Error

Target

Derivation

1. Initial program 61.8

   \[\left(1 + t \cdot 2 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 2 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 2 \cdot 10^{-16}\right)\right)\]

2. Simplified50.4

   \[\leadsto \color{blue}{(\left(2 \cdot 10^{-16} \cdot t\right) \cdot -2 + \left((\left(2 \cdot 10^{-16} \cdot t\right) \cdot \left(2 \cdot 10^{-16} \cdot t\right) + \left(2 \cdot 10^{-16} \cdot t\right))_*\right))_* + 2 \cdot 10^{-16} \cdot t}\]

3. Taylor expanded around inf 0.3

   \[\leadsto \color{blue}{3.9999999999999997 \cdot 10^{-32} \cdot {t}^{2}}\]

4. Simplified0.3

   \[\leadsto \color{blue}{\left(t \cdot t\right) \cdot 3.9999999999999997 \cdot 10^{-32}}\]
5. Using strategy rm

6. Applied *-commutative0.3

   \[\leadsto \color{blue}{\left(t \cdot t\right)} \cdot 3.9999999999999997 \cdot 10^{-32}\]

7. Applied associate-*l*0.3

   \[\leadsto \color{blue}{t \cdot \left(t \cdot 3.9999999999999997 \cdot 10^{-32}\right)}\]

8. Final simplification0.3

   \[\leadsto t \cdot \left(t \cdot 3.9999999999999997 \cdot 10^{-32}\right)\]

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (t)
  :name "fma_test1"
  :pre (<= 0.9 t 1.1)

  :herbie-target
  (fma (+ 1 (* t 2e-16)) (+ 1 (* t 2e-16)) (- -1 (* 2 (* t 2e-16))))

  (+ (* (+ 1 (* t 2e-16)) (+ 1 (* t 2e-16))) (- -1 (* 2 (* t 2e-16)))))