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. Applied simplify57.6

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

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. Applied simplify0.4

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

Runtime

Time bar (total: 24.6s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' +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)))))