Details

analyze2.0s

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

sample101.0ms

Algorithm

intervals

Results

37.0ms	406×	body	80	invalid
20.0ms	256×	body	80	valid

simplify392.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (389.0ms)

Iter	Nodes	Cost
0	4955	29
1	4955	29

prune10.0ms

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: 12.6b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (.f64 c t) (.f64 i y))
4.1b	(.f64 b (-.f64 (.f64 c z) (*.f64 i a)))
4.8b	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
6.2b	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

rewrite31.0ms

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:

4.0ms	(-.f64 (.f64 c t) (.f64 i y))
7.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 i a)))
10.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
8.0ms	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 (.f64 c t) (.f64 i y))
22.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 i a)))
21.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
22.0ms	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

simplify55.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4926	937
1	4926	937

prune188.0ms

Filtered

62 candidates to 89 candidates (-43.5%)

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: 7.2b

Counts

90 → 22

localize23.0ms

Local error

Found 4 expressions with local error:

2.2b	(.f64 (-.f64 (.f64 y z) (*.f64 t a)) (cbrt.f64 x))
2.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 (.f64 y z) (*.f64 t a)) (cbrt.f64 x)))
4.1b	(.f64 b (-.f64 (.f64 c z) (*.f64 i a)))
6.2b	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

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

series118.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (-.f64 (.f64 y z) (*.f64 t a)) (cbrt.f64 x))
28.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 (.f64 y z) (*.f64 t a)) (cbrt.f64 x)))
22.0ms	(.f64 b (-.f64 (.f64 c z) (*.f64 i a)))
24.0ms	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4997	1125
1	4997	1125

prune159.0ms

Filtered

69 candidates to 104 candidates (-50.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	103	23	126

Merged error: 7.2b

Counts

126 → 23

localize252.0ms

Local error

Found 4 expressions with local error:

0.9b	(.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (-.f64 (.f64 c z) (*.f64 i a)) (cbrt.f64 b)))
3.3b	(.f64 (-.f64 (.f64 c z) (*.f64 i a)) (cbrt.f64 b))
4.8b	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
6.2b	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

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

series119.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (.f64 (-.f64 (.f64 c z) (*.f64 i a)) (cbrt.f64 b)))
44.0ms	(.f64 (-.f64 (.f64 c z) (*.f64 i a)) (cbrt.f64 b))
25.0ms	(.f64 x (-.f64 (.f64 y z) (*.f64 t a)))
22.0ms	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

simplify33.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5459	1125

prune167.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	2	20	22
Picked	1	0	1
Done	0	0	0
Total	103	24	127

Merged error: 7.2b

Counts

127 → 24

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

6.0ms	(cbrt.f64 (.f64 x (-.f64 (.f64 y z) (*.f64 t a))))
5.0ms	(cbrt.f64 (.f64 x (-.f64 (.f64 y z) (*.f64 t a))))
6.0ms	(cbrt.f64 (.f64 x (-.f64 (.f64 y z) (*.f64 t a))))
7.0ms	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt.f64 (.f64 x (-.f64 (.f64 y z) (*.f64 t a))))
45.0ms	(cbrt.f64 (.f64 x (-.f64 (.f64 y z) (*.f64 t a))))
48.0ms	(cbrt.f64 (.f64 x (-.f64 (.f64 y z) (*.f64 t a))))
21.0ms	(.f64 j (-.f64 (.f64 c t) (*.f64 i y)))

simplify48.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5279	828

prune38.0ms

Filtered

56 candidates to 67 candidates (-19.6%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	23	23
Picked	0	1	1
Done	0	0	0
Total	66	25	91

Merged error: 7.2b

Counts

91 → 25

regimes1.8s

Accuracy

5.9% (3.9b remaining)

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

bsearch115.0ms

Steps

Iters	Range		Point
9	-5.584431832701351e-304	9.540812839880452e-307	4.604505332732512e-307
10	-1.5784648390102658e-267	-6.065866125743898e-278	-5.952273793629655e-268

simplify14.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	609	112
1	609	112

end0.0ms

sample2.6s

Algorithm

intervals

Results

916.0ms	10999×	body	80	invalid
671.0ms	8000×	body	80	valid

Details

analyze2.0s

sample101.0ms

simplify392.0ms

prune10.0ms

localize20.0ms

rewrite31.0ms

series77.0ms

simplify55.0ms

prune188.0ms

localize23.0ms

rewrite38.0ms

series118.0ms

simplify44.0ms

prune159.0ms

localize252.0ms

rewrite39.0ms

series119.0ms

simplify33.0ms

prune167.0ms

localize28.0ms

rewrite25.0ms

series159.0ms

simplify48.0ms

prune38.0ms

regimes1.8s

bsearch115.0ms

simplify14.0ms

end0.0ms

sample2.6s

Profiling