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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. Initial simplification57.6

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

3. Taylor expanded around 0 0.3

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

5. Applied add-sqr-sqrt0.6

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

7. Applied sqrt-prod0.4

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

8. Applied associate-*l*0.4

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

9. Final simplification0.4

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

Runtime

Time bar (total: 7.7s)Debug logProfile

herbie shell --seed 2018263 +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)))))