Details

analyze439.0ms

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%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample46.0ms

Algorithm

intervals

Results

12.0ms	35×	body	2560	valid
8.0ms	36×	body	1280	valid
7.0ms	157×	body	80	valid
2.0ms	13×	body	640	valid
2.0ms	29×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	11×	body	80	invalid
0.0ms	5×	body	160	valid

simplify492.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 37.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5743	1403

prune80.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 6.1b

Counts

95 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.7b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
31×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 216

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
12.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
46.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
62.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5864	5186

prune103.0ms

Filtered

173 candidates to 228 candidates (-31.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	229	8	237

Merged error: 6.0b

Counts

237 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
15.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5326	1109

prune47.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 6.0b

Counts

91 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
0.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-r_binary64` `add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
9×	`distribute-lft-neg-in_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`associate-l_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `neg-mul-1_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

19.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
15.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
17.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4947	1521
1	4947	1521

prune49.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 6.0b

Counts

120 → 9

regimes231.0ms

Accuracy

93.6% (1.5b remaining)

Error of 7.0b against oracle of 5.4b and baseline of 29.7b

bsearch66.0ms

Steps

Iters	Range		Point
6	7.136825276148826e+59	7.686660821049002e+60	7.171533889314125e+60
9	-2.388762614608786e-268	-4.198885354987093e-275	-7.399951737087807e-272
6	-2.52003804291059e+51	-2.9803183390229107e+50	-2.4839011960233026e+51

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	57
1	82	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

284.0ms	1089×	body	2560	valid
232.0ms	5071×	body	80	valid
193.0ms	912×	body	1280	valid
76.0ms	460×	body	640	valid
43.0ms	131×	body	5120	valid
33.0ms	763×	body	80	nan
31.0ms	222×	body	320	valid
11.0ms	238×	body	80	invalid
10.0ms	115×	body	160	valid

Details

analyze439.0ms

sample46.0ms

simplify492.0ms

prune9.0ms

localize10.0ms

rewrite43.0ms

series72.0ms

simplify62.0ms

prune80.0ms

localize10.0ms

rewrite47.0ms

series130.0ms

simplify73.0ms

prune103.0ms

localize9.0ms

rewrite26.0ms

series91.0ms

simplify49.0ms

prune47.0ms

localize11.0ms

rewrite38.0ms

series57.0ms

simplify57.0ms

prune49.0ms

regimes231.0ms

bsearch66.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling