Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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 r13090 = x;
        double r13091 = y;
        double r13092 = 1.0;
        double r13093 = r13091 - r13092;
        double r13094 = z;
        double r13095 = r13093 * r13094;
        double r13096 = r13090 - r13095;
        double r13097 = t;
        double r13098 = r13097 - r13092;
        double r13099 = a;
        double r13100 = r13098 * r13099;
        double r13101 = r13096 - r13100;
        double r13102 = r13091 + r13097;
        double r13103 = 2.0;
        double r13104 = r13102 - r13103;
        double r13105 = b;
        double r13106 = r13104 * r13105;
        double r13107 = r13101 + r13106;
        return r13107;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r13108 = b;
        double r13109 = y;
        double r13110 = t;
        double r13111 = r13109 + r13110;
        double r13112 = 2.0;
        double r13113 = r13111 - r13112;
        double r13114 = z;
        double r13115 = 1.0;
        double r13116 = r13115 - r13109;
        double r13117 = a;
        double r13118 = r13115 - r13110;
        double r13119 = x;
        double r13120 = fma(r13117, r13118, r13119);
        double r13121 = fma(r13114, r13116, r13120);
        double r13122 = fma(r13108, r13113, r13121);
        return r13122;
}

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 2019235 +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)))