Details

analyze473.0ms (5.6%)

Algorithm

1×

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample42.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	30×	body	2048	valid
10.0ms	179×	body	128	valid
6.0ms	29×	body	1024	valid
2.0ms	6×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify422.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (262.0ms)

Iter	Nodes	Cost
0	1707	24
1	1707	24

prune4.0ms (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: 30.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1446`
13×	`*-un-lft-identity_binary64_1425`
9×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`add-log-exp_binary64_1461`
7×	`add-cube-cbrt_binary64_1457`
6×	`times-frac_binary64_1431` `sqrt-prod_binary64_1440` `difference-of-squares_binary64_1394` `associate-/l*_binary64_1372`
5×	`pow1_binary64_1483`
4×	`flip--_binary64_1400` `flip3--_binary64_1429`
3×	`distribute-lft-out--_binary64_1379`
2×	`diff-log_binary64_1514` `sub-neg_binary64_1418` `sqrt-div_binary64_1441` `div-exp_binary64_1473` `associate-/l/_binary64_1374` `cbrt-undiv_binary64_1456`
1×	`frac-2neg_binary64_1436` `associate-/r*_binary64_1371` `prod-exp_binary64_1471` `pow1/2_binary64_1502` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `div-sub_binary64_1430` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `rem-sqrt-square_binary64_1438`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series521.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6789	1967

prune132.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 5.3b

Counts

83 → 12

Compiler

Compiled 2207 to 1346 computations (39% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
2.3b	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
10.2b	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
22×	`times-frac_binary64_1431`
21×	`*-un-lft-identity_binary64_1425`
17×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
13×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
12×	`add-sqr-sqrt_binary64_1446`
11×	`add-cube-cbrt_binary64_1457` `associate-/l*_binary64_1372`
6×	`associate-/r/_binary64_1373` `add-log-exp_binary64_1461`
5×	`associate-/r*_binary64_1371` `distribute-lft-out_binary64_1378` `pow1_binary64_1483`
4×	`flip3-+_binary64_1428` `div-inv_binary64_1422` `flip-+_binary64_1399`
3×	`sqrt-prod_binary64_1440`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `sqrt-div_binary64_1441`
1×	`flip--_binary64_1400` `pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `sum-log_binary64_1513` `+-commutative_binary64_1357` `associate-/l/_binary64_1374` `rem-sqrt-square_binary64_1438` `flip3--_binary64_1429`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series899.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
283.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
115.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5567	3147

prune160.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Merged error: 5.2b

Counts

126 → 13

Compiler

Compiled 3452 to 2129 computations (38.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1425`
9×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`add-sqr-sqrt_binary64_1446` `add-log-exp_binary64_1461`
7×	`add-cube-cbrt_binary64_1457`
5×	`pow1_binary64_1483`
4×	`times-frac_binary64_1431` `associate-/r*_binary64_1371`
3×	`distribute-lft-out_binary64_1378` `sqrt-prod_binary64_1440`
2×	`flip--_binary64_1400` `flip3-+_binary64_1428` `sqrt-div_binary64_1441` `associate-/r/_binary64_1373` `flip-+_binary64_1399` `div-exp_binary64_1473` `flip3--_binary64_1429` `cbrt-undiv_binary64_1456`
1×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `prod-exp_binary64_1471` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `sum-log_binary64_1513` `associate-/l*_binary64_1372` `+-commutative_binary64_1357` `rem-sqrt-square_binary64_1438`

Counts

4 → 63

Calls

4 calls:

10.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series654.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4886	1665
1	4886	1665

prune110.0ms (1.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	73	15	88

Merged error: 5.2b

Counts

88 → 15

Compiler

Compiled 2326 to 1557 computations (33.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
22.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1446`
17×	`*-un-lft-identity_binary64_1425`
13×	`add-cube-cbrt_binary64_1457` `associate-r_binary64_1367`
10×	`times-frac_binary64_1431`
9×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`add-log-exp_binary64_1461`
7×	`pow1_binary64_1483`
4×	`associate-l_binary64_1368`
3×	`flip3-+_binary64_1428` `sqrt-prod_binary64_1440` `flip-+_binary64_1399`
2×	`flip--_binary64_1400` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `sqrt-div_binary64_1441` `distribute-lft-out_binary64_1378` `associate-*l/_binary64_1370` `flip3--_binary64_1429` `frac-times_binary64_1435`
1×	`diff-log_binary64_1514` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `associate-r/_binary64_1369` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `+-commutative_binary64_1357` `rem-sqrt-square_binary64_1438` `cbrt-undiv_binary64_1456` `-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 75

Calls

4 calls:

14.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series438.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c))
120.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5150	2035

prune102.0ms (1.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	87	15	102

Merged error: 5.2b

Counts

102 → 15

Compiler

Compiled 2156 to 1332 computations (38.2% saved)

regimes1.3s (15.9%)

Compiler: Compiled 7757 to 6063 computations (21.8% saved)

bsearch110.0ms (1.3%)

Steps

Iters	Range	Point
7	1.3831530327156415e+87	1.50810462671978e+89	1.474316731636549e+89
8	-3.7448139070813874e-255	-1.8350954815756547e-259	-3.4742121233166865e-259
10	-1.5872384102599588e+153	-4.592229352985525e+142	-8.575640252968764e+151

Iters

Range

Point

1.3831530327156415e+87

1.50810462671978e+89

1.474316731636549e+89

-3.7448139070813874e-255

-1.8350954815756547e-259

-3.4742121233166865e-259

-1.5872384102599588e+153

-4.592229352985525e+142

-8.575640252968764e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	97
1	149	97

end0.0ms (0%)

sample2.5s (29.4%)

Algorithm

1×

intervals

Results

307.0ms	1165×	body	2048	valid
301.0ms	5167×	body	128	valid
151.0ms	715×	body	1024	valid
140.0ms	409×	body	4096	valid
62.0ms	380×	body	512	valid
36.0ms	678×	body	128	nan
22.0ms	398×	body	128	invalid
21.0ms	164×	body	256	valid

Compiler

Compiled 1480 to 1148 computations (22.4% saved)

Details

analyze473.0ms (5.6%)

sample42.0ms (0.5%)

simplify422.0ms (5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite38.0ms (0.5%)

series521.0ms (6.2%)

simplify79.0ms (0.9%)

prune132.0ms (1.6%)

localize14.0ms (0.2%)

rewrite55.0ms (0.7%)

series899.0ms (10.7%)

simplify58.0ms (0.7%)

prune160.0ms (1.9%)

localize14.0ms (0.2%)

rewrite34.0ms (0.4%)

series654.0ms (7.8%)

simplify99.0ms (1.2%)

prune110.0ms (1.3%)

localize13.0ms (0.2%)

rewrite37.0ms (0.4%)

series438.0ms (5.2%)

simplify72.0ms (0.9%)

prune102.0ms (1.2%)

regimes1.3s (15.9%)

bsearch110.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.5s (29.4%)

Profiling