Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	200×	body	80	valid
5.0ms	18×	body	2560	valid
4.0ms	12×	body	5120	valid
3.0ms	16×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt`
3×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

3 → 38

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	178	275
1	689	252
2	2017	248
3	5001	246

prune286.0ms

Filtered

47 candidates to 38 candidates (19.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Merged error: 16.2b

Counts

48 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.3b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`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` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
10.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune789.0ms

Filtered

136 candidates to 71 candidates (47.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	137	7	144

Merged error: 16.2b

Counts

144 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify141.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (135.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune905.0ms

Filtered

72 candidates to 60 candidates (16.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Merged error: 16.2b

Counts

79 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
13.4b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
26.7b	(sqrt (+ (* re re) (* im im)))
26.7b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
8×	`pow1`
6×	`log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1` `pow1/2` `log-pow`
2×	`rem-sqrt-square` `log-div` `exp-diff`
1×	`+-commutative` `sum-log` `rem-exp-log`

Counts

4 → 63

Calls

4 calls:

5.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
16.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 4 (101.0ms)

Iter	Nodes	Cost
0	208	622
1	485	555
2	1193	507
3	3624	495
4	5003	493

prune730.0ms

Filtered

75 candidates to 62 candidates (17.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	75	7	82

Merged error: 16.2b

Counts

82 → 7

regimes285.0ms

Accuracy

53.9% (9.9b remaining)

Error of 27.8b against oracle of 17.9b and baseline of 39.3b

bsearch138.0ms

Steps

Iters	Range	Point
6	1.3653351403313602e+73	1.322226463547956e+74	1.2936263172600616e+74
7	-8.271287922560956e-294	-4.441296914487316e-296	-8.807734856601981e-295
7	-3.9997756247504785e-189	-4.9313450592572685e-191	-1.5391970346231962e-190

Iters

Range

Point

1.3653351403313602e+73

1.322226463547956e+74

1.2936263172600616e+74

-8.271287922560956e-294

-4.441296914487316e-296

-8.807734856601981e-295

-3.9997756247504785e-189

-4.9313450592572685e-191

-1.5391970346231962e-190

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	62
1	53	62

end0.0ms

sample946.0ms

Algorithm

intervals

Results

279.0ms	6050×	body	80	valid
183.0ms	698×	body	2560	valid
104.0ms	479×	body	1280	valid
91.0ms	282×	body	5120	valid
45.0ms	267×	body	640	valid
19.0ms	151×	body	320	valid
6.0ms	73×	body	160	valid

Details

sample40.0ms

simplify4.0ms

prune4.0ms

localize9.0ms

rewrite14.0ms

series18.0ms

simplify61.0ms

prune286.0ms

localize12.0ms

rewrite40.0ms

series28.0ms

simplify49.0ms

prune789.0ms

localize19.0ms

rewrite16.0ms

series24.0ms

simplify141.0ms

prune905.0ms

localize20.0ms

rewrite31.0ms

series25.0ms

simplify108.0ms

prune730.0ms

regimes285.0ms

bsearch138.0ms

simplify2.0ms

end0.0ms

sample946.0ms

Profiling