Details

analyze459.0ms

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

sample36.0ms

Algorithm

intervals

Results

8.0ms	171×	body	128	valid
8.0ms	32×	body	2048	valid
6.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	12×	body	128	nan
1.0ms	6×	body	256	valid
1.0ms	10×	body	128	invalid

simplify268.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (262.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms

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: 32.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5315	1975

prune115.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 7.6b

Counts

83 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
22.7b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
3×	`distribute-lft-out--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
62.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
133.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
120.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify74.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4920	1956
1	4920	1956

prune80.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	81	12	93

Merged error: 7.6b

Counts

93 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac_binary64`
438×	`add-sqr-sqrt_binary64`
363×	`*-un-lft-identity_binary64`
289×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`
71×	`associate-/r*_binary64`
40×	`sqrt-prod_binary64`
37×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
17×	`div-inv_binary64`
13×	`add-cbrt-cube_binary64`
9×	`div-exp_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64`
5×	`associate-/r/_binary64`
3×	`flip3--_binary64` `rec-exp_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 349

Calls

4 calls:

30.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify175.0ms

Algorithm

egg-herbie

Counts

361 → 361

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5028	16201

prune398.0ms

Filtered

197 candidates to 361 candidates (-83.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	358	3	361
Fresh	2	8	10
Picked	0	1	1
Done	1	0	1
Total	361	12	373

Merged error: 7.5b

Counts

373 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

3251×	`times-frac_binary64`
1760×	`add-sqr-sqrt_binary64`
1505×	`*-un-lft-identity_binary64`
1251×	`add-cube-cbrt_binary64`
254×	`difference-of-squares_binary64`
130×	`sqrt-prod_binary64`
129×	`div-inv_binary64`
127×	`distribute-lft-out--_binary64`
71×	`associate-/r*_binary64`
51×	`add-exp-log_binary64`
32×	`div-exp_binary64`
25×	`add-cbrt-cube_binary64`
15×	`cbrt-undiv_binary64` `associate-/r/_binary64`
13×	`associate-/l*_binary64`
11×	`rec-exp_binary64`
8×	`add-log-exp_binary64`
5×	`pow1_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 1080

Calls

4 calls:

50.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify498.0ms

Algorithm

egg-herbie

Counts

1092 → 1092

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4973	62960
1	4973	62960

prune1.2s

Filtered

365 candidates to 1092 candidates (-199.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	1092	0	1092
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	1092	12	1104

Merged error: 7.5b

Counts

1104 → 12

regimes158.0ms

Accuracy

87.4% (3.6b remaining)

Error of 9.5b against oracle of 5.8b and baseline of 34.5b

bsearch103.0ms

Steps

Iters	Range		Point
10	1.5757228470318066e+77	3.2530300906878165e+89	8.921968209640008e+83
8	1.8161254003942607e-230	8.748784198709219e-228	3.360570160473105e-229
9	-1.2108387767994494e+85	-2.126540003356247e+79	-4.270668456863539e+83

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	111	94
1	111	94

end0.0ms

sample1.1s

Algorithm

intervals

Results

274.0ms	1106×	body	2048	valid
258.0ms	5216×	body	128	valid
148.0ms	737×	body	1024	valid
113.0ms	360×	body	4096	valid
59.0ms	385×	body	512	valid
36.0ms	658×	body	128	nan
19.0ms	196×	body	256	valid
18.0ms	360×	body	128	invalid

Details

analyze459.0ms

sample36.0ms

simplify268.0ms

prune4.0ms

localize15.0ms

rewrite36.0ms

series503.0ms

simplify61.0ms

prune115.0ms

localize11.0ms

rewrite38.0ms

series530.0ms

simplify74.0ms

prune80.0ms

localize12.0ms

rewrite111.0ms

series540.0ms

simplify175.0ms

prune398.0ms

localize13.0ms

rewrite336.0ms

series567.0ms

simplify498.0ms

prune1.2s

regimes158.0ms

bsearch103.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling