Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
5.0ms	25×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	9×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

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: 39.9b

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)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* re re) (* im im))
176.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
49.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune181.0ms

Filtered

66 candidates to 52 candidates (78.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Merged error: 17.0b

Counts

67 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
7.3b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
20.2b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
198.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
69.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune291.0ms

Filtered

111 candidates to 77 candidates (69.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	108	8	116

Merged error: 7.9b

Counts

116 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
7.3b	(sqrt (* 2.0 (/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
153×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
51×	`unpow-prod-down`
25×	`distribute-lft-out`
17×	`add-exp-log` `sqr-pow`
16×	`associate-/r*`
9×	`div-exp` `add-cbrt-cube` `div-inv`
8×	`pow1`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`sqrt-prod`
3×	`cbrt-undiv` `sqrt-pow1` `sqrt-div`
2×	`pow-to-exp` `flip3-+` `pow1/2` `pow-exp` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `sum-log` `associate-/r/`

Counts

4 → 193

Calls

4 calls:

13.0ms	(/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
15.0ms	(sqrt (* 2.0 (/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
203.0ms	(sqrt (* 2.0 (/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify130.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	788	2657
1	3660	2402
2	5001	2402

prune401.0ms

Filtered

205 candidates to 101 candidates (49.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	205	8	213

Merged error: 5.9b

Counts

213 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
26.7b	(sqrt (* 2.0 (pow im 2)))
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
32×	`sqrt-prod`
28×	`times-frac`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`sqrt-div` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

12.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (* 2.0 (pow im 2)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (sqrt (* 2.0 (pow im 2))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (* 2.0 (pow im 2)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	387	1210
1	1325	1133
2	5002	1103

prune297.0ms

Filtered

103 candidates to 76 candidates (73.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	103	8	111

Merged error: 1.5b

Counts

111 → 8

regimes155.0ms

Accuracy

35.3% (23.4b remaining)

Error of 24.7b against oracle of 1.2b and baseline of 37.4b

bsearch401.0ms

Steps

Iters	Range		Point
5	1.3412804874082685e+153	3.9681903726503234e+153	3.885268929088002e+153
7	5.010844430904658e-140	2.4260554139808026e-138	5.102891077677831e-140
4	6.644118788358932e-151	1.1547103741053848e-150	8.63595642539124e-151
7	3.3202865819431243e-209	2.0944792406008134e-207	4.5140644322302014e-209
8	2.1029768332911183e-231	5.753371363299303e-227	4.205475490284948e-228
6	-2.8328869128000004e-287	-2.7451405566650213e-288	-2.4153073964829095e-287
10	-2.5170109662579546e-211	-5.785550335923721e-221	-3.5788710567103776e-219
10	-2.368742889503448e-151	-4.8620484299604695e-170	-1.0671882111443487e-167
7	-5.502474362749991e-90	-5.6767130417445485e-92	-2.5541913287747073e-90
5	-3.1158541889032954e-21	-1.220833253698676e-21	-1.8947234387707964e-21
9	-2.3268372888139707e+24	-856385374775412.2	-873649614256418.2

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	84
1	115	84
2	116	84
3	116	84

end0.0ms

sample667.0ms

Algorithm

intervals

Results

206.0ms	6020×	body	80	valid
138.0ms	728×	body	2560	valid
73.0ms	475×	body	1280	valid
63.0ms	274×	body	5120	valid
34.0ms	287×	body	640	valid
12.0ms	130×	body	320	valid
5.0ms	86×	body	160	valid