Details

analyze611.0ms

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

sample39.0ms

Algorithm

intervals

Results

9.0ms	29×	body	2048	valid
7.0ms	167×	body	128	valid
5.0ms	17×	body	4096	valid
4.0ms	22×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	15×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	4×	body	128	invalid

simplify235.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune3.0ms

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: 35.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
13.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
63.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
121.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4957	2470
1	4957	2470

prune104.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	89	12	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	12	102

Merged error: 7.2b

Counts

102 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.1b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.9b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_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 → 126

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
290.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
374.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
112.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5022	3980

prune106.0ms

Filtered

105 candidates to 138 candidates (-31.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 7.1b

Counts

150 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite37.0ms

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×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
7.0ms	(-.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)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

359.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
50.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
119.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4883	2111
1	4883	2111

prune69.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 7.1b

Counts

104 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.7b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64`
121×	`add-sqr-sqrt_binary64`
94×	`*-un-lft-identity_binary64`
68×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
13×	`distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`div-exp_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 150

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
216.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
109.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5264	4809

prune83.0ms

Filtered

93 candidates to 162 candidates (-74.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	162	11	173

Merged error: 7.1b

Counts

173 → 11

regimes177.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.7b

bsearch89.0ms

Steps

Iters	Range		Point
11	7.212430564885515e+49	1.4420584786128615e+69	7.134037556178e+68
8	9.89014048838918e-265	1.7864489742358626e-260	2.775170470029038e-264
7	-2.5062439911161653e+154	-6.22070125447831e+152	-6.27171376998663e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	115	82
1	115	82

end0.0ms

sample978.0ms

Algorithm

intervals

Results

247.0ms	1163×	body	2048	valid
212.0ms	5193×	body	128	valid
122.0ms	728×	body	1024	valid
98.0ms	378×	body	4096	valid
42.0ms	355×	body	512	valid
33.0ms	786×	body	128	nan
15.0ms	183×	body	256	valid
10.0ms	244×	body	128	invalid

Details

analyze611.0ms

sample39.0ms

simplify235.0ms

prune3.0ms

localize11.0ms

rewrite50.0ms

series447.0ms

simplify79.0ms

prune104.0ms

localize9.0ms

rewrite54.0ms

series896.0ms

simplify76.0ms

prune106.0ms

localize9.0ms

rewrite37.0ms

series633.0ms

simplify72.0ms

prune69.0ms

localize9.0ms

rewrite49.0ms

series512.0ms

simplify101.0ms

prune83.0ms

regimes177.0ms

bsearch89.0ms

simplify3.0ms

end0.0ms

sample978.0ms

Profiling