Details

analyze427.0ms (11.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample38.0ms (1%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	80	valid
2.0ms	25×	body	80	nan

simplify162.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	4829	28
1	4829	28

prune9.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.6b

Counts

2 → 1

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

8.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (log base) (log base))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (log base) (log base))
11.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
10.0ms	(* (atan2 im re) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify43.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4942	1828
1	4942	1828

prune271.0ms (7.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 0.1b

Counts

121 → 10

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(/ (atan2 im re) (log base))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

3.0ms

(/ (atan2 im re) (log base))

series11.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

11.0ms

(/ (atan2 im re) (log base))

simplify56.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4938	330
1	4938	330

prune107.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	26	8	34
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	29	15	44

Merged error: 0.0b

Counts

44 → 15

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(/ 1 (log base))
0.3b	(* (atan2 im re) (/ 1 (log base)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`times-frac`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
12×	`pow1`
9×	`add-cbrt-cube`
7×	`log-pow`
4×	`div-exp` `prod-exp` `associate-/r*`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 74

Calls

2 calls:

7.0ms	(* (atan2 im re) (/ 1 (log base)))
3.0ms	(/ 1 (log base))

series27.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ 1 (log base))
11.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5190	556

prune150.0ms (4.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	81	14	95

Merged error: 0.0b

Counts

95 → 14

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (pow (log base) 3))
0.3b	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
0.7b	(cbrt (/ 1 (pow (log base) 3)))
0.7b	(pow (log base) 3)

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

134×	`times-frac`
106×	`add-sqr-sqrt`
101×	`cbrt-prod`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
49×	`associate-r`
46×	`unpow-prod-down` `cube-prod`
29×	`pow1`
22×	`log-pow`
16×	`add-exp-log`
14×	`associate-/r*`
13×	`sqr-pow`
11×	`cube-mult` `unpow3`
10×	`unswap-sqr`
8×	`add-cbrt-cube`
6×	`div-exp`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`rec-exp` `pow-unpow` `1-exp` `associate-l` `div-inv` `associate-/l*`
2×	`cbrt-div`
1×	`cbrt-undiv` `pow-flip` `pow-pow` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `inv-pow` `rem-cube-cbrt`

Counts

4 → 235

Calls

4 calls:

15.0ms	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))
5.0ms	(/ 1 (pow (log base) 3))
5.0ms	(cbrt (/ 1 (pow (log base) 3)))
2.0ms	(pow (log base) 3)

series70.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (pow (log base) 3))
18.0ms	(pow (log base) 3)
17.0ms	(cbrt (/ 1 (pow (log base) 3)))
11.0ms	(* (atan2 im re) (cbrt (/ 1 (pow (log base) 3))))

simplify71.0ms (2%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4975	2477
1	4975	2477

prune466.0ms (12.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	246	15	261

Merged error: 0b

Counts

261 → 15

regimes420.0ms (11.7%)

Accuracy

Total 0.3b remaining (89.4%)

Threshold costs 0.3b (89.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	8
1	10	8

end0.0ms (0%)

sample1.0s (29.1%)

Algorithm

1×

intervals

Results

751.0ms	8000×	body	80	valid
95.0ms	1063×	body	80	nan

Details

analyze427.0ms (11.8%)

sample38.0ms (1%)

simplify162.0ms (4.5%)

prune9.0ms (0.2%)

localize19.0ms (0.5%)

rewrite26.0ms (0.7%)

series41.0ms (1.1%)

simplify43.0ms (1.2%)

prune271.0ms (7.5%)

localize6.0ms (0.2%)

rewrite4.0ms (0.1%)

series11.0ms (0.3%)

simplify56.0ms (1.6%)

prune107.0ms (3%)

localize8.0ms (0.2%)

rewrite12.0ms (0.3%)

series27.0ms (0.8%)

simplify58.0ms (1.6%)

prune150.0ms (4.2%)

localize11.0ms (0.3%)

rewrite40.0ms (1.1%)

series70.0ms (1.9%)

simplify71.0ms (2%)

prune466.0ms (12.9%)

regimes420.0ms (11.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.0s (29.1%)

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