Average Error: 61.9 → 0
Time: 16.7s
Precision: 64
Internal Precision: 1088
\[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]
↓
\[\Re(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right)\right)\right) + \left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right)\right))\]

Error

Derivation

  1. Initial program 61.9

    \[\Re(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

  2. Initial simplification0

    \[\leadsto \Re(\left(\left(\left(-2 + 7\right) + \frac{4}{\frac{2}{\sqrt{3}}} i\right) + \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\left(6 + \frac{\sqrt{3} \cdot -2}{2} i\right) + \left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right)\right)\right))\]

  3. Final simplification0

    \[\leadsto \Re(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right)\right)\right) + \left(5 + \frac{4}{\frac{2}{\sqrt{3}}} i\right)\right))\]

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore ()
  :name "3.9.2 real part (p56)"
  (re (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))

Details

Time bar (total: 3.2s)Debug log

start797.0ms

Algorithm
halfpoints

setup379.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.6b
(*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))
1.6b
(*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))
1.0b
(/ 4 (/ 2 (sqrt 3)))
1.0b
(/ 2 (sqrt 3))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 36
Calls

4 calls. Slowest were:

1.0ms
(*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))
1.0ms
(*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))
0.0ms
(/ 4 (/ 2 (sqrt 3)))

series0.0ms

Counts
4 → 4
Calls

4 calls. Slowest were:

0.0ms
(*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))
0.0ms
(*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))
0.0ms
(/ 2 (sqrt 3))
0.0ms
(/ 4 (/ 2 (sqrt 3)))

simplify1.1s

Counts
16 → 40
Calls

16 calls. Slowest were:

210.0ms
(re (+.c (complex (+ -2 7) (/ 4 (/ 2 (sqrt 3)))) (*.c (*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2))) (+.c (complex 6 (/ (* (sqrt 3) -2) 2)) (*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))))))
204.0ms
(re (+.c (complex (+ -2 7) (/ 4 (/ 2 (sqrt 3)))) (*.c (*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2))) (+.c (complex 6 (/ (* (sqrt 3) -2) 2)) (*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))))))
198.0ms
(re (+.c (complex (+ -2 7) (/ 4 (/ 2 (sqrt 3)))) (*.c (*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2))) (+.c (complex 6 (/ (* (sqrt 3) -2) 2)) (*.c (complex -1/2 (/ (sqrt 3) 2)) (complex -1/2 (/ (sqrt 3) 2)))))))

prune814.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b