Details

analyze341.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample32.0ms

Algorithm

intervals

Results

10.0ms	206×	body	80	valid
5.0ms	17×	body	2560	valid
3.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
2.0ms	5×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	248	15
1	248	15

prune2.0ms

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: 35.9b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64` `sqrt-prod_binary64`
4×	`add-cube-cbrt_binary64` `sqrt-div_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64`
2×	`pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`

Counts

3 → 42

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4935	610
1	4935	610

prune58.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 7.6b

Counts

52 → 6

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `sqrt-prod_binary64`

Counts

1 → 13

Calls

1 calls:

7.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify36.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4961	162
1	4961	162

prune24.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	13	9	22

Merged error: 7.6b

Counts

22 → 9

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
2×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

2 → 51

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 im re))
9.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

series31.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(sqrt.f64 (-.f64 im re))
20.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4971	522
1	4971	522

prune39.0ms

Filtered

38 candidates to 57 candidates (-50.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	56	10	66

Merged error: 7.6b

Counts

66 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
0.4b	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
0.4b	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
0.5b	(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 im re))) (cbrt.f64 (sqrt.f64 (-.f64 im re))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

76×	`cbrt-prod_binary64`
58×	`add-sqr-sqrt_binary64`
47×	`sqrt-prod_binary64`
42×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64` `sqrt-div_binary64`
15×	`swap-sqr_binary64`
11×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

4.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
5.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
14.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 im re))) (cbrt.f64 (sqrt.f64 (-.f64 im re))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
25.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
28.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
26.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 im re))) (cbrt.f64 (sqrt.f64 (-.f64 im re))))

simplify48.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5022	1536

prune62.0ms

Filtered

93 candidates to 138 candidates (-48.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	138	10	148

Merged error: 7.6b

Counts

148 → 10

regimes359.0ms

Accuracy

39% (11.9b remaining)

Error of 21.8b against oracle of 9.9b and baseline of 29.4b

bsearch91.0ms

Steps

Iters	Range		Point
9	7.603886682554703e+68	5.148728625185675e+76	5.07518301516914e+76
8	3.6722858510978776e-39	2.4335968002353986e-36	3.7260543194433134e-39
8	-1.6658589426454458e-143	-4.694405406411998e-146	-4.760511237683924e-146
8	-2.0778714232793923e+120	-6.558130905690867e+117	-8.727844172951264e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	78
1	66	78

end0.0ms

sample1.0s

Algorithm

intervals

Results

286.0ms	6017×	body	80	valid
192.0ms	671×	body	2560	valid
115.0ms	504×	body	1280	valid
102.0ms	8000×	pre	80	true
96.0ms	291×	body	5120	valid
54.0ms	282×	body	640	valid
22.0ms	166×	body	320	valid
6.0ms	69×	body	160	valid

Details

analyze341.0ms

sample32.0ms

simplify20.0ms

prune2.0ms

localize13.0ms

rewrite22.0ms

series42.0ms

simplify61.0ms

prune58.0ms

localize6.0ms

rewrite7.0ms

series18.0ms

simplify36.0ms

prune24.0ms

localize6.0ms

rewrite14.0ms

series31.0ms

simplify45.0ms

prune39.0ms

localize10.0ms

rewrite33.0ms

series105.0ms

simplify48.0ms

prune62.0ms

regimes359.0ms

bsearch91.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling