Details

analyze456.0ms (6.6%)

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
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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	166×	body	128	valid
7.0ms	30×	body	2048	valid
5.0ms	24×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	16×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	10×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify232.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (0.1%)

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: 36.3b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1477`
21×	`*-un-lft-identity_binary64_1455`
10×	`add-log-exp_binary64_1494`
9×	`sqrt-prod_binary64_1471` `add-cbrt-cube_binary64_1491` `add-cube-cbrt_binary64_1490` `add-exp-log_binary64_1493`
7×	`cancel-sign-sub-inv_binary64_1421` `associate-/l*_binary64_1400` `times-frac_binary64_1461`
6×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
5×	`pow1_binary64_1516`
4×	`flip--_binary64_1430` `flip3--_binary64_1459`
3×	`distribute-rgt-neg-in_binary64_1413` `diff-log_binary64_1547`
2×	`sqrt-div_binary64_1472` `associate-/l/_binary64_1402` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `sub-neg_binary64_1448`
1×	`prod-exp_binary64_1504` `sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `neg-log_binary64_1548` `neg-sub0_binary64_1450` `clear-num_binary64_1454` `associate-/r*_binary64_1399` `associate--l-_binary64_1393` `frac-2neg_binary64_1466` `cbrt-unprod_binary64_1488` `pow1/2_binary64_1535` `div-inv_binary64_1452` `div-sub_binary64_1460`

Counts

4 → 82

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
14.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series464.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
126.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5923	2287

prune491.0ms (7.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 6.5b

Counts

95 → 10

Compiler

Compiled 9728 to 6404 computations (34.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
10.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite58.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
30×	`times-frac_binary64_1461`
28×	`add-sqr-sqrt_binary64_1477`
19×	`*-un-lft-identity_binary64_1455`
17×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
13×	`prod-exp_binary64_1504` `associate-/l*_binary64_1400` `cbrt-unprod_binary64_1488`
11×	`add-cube-cbrt_binary64_1490`
8×	`difference-of-squares_binary64_1424`
7×	`sqrt-prod_binary64_1471` `associate-/r*_binary64_1399`
6×	`associate-/r/_binary64_1401` `add-log-exp_binary64_1494`
5×	`pow1_binary64_1516` `flip--_binary64_1430` `flip3--_binary64_1459`
4×	`distribute-lft-out--_binary64_1407` `div-inv_binary64_1452`
2×	`sqrt-div_binary64_1472` `clear-num_binary64_1454` `frac-2neg_binary64_1466`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `associate-/l/_binary64_1402` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `pow1/2_binary64_1535`

Counts

4 → 110

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.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))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series904.0ms (13.2%)

Counts

4 → 12

Calls

4 calls:

395.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
324.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	3511
1	4973	3511

prune290.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	123	9	132

Merged error: 6.5b

Counts

132 → 9

Compiler

Compiled 5978 to 3680 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1477`
27×	`*-un-lft-identity_binary64_1455`
18×	`times-frac_binary64_1461`
17×	`add-cube-cbrt_binary64_1490`
10×	`difference-of-squares_binary64_1424`
8×	`sqrt-prod_binary64_1471` `add-log-exp_binary64_1494`
6×	`associate-/r*_binary64_1399` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516`
4×	`flip--_binary64_1430` `cancel-sign-sub-inv_binary64_1421` `flip3--_binary64_1459`
3×	`associate-/l*_binary64_1400`
2×	`associate-/r/_binary64_1401` `sqrt-div_binary64_1472` `diff-log_binary64_1547` `sub-neg_binary64_1448`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `pow1/2_binary64_1535` `div-inv_binary64_1452`

Counts

4 → 85

Calls

4 calls:

12.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series741.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

434.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4886	2453
1	4886	2453

prune201.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Merged error: 6.5b

Counts

106 → 9

Compiler

Compiled 3471 to 2105 computations (39.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_1461`
122×	`add-sqr-sqrt_binary64_1477`
95×	`*-un-lft-identity_binary64_1455`
69×	`add-cube-cbrt_binary64_1490`
26×	`difference-of-squares_binary64_1424`
22×	`associate-/r*_binary64_1399`
16×	`sqrt-prod_binary64_1471`
15×	`add-exp-log_binary64_1493`
13×	`distribute-lft-out--_binary64_1407`
9×	`add-cbrt-cube_binary64_1491`
8×	`add-log-exp_binary64_1494`
7×	`div-exp_binary64_1506`
6×	`pow1_binary64_1516`
5×	`div-inv_binary64_1452`
4×	`cancel-sign-sub-inv_binary64_1421`
3×	`flip--_binary64_1430` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400` `flip3--_binary64_1459`
2×	`sqrt-div_binary64_1472` `1-exp_binary64_1499` `diff-log_binary64_1547` `sub-neg_binary64_1448` `rec-exp_binary64_1505`
1×	`sqrt-pow1_binary64_1473` `associate-/r/_binary64_1401` `inv-pow_binary64_1540` `rem-sqrt-square_binary64_1468` `clear-num_binary64_1454` `pow-flip_binary64_1529` `frac-2neg_binary64_1466` `pow1/2_binary64_1535`

Counts

4 → 156

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
12.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series537.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4979	5518
1	4979	5518

prune239.0ms (3.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	168	9	177

Merged error: 6.5b

Counts

177 → 9

Compiler

Compiled 5232 to 2970 computations (43.2% saved)

regimes102.0ms (1.5%)

Compiler: Compiled 522 to 408 computations (21.8% saved)

bsearch96.0ms (1.4%)

Steps

Iters	Range		Point
6	3.453198629799523e+50	2.437223188812816e+51	2.404688834790521e+51
8	6.935416206472007e-143	6.859135451625387e-140	2.2068850198815852e-141
8	-6.563919617033063e+159	-1.3263602242760849e+157	-1.338340640721482e+157

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	124
1	149	124

end0.0ms (0%)

sample1.4s (20.7%)

Algorithm

1×

intervals

Results

270.0ms	1092×	body	2048	valid
270.0ms	5243×	body	128	valid
141.0ms	719×	body	1024	valid
127.0ms	415×	body	4096	valid
55.0ms	369×	body	512	valid
35.0ms	684×	body	128	nan
22.0ms	392×	body	128	invalid
18.0ms	162×	body	256	valid

Compiler

Compiled 313 to 223 computations (28.8% saved)

Details

analyze456.0ms (6.6%)

sample37.0ms (0.5%)

simplify232.0ms (3.4%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite48.0ms (0.7%)

series464.0ms (6.8%)

simplify65.0ms (0.9%)

prune491.0ms (7.2%)

localize15.0ms (0.2%)

rewrite58.0ms (0.9%)

series904.0ms (13.2%)

simplify92.0ms (1.3%)

prune290.0ms (4.2%)

localize12.0ms (0.2%)

rewrite41.0ms (0.6%)

series741.0ms (10.8%)

simplify120.0ms (1.8%)

prune201.0ms (2.9%)

localize13.0ms (0.2%)

rewrite59.0ms (0.9%)

series537.0ms (7.8%)

simplify108.0ms (1.6%)

prune239.0ms (3.5%)

regimes102.0ms (1.5%)

bsearch96.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.7%)

Profiling