Details

analyze2.1s

Algorithm

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

sample100.0ms

Algorithm

intervals

Results

38.0ms	393×	body	80	invalid
21.0ms	256×	body	80	valid

simplify399.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (396.0ms)

Iter	Nodes	Cost
0	4955	29
1	4955	29

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (.f64 c a) (.f64 y i))
3.3b	(.f64 b (-.f64 (.f64 c z) (*.f64 t i)))
5.3b	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
6.2b	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
7×	`sub-neg_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`diff-log_binary64`

Counts

4 → 77

Calls

4 calls:

5.0ms	(-.f64 (.f64 c a) (.f64 y i))
7.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 t i)))
7.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
7.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 c a) (.f64 y i))
22.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 t i)))
23.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
21.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4937	937
1	4937	937

prune180.0ms

Filtered

68 candidates to 89 candidates (-30.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	67	22	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	22	90

Merged error: 7.4b

Counts

90 → 22

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b	(.f64 (-.f64 (.f64 y z) (*.f64 a t)) (cbrt.f64 x))
3.3b	(.f64 b (-.f64 (.f64 c z) (*.f64 t i)))
3.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 (.f64 y z) (*.f64 a t)) (cbrt.f64 x)))
6.2b	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1_binary64` `add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
11×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
10×	`associate-l_binary64`
6×	`associate-*r/_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `unswap-sqr_binary64` `flip--_binary64` `cbrt-prod_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 92

Calls

4 calls:

8.0ms	(.f64 (-.f64 (.f64 y z) (*.f64 a t)) (cbrt.f64 x))
7.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 t i)))
13.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 (.f64 y z) (*.f64 a t)) (cbrt.f64 x)))
7.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (-.f64 (.f64 y z) (*.f64 a t)) (cbrt.f64 x))
22.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 t i)))
30.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 (.f64 y z) (*.f64 a t)) (cbrt.f64 x)))
21.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5004	1125

prune164.0ms

Filtered

72 candidates to 104 candidates (-44.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	102	24	126

Merged error: 7.4b

Counts

126 → 24

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (-.f64 (.f64 c z) (*.f64 i t)) (cbrt.f64 b)))
2.3b	(.f64 (-.f64 (.f64 c z) (*.f64 i t)) (cbrt.f64 b))
5.3b	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
6.2b	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1_binary64` `add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
11×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
10×	`associate-l_binary64`
6×	`associate-*r/_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `unswap-sqr_binary64` `flip--_binary64` `cbrt-prod_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 92

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (-.f64 (.f64 c z) (*.f64 i t)) (cbrt.f64 b)))
9.0ms	(.f64 (-.f64 (.f64 c z) (*.f64 i t)) (cbrt.f64 b))
7.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
7.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (-.f64 (.f64 c z) (*.f64 i t)) (cbrt.f64 b)))
44.0ms	(.f64 (-.f64 (.f64 c z) (*.f64 i t)) (cbrt.f64 b))
21.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
21.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))

simplify34.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5457	1125

prune171.0ms

Filtered

72 candidates to 104 candidates (-44.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	104	24	128

Merged error: 7.4b

Counts

128 → 24

localize26.0ms

Local error

Found 4 expressions with local error:

6.2b	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))
6.5b	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))
6.5b	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))
6.5b	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-*r/_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
2×	`sub-neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

4 calls:

7.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))
6.0ms	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))
6.0ms	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))
6.0ms	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(.f64 j (-.f64 (.f64 c a) (*.f64 y i)))
47.0ms	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))
44.0ms	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))
46.0ms	(cbrt.f64 (.f64 j (-.f64 (.f64 c a) (*.f64 y i))))

simplify49.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5216	828

prune44.0ms

Filtered

56 candidates to 67 candidates (-19.6%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	1	22	23
Picked	0	1	1
Done	0	0	0
Total	65	26	91

Merged error: 7.4b

Counts

91 → 26

regimes2.1s

Accuracy

8.6% (3.8b remaining)

Error of 12.6b against oracle of 8.7b and baseline of 12.9b

bsearch104.0ms

Steps

Iters	Range		Point
8	2.300675244768473e-261	3.9645244304036894e-257	7.344975106800539e-261
10	-1.5784648390102658e-267	-6.739337338453548e-280	-4.861196230115033e-268

simplify14.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	634	113
1	634	113

end0.0ms

sample2.7s

Algorithm

intervals

Results

977.0ms	10989×	body	80	invalid
704.0ms	8000×	body	80	valid

Details

analyze2.1s

sample100.0ms

simplify399.0ms

prune14.0ms

localize21.0ms

rewrite28.0ms

series79.0ms

simplify53.0ms

prune180.0ms

localize28.0ms

rewrite38.0ms

series115.0ms

simplify50.0ms

prune164.0ms

localize24.0ms

rewrite39.0ms

series112.0ms

simplify34.0ms

prune171.0ms

localize26.0ms

rewrite26.0ms

series160.0ms

simplify49.0ms

prune44.0ms

regimes2.1s

bsearch104.0ms

simplify14.0ms

end0.0ms

sample2.7s

Profiling