Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	189×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	34×	body	1024	valid
2.0ms	23×	body	512	valid
1.0ms	8×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify309.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	5139	19

prune2.0ms (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: 16.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1455`
26×	`add-sqr-sqrt_binary64_1477`
25×	`times-frac_binary64_1461`
19×	`distribute-lft-out_binary64_1406`
14×	`add-cube-cbrt_binary64_1490`
6×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
5×	`associate-/r_binary64_1399` `associate-/l_binary64_1400`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `pow1_binary64_1516` `associate-/l/_binary64_1402` `flip3-+_binary64_1458` `div-sub_binary64_1460`
1×	`associate-+l-_binary64_1390` `div-exp_binary64_1506` `clear-num_binary64_1454` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385` `flip3--_binary64_1459`

Counts

2 → 65

Calls

2 calls:

21.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series154.0ms (3%)

Counts

2 → 6

Calls

2 calls:

90.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
64.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5220	1488

prune231.0ms (4.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 16.1b

Counts

72 → 10

Compiler

Compiled 4709 to 3044 computations (35.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite86.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`*-un-lft-identity_binary64_1455`
68×	`add-sqr-sqrt_binary64_1477`
58×	`times-frac_binary64_1461`
37×	`add-cube-cbrt_binary64_1490`
24×	`distribute-lft-out_binary64_1406`
13×	`distribute-lft-out--_binary64_1407` `associate-/r_binary64_1399` `associate-/l_binary64_1400`
12×	`difference-of-squares_binary64_1424`
10×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
6×	`add-log-exp_binary64_1494`
4×	`associate-/r/_binary64_1401` `pow1_binary64_1516` `associate-/l/_binary64_1402`
3×	`div-exp_binary64_1506` `clear-num_binary64_1454` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `cancel-sign-sub-inv_binary64_1421` `div-inv_binary64_1452` `flip3--_binary64_1459`
2×	`flip-+_binary64_1429` `frac-sub_binary64_1464` `flip3-+_binary64_1458` `difference-of-sqr-1_binary64_1425`
1×	`diff-log_binary64_1547` `sub-neg_binary64_1448` `div-sub_binary64_1460`

Counts

4 → 143

Calls

4 calls:

38.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series328.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
95.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
66.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
54.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5352	3804

prune526.0ms (10.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	148	7	155
Fresh	9	0	9
Picked	0	1	1
Done	0	0	0
Total	157	8	165

Merged error: 3.5b

Counts

165 → 8

Compiler

Compiled 11234 to 7395 computations (34.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
8.0b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
8.0b	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))

rewrite59.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64_1455`
63×	`cbrt-prod_binary64_1486`
48×	`times-frac_binary64_1461`
43×	`add-sqr-sqrt_binary64_1477`
32×	`add-cube-cbrt_binary64_1490`
27×	`distribute-lft-out_binary64_1406`
6×	`associate-/r/_binary64_1401` `add-log-exp_binary64_1494`
4×	`pow1_binary64_1516` `difference-of-squares_binary64_1424` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`pow1/3_binary64_1537` `flip-+_binary64_1429` `cbrt-div_binary64_1487` `cancel-sign-sub-inv_binary64_1421` `flip3-+_binary64_1458` `div-inv_binary64_1452`
2×	`difference-of-sqr-1_binary64_1425`
1×	`distribute-lft-out--_binary64_1407` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459`

Counts

4 → 111

Calls

4 calls:

16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
10.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))

series552.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
152.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
152.0ms	(cbrt.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)))
92.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4917	2658
1	4917	2658

prune293.0ms (5.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	123	8	131

Merged error: 3.5b

Counts

131 → 8

Compiler

Compiled 6578 to 4025 computations (38.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
10.2b	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))

rewrite119.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64_1455`
79×	`add-sqr-sqrt_binary64_1477`
66×	`times-frac_binary64_1461`
50×	`log-prod_binary64_1541`
38×	`add-cube-cbrt_binary64_1490`
25×	`exp-sum_binary64_1501`
19×	`distribute-lft-out--_binary64_1407`
16×	`difference-of-squares_binary64_1424`
12×	`distribute-lft-out_binary64_1406`
9×	`add-exp-log_binary64_1493`
6×	`pow1_binary64_1516` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
5×	`associate-/r*_binary64_1399`
4×	`exp-prod_binary64_1507`
3×	`cancel-sign-sub-inv_binary64_1421` `associate-/l*_binary64_1400` `div-inv_binary64_1452`
2×	`associate-/r/_binary64_1401` `log-div_binary64_1542` `div-exp_binary64_1506` `rem-log-exp_binary64_1496` `difference-of-sqr-1_binary64_1425` `log-pow_binary64_1544`
1×	`flip-+_binary64_1429` `clear-num_binary64_1454` `exp-diff_binary64_1503` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `rem-exp-log_binary64_1495` `flip3--_binary64_1459`

Counts

4 → 132

Calls

4 calls:

43.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
35.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series566.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
172.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
114.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
56.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify126.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4926	4516
1	4926	4516

prune339.0ms (6.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	138	6	144
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	143	9	152

Merged error: 3.5b

Counts

152 → 9

Compiler

Compiled 7087 to 4755 computations (32.9% saved)

regimes77.0ms (1.5%)

Compiler: Compiled 714 to 522 computations (26.9% saved)

bsearch21.0ms (0.4%)

Steps

Iters	Range		Point
9	243337813346637.84	7.858114887426349e+21	246764853843484.7

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	219	71
1	219	71

end0.0ms (0%)

sample1.0s (20%)

Algorithm

1×

intervals

Results

206.0ms	6032×	body	128	valid
144.0ms	8000×	pre	128	true
125.0ms	1014×	body	1024	valid
52.0ms	560×	body	512	valid
19.0ms	106×	body	2048	valid
18.0ms	288×	body	256	valid

Compiler

Compiled 423 to 309 computations (27% saved)

Details

analyze3.0ms (0.1%)

sample30.0ms (0.6%)

simplify309.0ms (6%)

prune2.0ms (0%)

localize12.0ms (0.2%)

rewrite40.0ms (0.8%)

series154.0ms (3%)

simplify61.0ms (1.2%)

prune231.0ms (4.4%)

localize14.0ms (0.3%)

rewrite86.0ms (1.7%)

series328.0ms (6.3%)

simplify77.0ms (1.5%)

prune526.0ms (10.1%)

localize16.0ms (0.3%)

rewrite59.0ms (1.1%)

series552.0ms (10.6%)

simplify88.0ms (1.7%)

prune293.0ms (5.6%)

localize15.0ms (0.3%)

rewrite119.0ms (2.3%)

series566.0ms (10.9%)

simplify126.0ms (2.4%)

prune339.0ms (6.5%)

regimes77.0ms (1.5%)

bsearch21.0ms (0.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.0s (20%)

Profiling