Details

analyze458.0ms

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
7.0ms	32×	body	2048	valid
5.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	6×	body	256	valid
1.0ms	12×	body	128	nan
0.0ms	10×	body	128	invalid

simplify268.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (261.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune6.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5008	1963

prune107.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

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:

28.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
73.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
129.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify203.0ms

Algorithm

egg-herbie

Counts

361 → 361

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4967	16201
1	4967	16201

prune374.0ms

Filtered

196 candidates to 361 candidates (-84.2%)

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	0	0	0
Total	360	12	372

Merged error: 7.5b

Counts

372 → 12

localize14.0ms

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

rewrite345.0ms

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:

52.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
130.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify483.0ms

Algorithm

egg-herbie

Counts

1092 → 1092

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5007	62960

prune1.1s

Filtered

364 candidates to 1092 candidates (-200.0%)

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
74.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
116.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4961	2223
1	4961	2223

prune77.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	91	12	103

Merged error: 7.5b

Counts

103 → 12

regimes155.0ms

Accuracy

87.6% (3.6b remaining)

Error of 9.4b against oracle of 5.9b and baseline of 34.5b

bsearch107.0ms

Steps

Iters	Range	Point
10	1.5757228470318066e+77	3.2530300906878165e+89	2.2542282560766223e+78
9	1.3415096921594693e-205	1.2458390212654827e-200	3.9440742229641566e-203
9	-1.2108387767994494e+85	-2.126540003356247e+79	-4.270668456863539e+83

Iters

Range

Point

1.5757228470318066e+77

3.2530300906878165e+89

2.2542282560766223e+78

1.3415096921594693e-205

1.2458390212654827e-200

3.9440742229641566e-203

-1.2108387767994494e+85

-2.126540003356247e+79

-4.270668456863539e+83

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	94
1	108	94

end0.0ms

sample1.1s

Algorithm

intervals

Results

265.0ms	1106×	body	2048	valid
264.0ms	5216×	body	128	valid
147.0ms	737×	body	1024	valid
106.0ms	360×	body	4096	valid
53.0ms	385×	body	512	valid
30.0ms	658×	body	128	nan
18.0ms	196×	body	256	valid
17.0ms	360×	body	128	invalid

Details

analyze458.0ms

sample36.0ms

simplify268.0ms

prune6.0ms

localize11.0ms

rewrite37.0ms

series510.0ms

simplify68.0ms

prune107.0ms

localize13.0ms

rewrite113.0ms

series583.0ms

simplify203.0ms

prune374.0ms

localize14.0ms

rewrite345.0ms

series569.0ms

simplify483.0ms

prune1.1s

localize12.0ms

rewrite42.0ms

series524.0ms

simplify59.0ms

prune77.0ms

regimes155.0ms

bsearch107.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling