(fma (/ x y) y (- x))

Average Error: 61.1 → 61.1

Time: 1.5s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 61.1

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

2. Final simplification 61.1

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

Reproduce

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