Average Error: 0.0 → 0.0
Time: 34.7s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r124531 = x;
        double r124532 = y;
        double r124533 = 1.0;
        double r124534 = r124532 - r124533;
        double r124535 = z;
        double r124536 = r124534 * r124535;
        double r124537 = r124531 - r124536;
        double r124538 = t;
        double r124539 = r124538 - r124533;
        double r124540 = a;
        double r124541 = r124539 * r124540;
        double r124542 = r124537 - r124541;
        double r124543 = r124532 + r124538;
        double r124544 = 2.0;
        double r124545 = r124543 - r124544;
        double r124546 = b;
        double r124547 = r124545 * r124546;
        double r124548 = r124542 + r124547;
        return r124548;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r124549 = b;
        double r124550 = y;
        double r124551 = t;
        double r124552 = r124550 + r124551;
        double r124553 = 2.0;
        double r124554 = r124552 - r124553;
        double r124555 = z;
        double r124556 = 1.0;
        double r124557 = r124556 - r124550;
        double r124558 = a;
        double r124559 = r124556 - r124551;
        double r124560 = x;
        double r124561 = fma(r124558, r124559, r124560);
        double r124562 = fma(r124555, r124557, r124561);
        double r124563 = fma(r124549, r124554, r124562);
        return r124563;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))