Error

Try it out

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. Simplified57.6

   \[\leadsto \color{blue}{(-2 \cdot \left(2 \cdot 10^{-16} \cdot t\right) + \left((\left((t \cdot \left( 2 \cdot 10^{-16} \right) + 1)_*\right) \cdot \left((t \cdot \left( 2 \cdot 10^{-16} \right) + 1)_*\right) + -1)_*\right))_*}\]

3. Taylor expanded around inf 0.3

   \[\leadsto \color{blue}{3.9999999999999997 \cdot 10^{-32} \cdot {t}^{2}}\]
4. Using strategy rm

5. Applied unpow20.3

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

6. Applied associate-*r*0.3

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

8. Applied add-sqr-sqrt0.6

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

9. Taylor expanded around 0 0.3

   \[\leadsto \color{blue}{{t}^{2} \cdot {\left(\sqrt{3.9999999999999997 \cdot 10^{-32}}\right)}^{2}}\]

10. Simplified0.3

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

11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019026 +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)))))