Details

analyze328.0ms

Algorithm: search

sample37.0ms

Algorithm

intervals

Results

12.0ms	194×	body	80	valid
6.0ms	21×	body	2560	valid
3.0ms	9×	body	5120	valid
3.0ms	11×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	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

prune4.0ms

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: 39.3b

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)
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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))
8.0ms	(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:

7.0ms	(+ (* re re) (* im im))
22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (86.0ms)

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

prune130.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 18.0b

Counts

64 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.7b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

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)))

series27.0ms

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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (33.0ms)

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

prune155.0ms

Filtered

75 candidates to 136 candidates (-81.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	133	9	142

Merged error: 18.0b

Counts

142 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

13.6b	(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(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:

21.0ms	(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(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:

8.0ms	(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	172	663
1	540	575
2	1978	556
3	5002	527

prune158.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	68	9	77

Merged error: 18.0b

Counts

77 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

14.5b	(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (exp (log (sqrt (+ (* re re) (* im im)))))))) re)
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(sqrt (+ (* re re) (* im im)))
30.2b	(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:

23.0ms	(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (exp (log (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:

8.0ms	(+ (* (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (cbrt (sqrt (exp (log (sqrt (+ (* re re) (* im im)))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	176	699
1	556	595
2	1975	576
3	5001	547

prune139.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

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: 18.0b

Counts

77 → 9

regimes330.0ms

Accuracy

59.4% (8.7b remaining)

Error of 26.8b against oracle of 18.1b and baseline of 39.5b

bsearch77.0ms

Steps

Iters	Range		Point
10	1.0366480481021398e+65	1.7535236682861156e+76	3.9379725622952346e+70
10	-4.206818744383426e-296	-8.427940723012045e-308	-8.512305947113228e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

analyze326.0ms

Algorithm: search

sample967.0ms

Algorithm

intervals

Results

296.0ms	6004×	body	80	valid
208.0ms	709×	body	2560	valid
116.0ms	496×	body	1280	valid
102.0ms	290×	body	5120	valid
50.0ms	273×	body	640	valid
21.0ms	156×	body	320	valid
7.0ms	72×	body	160	valid

Details

analyze328.0ms

sample37.0ms

simplify5.0ms

prune4.0ms

localize10.0ms

rewrite23.0ms

series42.0ms

simplify92.0ms

prune130.0ms

localize12.0ms

rewrite39.0ms

series27.0ms

simplify46.0ms

prune155.0ms

localize18.0ms

rewrite36.0ms

series25.0ms

simplify72.0ms

prune158.0ms

localize26.0ms

rewrite36.0ms

series25.0ms

simplify76.0ms

prune139.0ms

regimes330.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

analyze326.0ms

sample967.0ms

Profiling