Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	199×	body	80	valid
6.0ms	22×	body	2560	valid
3.0ms	13×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	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

prune2.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
27.9b	(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)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
232.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (87.0ms)

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

prune168.0ms

Filtered

63 candidates to 52 candidates (82.5%)

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: 17.1b

Counts

64 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.8b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

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)))))
17.0ms	(+ (* (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)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
45.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (37.0ms)

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

prune267.0ms

Filtered

136 candidates to 73 candidates (53.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 17.1b

Counts

143 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
10.5b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
17.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
48.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	394	992
1	1342	878
2	5001	845

prune308.0ms

Filtered

103 candidates to 66 candidates (64.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	103	9	112

Merged error: 17.1b

Counts

112 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

11.7b	(+ (* (* (pow (fabs (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3) (pow (sqrt (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3)) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))
27.9b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
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`

Counts

4 → 56

Calls

4 calls:

22.0ms	(+ (* (* (pow (fabs (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3) (pow (sqrt (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3)) (sqrt (sqrt (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)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (* (* (pow (fabs (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3) (pow (sqrt (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) 3)) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	243	805
1	928	730
2	5002	723

prune360.0ms

Filtered

68 candidates to 61 candidates (89.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	68	9	77

Merged error: 17.1b

Counts

77 → 9

regimes205.0ms

Accuracy

46.1% (11.2b remaining)

Error of 29.1b against oracle of 17.9b and baseline of 38.7b

bsearch190.0ms

Steps

Iters	Range		Point
7	1.2487597879152912e+135	1.1916238701154316e+137	2.1461281772959796e+136
9	1.5193199391667695e-195	3.690810068803692e-188	3.6220463705042686e-188
9	-2.441362357665468e-139	-1.4120451836584926e-148	-1.5876610823053962e-148
6	-3.063756814709072e+153	-3.9181749288217183e+152	-3.0250291206045395e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	37
1	52	37

end0.0ms

sample884.0ms

Algorithm

intervals

Results

285.0ms	6055×	body	80	valid
184.0ms	700×	body	2560	valid
105.0ms	482×	body	1280	valid
90.0ms	273×	body	5120	valid
48.0ms	268×	body	640	valid
19.0ms	146×	body	320	valid
7.0ms	76×	body	160	valid

Details

sample31.0ms

simplify5.0ms

prune2.0ms

localize10.0ms

rewrite22.0ms

series341.0ms

simplify97.0ms

prune168.0ms

localize12.0ms

rewrite44.0ms

series158.0ms

simplify50.0ms

prune267.0ms

localize16.0ms

rewrite35.0ms

series229.0ms

simplify56.0ms

prune308.0ms

localize23.0ms

rewrite36.0ms

series215.0ms

simplify40.0ms

prune360.0ms

regimes205.0ms

bsearch190.0ms

simplify2.0ms

end0.0ms

sample884.0ms

Profiling