Details

analyze502.0ms (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample111.0ms (1.9%)

Algorithm

1×

intervals

Results

42.0ms	132×	body	2048	nan
26.0ms	256×	body	128	valid
17.0ms	68×	body	1024	nan
5.0ms	26×	body	512	nan
2.0ms	15×	body	256	nan
1.0ms	22×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify533.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (239.0ms)

Iter	Nodes	Cost
0	5150	14

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
28.6b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1425`
7×	`add-sqr-sqrt_binary64_1446`
6×	`sqrt-prod_binary64_1440`
5×	`add-cube-cbrt_binary64_1457` `pow1_binary64_1483` `add-log-exp_binary64_1461`
4×	`log-prod_binary64_1508` `add-exp-log_binary64_1460`
3×	`add-cbrt-cube_binary64_1458`
2×	`flip3-+_binary64_1428` `sqrt-div_binary64_1441` `distribute-lft-out_binary64_1378` `difference-of-squares_binary64_1394` `flip-+_binary64_1399` `log-div_binary64_1509`
1×	`flip--_binary64_1400` `pow1/2_binary64_1502` `difference-of-sqr-1_binary64_1395` `sqrt-pow1_binary64_1442` `sum-log_binary64_1513` `log-pow_binary64_1511` `+-commutative_binary64_1357` `rem-log-exp_binary64_1463` `rem-sqrt-square_binary64_1438` `flip3--_binary64_1429`

Counts

3 → 45

Calls

3 calls:

18.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
13.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
10.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series361.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

178.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
114.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
68.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5056	920

prune90.0ms (1.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	1	55

Merged error: 0b

Counts

55 → 1

Compiler

Compiled 818 to 541 computations (33.9% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite65.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1446`
19×	`sqrt-prod_binary64_1440`
17×	`*-un-lft-identity_binary64_1425`
14×	`sqrt-div_binary64_1441`
10×	`add-cube-cbrt_binary64_1457` `associate-r_binary64_1367` `pow1_binary64_1483`
7×	`associate-l_binary64_1368` `add-exp-log_binary64_1460`
6×	`flip3-+_binary64_1428` `add-cbrt-cube_binary64_1458` `flip-+_binary64_1399` `add-log-exp_binary64_1461`
4×	`unswap-sqr_binary64_1393` `frac-times_binary64_1435`
3×	`flip--_binary64_1400` `pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `log-prod_binary64_1508` `flip3--_binary64_1429` `pow-prod-down_binary64_1493`
2×	`associate-r/_binary64_1369` `distribute-lft-out_binary64_1378` `difference-of-squares_binary64_1394` `log-div_binary64_1509` `associate-l/_binary64_1370`
1×	`distribute-lft-out--_binary64_1379` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `difference-of-sqr-1_binary64_1395` `sqrt-unprod_binary64_1444` `sum-log_binary64_1513` `log-pow_binary64_1511` `+-commutative_binary64_1357` `rem-log-exp_binary64_1463` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 84

Calls

4 calls:

30.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
6.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series439.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
125.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
93.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
49.0ms	(sqrt.f64 (+.f64 x 1))

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5075	1933

prune188.0ms (3.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	1	97

Merged error: 0b

Counts

97 → 1

Compiler

Compiled 1868 to 1413 computations (24.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample3.2s (55.6%)

Algorithm

1×

intervals

Results

1.3s	4034×	body	2048	nan
650.0ms	8000×	body	128	valid
474.0ms	1929×	body	1024	nan
190.0ms	1045×	body	512	nan
63.0ms	497×	body	256	nan
32.0ms	501×	body	128	nan
3.0ms	8×	body	4096	nan

Compiler

Compiled 34 to 29 computations (14.7% saved)

Details

analyze502.0ms (8.7%)

sample111.0ms (1.9%)

simplify533.0ms (9.2%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite47.0ms (0.8%)

series361.0ms (6.3%)

simplify78.0ms (1.4%)

prune90.0ms (1.6%)

localize19.0ms (0.3%)

rewrite65.0ms (1.1%)

series439.0ms (7.6%)

simplify103.0ms (1.8%)

prune188.0ms (3.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.2s (55.6%)

Profiling