Details

analyze471.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample46.0ms

Algorithm

intervals

Results

12.0ms	34×	body	2560	valid
9.0ms	34×	body	1280	valid
8.0ms	150×	body	80	valid
4.0ms	20×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	22×	body	80	nan
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	6×	body	80	invalid

simplify250.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (248.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune6.0ms

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: 38.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
1.4b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64` `associate-/l*_binary64` `times-frac_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `distribute-rgt-neg-in_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 75

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
4.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
7.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
14.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5861	1427

prune130.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 6.0b

Counts

88 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
5.0b	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
10.7b	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
11×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
4×	`distribute-lft-out--_binary64` `div-inv_binary64`
2×	`clear-num_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 → 109

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
17.0ms	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
14.0ms	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
48.0ms	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
112.0ms	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5287	2385

prune129.0ms

Filtered

82 candidates to 121 candidates (-47.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	122	8	130

Merged error: 6.0b

Counts

130 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite33.0ms

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:

13.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4905	1589
1	4905	1589

prune111.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 6.0b

Counts

101 → 8

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify4.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Merged error: 6.0b

Counts

8 → 8

regimes233.0ms

Accuracy

93% (1.7b remaining)

Error of 7.3b against oracle of 5.6b and baseline of 29.7b

bsearch45.0ms

Steps

Iters	Range		Point
6	5.497054777965939e+32	2.720772085466593e+33	2.673025417100217e+33
9	1.5217707132634722e-201	2.4731489252075214e-192	1.5461279104521085e-201
0	-1.604960284102343e+99	-1.5858680620401842e+99	-1.5954141730712636e+99

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	221	63
1	221	63

end0.0ms

sample1.3s

Algorithm

intervals

Results

344.0ms	1098×	body	2560	valid
265.0ms	5069×	body	80	valid
217.0ms	881×	body	1280	valid
94.0ms	477×	body	640	valid
44.0ms	116×	body	5120	valid
36.0ms	236×	body	320	valid
32.0ms	659×	body	80	nan
21.0ms	408×	body	80	invalid
12.0ms	123×	body	160	valid

Details

analyze471.0ms

sample46.0ms

simplify250.0ms

prune6.0ms

localize11.0ms

rewrite33.0ms

series57.0ms

simplify45.0ms

prune130.0ms

localize12.0ms

rewrite45.0ms

series184.0ms

simplify41.0ms

prune129.0ms

localize13.0ms

rewrite33.0ms

series90.0ms

simplify75.0ms

prune111.0ms

localize4.0ms

rewrite0.0ms

series0.0ms

simplify4.0ms

prune0.0ms

regimes233.0ms

bsearch45.0ms

simplify4.0ms

end0.0ms

sample1.3s

Profiling