;
        double r4030412 = r4030409 - r4030402;
        double r4030413 = x;
        double r4030414 = fma(r4030411, r4030412, r4030413);
        double r4030415 = fma(r4030408, r4030410, r4030414);
        double r4030416 = fma(r4030406, r4030407, r4030415);
        return r4030416;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 +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)))