Average Error: 0.5 → 0.5

Time: 7.7s

Precision: 64

Internal Precision: 128

\[\sqrt{x - 1} \cdot \sqrt{x}\]

↓

\[\sqrt{x - 1} \cdot \sqrt{x}\]

Error

The X axis uses an exponential scale — Bits error versus x

The X axis uses an exponential scale — Bits error versus x

Derivation

Initial program 0.5
\[\sqrt{x - 1} \cdot \sqrt{x}\]
Final simplification0.5
\[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2019090 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1)) (sqrt x)))