Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\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(1 - y, z, \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 r13233 = x;
        double r13234 = y;
        double r13235 = 1.0;
        double r13236 = r13234 - r13235;
        double r13237 = z;
        double r13238 = r13236 * r13237;
        double r13239 = r13233 - r13238;
        double r13240 = t;
        double r13241 = r13240 - r13235;
        double r13242 = a;
        double r13243 = r13241 * r13242;
        double r13244 = r13239 - r13243;
        double r13245 = r13234 + r13240;
        double r13246 = 2.0;
        double r13247 = r13245 - r13246;
        double r13248 = b;
        double r13249 = r13247 * r13248;
        double r13250 = r13244 + r13249;
        return r13250;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r13251 = b;
        double r13252 = y;
        double r13253 = t;
        double r13254 = r13252 + r13253;
        double r13255 = 2.0;
        double r13256 = r13254 - r13255;
        double r13257 = 1.0;
        double r13258 = r13257 - r13252;
        double r13259 = z;
        double r13260 = a;
        double r13261 = r13257 - r13253;
        double r13262 = x;
        double r13263 = fma(r13260, r13261, r13262);
        double r13264 = fma(r13258, r13259, r13263);
        double r13265 = fma(r13251, r13256, r13264);
        return r13265;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +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)))