Details

sample12.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize5.0ms

Local error

Found 1 expressions with local error:

27.4b

(sqrt (+ (* re re) (* im im)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

4.0ms

(sqrt (+ (* re re) (* im im)))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

18 → 18

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	38	213
1	91	186
2	210	170
3	478	164
4	1047	164
5	2671	164
done	5000	164

prune48.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* re re) (* im im))))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
27.4b	(sqrt (+ (* re re) (* im im)))
27.4b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
28.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
40.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify273.0ms

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	127	2962
1	252	1890
2	750	1675