Details

analyze342.0ms

Algorithm: search

sample34.0ms

Algorithm

intervals

Results

10.0ms	204×	body	80	valid
5.0ms	9×	body	640	valid
4.0ms	15×	body	1280	valid
4.0ms	12×	body	2560	valid
2.0ms	6×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 39.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune129.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 17.6b

Counts

64 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
32.5b	(sqrt (+ (* re re) (* im im)))
32.5b	(sqrt (+ (* re re) (* im im)))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

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

series25.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	141	392
1	358	380
2	866	376
3	2557	375
4	5001	375

prune115.0ms

Filtered

61 candidates to 69 candidates (-13.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 17.6b

Counts

76 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.4b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.5b	(sqrt (+ (* re re) (* im im)))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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:

15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(+ (* (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)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

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

prune130.0ms

Filtered

74 candidates to 136 candidates (-83.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Merged error: 17.6b

Counts

143 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
12.5b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
32.5b	(sqrt (+ (* re re) (* im im)))
32.5b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

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:

6.0ms	(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)))

simplify121.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 4 (111.0ms)

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

prune111.0ms

Filtered

62 candidates to 75 candidates (-21.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	74	8	82

Merged error: 17.6b

Counts

82 → 8

regimes444.0ms

Accuracy

50.2% (10.6b remaining)

Error of 28.9b against oracle of 18.3b and baseline of 39.5b

bsearch156.0ms

Steps

Iters	Range		Point
9	4.367983800832522e+59	3.6374539111637025e+64	1.1877173283244378e+62
10	-1.367212076401319e-299	4.630985363417236e-301	-2.1177384497007792e-304
3	-1.60603650358745e-258	-1.3138586487999243e-258	-1.3686419965725857e-258
5	-3.168101490300806e-185	-1.440446405010367e-185	-2.2067693612502508e-185
9	-1.1839139323395968e-37	-3.2321373794750325e-43	-3.2644670453862826e-43

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	47
1	55	47

end0.0ms

analyze338.0ms

Algorithm: search

sample974.0ms

Algorithm

intervals

Results

300.0ms	5975×	body	80	valid
223.0ms	730×	body	2560	valid
119.0ms	494×	body	1280	valid
104.0ms	281×	body	5120	valid
56.0ms	299×	body	640	valid
20.0ms	145×	body	320	valid
7.0ms	76×	body	160	valid

Details

analyze342.0ms

sample34.0ms

simplify5.0ms

prune3.0ms

localize11.0ms

rewrite22.0ms

series42.0ms

simplify94.0ms

prune129.0ms

localize16.0ms

rewrite20.0ms

series25.0ms

simplify84.0ms

prune115.0ms

localize16.0ms

rewrite41.0ms

series25.0ms

simplify52.0ms

prune130.0ms

localize19.0ms

rewrite32.0ms

series25.0ms

simplify121.0ms

prune111.0ms

regimes444.0ms

bsearch156.0ms

simplify2.0ms

end0.0ms

analyze338.0ms

sample974.0ms

Profiling