Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	199×	body	80	valid
4.0ms	17×	body	2560	valid
3.0ms	16×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 37.4b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div`
3×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 43

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series268.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune141.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	6	53

Merged error: 15.5b

Counts

53 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (+ (* re re) (* im im))) re)
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

11.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	135	456
1	332	432
2	839	424
3	2503	422
4	5002	420

prune206.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 15.5b

Counts

78 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.9b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity`
8×	`add-cube-cbrt` `log-prod` `exp-sum` `sqrt-prod`
6×	`exp-prod` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
3×	`pow1/2` `log-pow` `difference-of-squares`
2×	`log-div` `flip3--` `flip3-+` `exp-diff` `associate-*r/` `flip--` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 66

Calls

4 calls:

11.0ms	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
10.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
41.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	283	630
1	843	573
2	2616	551
3	5001	542

prune211.0ms

Filtered

78 candidates to 58 candidates (74.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	4	4
Picked	1	0	1
Done	1	0	1
Total	73	11	84

Merged error: 15.4b

Counts

84 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (sqrt (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.9b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
22×	`sqrt-prod`
16×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`pow1`
10×	`log-prod` `associate-r` `exp-sum`
6×	`add-exp-log` `exp-prod` `sqrt-div` `associate-l` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
4×	`sqrt-pow1` `pow1/2` `unswap-sqr`
3×	`pow-prod-down` `log-pow`
2×	`log-div` `flip3--` `flip3-+` `exp-diff` `associate-*r/` `flip--` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

15.0ms	(* (sqrt 2.0) (sqrt (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
10.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (sqrt 2.0) (sqrt (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
40.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
46.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify124.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	342	917
1	1173	850
2	4410	824
3	5002	818

prune250.0ms

Filtered

101 candidates to 72 candidates (71.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	98	14	112

Merged error: 15.4b

Counts

112 → 14

Details

sample29.0ms

simplify7.0ms

prune3.0ms

localize17.0ms

rewrite20.0ms

series268.0ms

simplify76.0ms

prune141.0ms

localize12.0ms

rewrite27.0ms

series169.0ms

simplify88.0ms

prune206.0ms

localize14.0ms

rewrite32.0ms

series306.0ms

simplify79.0ms

prune211.0ms

localize15.0ms

rewrite37.0ms

series307.0ms

simplify124.0ms

prune250.0ms

regimes284.0ms

bsearch3.0ms

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