Details

analyze322.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

sample49.0ms

Algorithm

intervals

Results

25.0ms	115×	body	5120	exit
7.0ms	198×	body	80	valid
3.0ms	16×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	19×	body	160	valid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	80	overflowed

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	6196	12

prune6.0ms

Filtered

1 candidates to 1 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: 13.2b

Counts

2 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
9×	`associate-/l*_binary64`
8×	`distribute-lft-out_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`associate-+r-_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 91

Calls

3 calls:

5.0ms	(/.f64 x (exp.f64 wj))
12.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
21.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series29.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/.f64 x (exp.f64 wj))
11.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
11.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5860	1345

prune70.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Merged error: 0.3b

Counts

102 → 5

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))
0.0b	(.f64 wj (+.f64 wj (.f64 x -2)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

4.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))
6.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))

series15.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))
7.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4935	405
1	4935	405

prune33.0ms

Filtered

28 candidates to 41 candidates (-46.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	39	7	46

Merged error: 0.3b

Counts

46 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 wj (.f64 x -2))) (cbrt.f64 (+.f64 wj (*.f64 x -2))))
0.7b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
0.7b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
0.7b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_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 → 87

Calls

4 calls:

9.0ms	(.f64 (cbrt.f64 (+.f64 wj (.f64 x -2))) (cbrt.f64 (+.f64 wj (*.f64 x -2))))
3.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
3.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
3.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 (cbrt.f64 (+.f64 wj (.f64 x -2))) (cbrt.f64 (+.f64 wj (*.f64 x -2))))
26.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
26.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
29.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4905	1190
1	4905	1190

prune102.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	97	9	106

Merged error: 0.3b

Counts

106 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (exp.f64 wj)))
0.0b	(/.f64 (-.f64 (/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj))) wj) (+.f64 wj 1))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj)))
4.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj))) wj) (+.f64 wj 1)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac_binary64`
293×	`add-sqr-sqrt_binary64`
209×	`*-un-lft-identity_binary64`
173×	`add-cube-cbrt_binary64`
169×	`sqrt-prod_binary64`
36×	`associate-/l*_binary64`
35×	`difference-of-squares_binary64`
16×	`associate-/r*_binary64`
13×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-inv_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`associate-+r-_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 303

Calls

4 calls:

5.0ms	(/.f64 x (sqrt.f64 (exp.f64 wj)))
48.0ms	(/.f64 (-.f64 (/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj))) wj) (+.f64 wj 1))
12.0ms	(/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj)))
54.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj))) wj) (+.f64 wj 1)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 x (sqrt.f64 (exp.f64 wj)))
11.0ms	(/.f64 (-.f64 (/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj))) wj) (+.f64 wj 1))
13.0ms	(/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj)))
11.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 (/.f64 x (sqrt.f64 (exp.f64 wj))) (sqrt.f64 (exp.f64 wj))) wj) (+.f64 wj 1)))

simplify102.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4943	4980
1	4943	4980

prune87.0ms

Filtered

156 candidates to 315 candidates (-101.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	315	9	324

Merged error: 0.3b

Counts

324 → 9

regimes83.0ms

Accuracy

59.9% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.2b

bsearch15.0ms

Steps

Iters	Range		Point
7	6.619660287227474e-11	6.670118013702167e-09	6.379665546272698e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	30
1	35	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

843.0ms	3873×	body	5120	exit
220.0ms	6200×	body	80	valid
89.0ms	778×	body	320	valid
80.0ms	477×	body	640	valid
41.0ms	545×	body	160	valid
3.0ms	80×	body	80	invalid
0.0ms	14×	body	80	overflowed

Details

analyze322.0ms

sample49.0ms

simplify74.0ms

prune6.0ms

localize7.0ms

rewrite41.0ms

series29.0ms

simplify57.0ms

prune70.0ms

localize5.0ms

rewrite10.0ms

series15.0ms

simplify57.0ms

prune33.0ms

localize9.0ms

rewrite20.0ms

series115.0ms

simplify62.0ms

prune102.0ms

localize10.0ms

rewrite137.0ms

series45.0ms

simplify102.0ms

prune87.0ms

regimes83.0ms

bsearch15.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling