Details

Time bar (total: 4.0s)

sample184.0ms

Algorithm
intervals
Results
17.0ms186×body80valid
13.0ms26×body2560valid
10.0ms18×body5120valid
6.0ms15×body1280valid
2.0msbody640valid
1.0msbody320valid
0.0msbody160valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
01215
11715
22415
33015
43515
done3515

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b
(+ (* re re) (* im im))
0.2b
(- (sqrt (+ (* re re) (* im im))) re)
28.9b
(sqrt (+ (* re re) (* im im)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
pow1 add-log-exp
*-un-lft-identity
add-cube-cbrt sqrt-prod
add-cbrt-cube sqrt-div add-exp-log
sqrt-pow1
flip3-+ flip3-- pow1/2 associate-*r/ flip-+ flip-- difference-of-squares
+-commutative rem-sqrt-square sum-log sub-neg diff-log pow-prod-down distribute-lft-out--
Counts
4 → 54
Calls
4 calls:
43.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
13.0ms
(+ (* re re) (* im im))
79.0ms
(- (sqrt (+ (* re re) (* im im))) re)
16.0ms
(sqrt (+ (* re re) (* im im)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
54.0ms
(+ (* re re) (* im im))
84.0ms
(- (sqrt (+ (* re re) (* im im))) re)
65.0ms
(sqrt (+ (* re re) (* im im)))

simplify730.0ms

Counts
66 → 66
Iterations

Useful iterations: done (727.0ms)

IterNodesCost
0114942
1276836
21287752
done5001728

prune347.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.2b
(- (sqrt (+ (* re re) (* im im))) re)
3.5b
(exp (log (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))
28.9b
(sqrt (+ (* re re) (* im im)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt pow1
*-un-lft-identity
exp-prod add-cube-cbrt
sqrt-div sqrt-prod add-log-exp
sqrt-pow1
log-prod add-cbrt-cube exp-sum associate-*r/ add-exp-log log-pow
flip3-- pow1/2 flip--
log-div exp-diff pow-prod-down difference-of-squares
rem-sqrt-square sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- rem-exp-log
Counts
4 → 64
Calls
4 calls:
34.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
36.0ms
(- (sqrt (+ (* re re) (* im im))) re)
114.0ms
(exp (log (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))
12.0ms
(sqrt (+ (* re re) (* im im)))

series639.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
73.0ms
(- (sqrt (+ (* re re) (* im im))) re)
283.0ms
(exp (log (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))))
43.0ms
(sqrt (+ (* re re) (* im im)))

simplify691.0ms

Counts
76 → 76
Iterations

Useful iterations: done (687.0ms)

IterNodesCost
01431256
12971064
21131965
done5000925

prune451.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.2b

localize1.0ms