Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(1, x - \left(y - 1\right) \cdot z, -a \cdot \left(t - 1\right)\right) + \mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(-a, t - 1, a \cdot \left(t - 1\right)\right)\right)\]
\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(1, x - \left(y - 1\right) \cdot z, -a \cdot \left(t - 1\right)\right) + \mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(-a, t - 1, a \cdot \left(t - 1\right)\right)\right)
double code(double x, double y, double z, double t, double a, double b) {
	return (((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return (fma(1.0, (x - ((y - 1.0) * z)), -(a * (t - 1.0))) + fma(b, ((y + t) - 2.0), fma(-a, (t - 1.0), (a * (t - 1.0)))));
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied *-un-lft-identity0.0

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

  4. Applied prod-diff0.0

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

  5. Applied associate-+l+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020092 +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)))