(fma (* x y) (/ 1 x) (- y))

Average Error: 61.2 → 61.2

Time: 1.6s

Precision: binary64

Math

\[\mathsf{fma}\left(x \cdot y, \frac{1}{x}, -y\right)\]

↓

\[\mathsf{fma}\left(x \cdot y, \frac{1}{x}, -y\right)\]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 61.2

   \[\mathsf{fma}\left(x \cdot y, \frac{1}{x}, -y\right)\]

2. Final simplification 61.2

   \[\leadsto \mathsf{fma}\left(x \cdot y, \frac{1}{x}, -y\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(fma (* x y) (/ 1 x) (- y))"
  :precision binary64
  (fma (* x y) (/ 1.0 x) (neg y)))