Average Error: 0.0 → 0.0
Time: 18.4s
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 r1568417 = x;
        double r1568418 = y;
        double r1568419 = 1.0;
        double r1568420 = r1568418 - r1568419;
        double r1568421 = z;
        double r1568422 = r1568420 * r1568421;
        double r1568423 = r1568417 - r1568422;
        double r1568424 = t;
        double r1568425 = r1568424 - r1568419;
        double r1568426 = a;
        double r1568427 = r1568425 * r1568426;
        double r1568428 = r1568423 - r1568427;
        double r1568429 = r1568418 + r1568424;
        double r1568430 = 2.0;
        double r1568431 = r1568429 - r1568430;
        double r1568432 = b;
        double r1568433 = r1568431 * r1568432;
        double r1568434 = r1568428 + r1568433;
        return r1568434;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1568435 = a;
        double r1568436 = 1.0;
        double r1568437 = t;
        double r1568438 = r1568436 - r1568437;
        double r1568439 = y;
        double r1568440 = r1568436 - r1568439;
        double r1568441 = z;
        double r1568442 = b;
        double r1568443 = r1568437 + r1568439;
        double r1568444 = 2.0;
        double r1568445 = r1568443 - r1568444;
        double r1568446 = x;
        double r1568447 = fma(r1568442, r1568445, r1568446);
        double r1568448 = fma(r1568440, r1568441, r1568447);
        double r1568449 = fma(r1568435, r1568438, r1568448);
        return r1568449;
}

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)))