Average Error: 0.0 → 0.0
Time: 20.6s
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 r53476 = x;
        double r53477 = y;
        double r53478 = 1.0;
        double r53479 = r53477 - r53478;
        double r53480 = z;
        double r53481 = r53479 * r53480;
        double r53482 = r53476 - r53481;
        double r53483 = t;
        double r53484 = r53483 - r53478;
        double r53485 = a;
        double r53486 = r53484 * r53485;
        double r53487 = r53482 - r53486;
        double r53488 = r53477 + r53483;
        double r53489 = 2.0;
        double r53490 = r53488 - r53489;
        double r53491 = b;
        double r53492 = r53490 * r53491;
        double r53493 = r53487 + r53492;
        return r53493;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r53494 = a;
        double r53495 = 1.0;
        double r53496 = t;
        double r53497 = r53495 - r53496;
        double r53498 = y;
        double r53499 = r53495 - r53498;
        double r53500 = z;
        double r53501 = b;
        double r53502 = r53496 + r53498;
        double r53503 = 2.0;
        double r53504 = r53502 - r53503;
        double r53505 = x;
        double r53506 = fma(r53501, r53504, r53505);
        double r53507 = fma(r53499, r53500, r53506);
        double r53508 = fma(r53494, r53497, r53507);
        return r53508;
}

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 2019174 +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)))