Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample37.0ms (1.2%)

Algorithm

1×

intervals

Results

19.0ms	137×	body	1024	valid
5.0ms	58×	body	512	valid
3.0ms	256×	pre	128	true
2.0ms	12×	body	2048	valid
1.0ms	30×	body	256	valid
0.0ms	19×	body	128	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify166.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	6
1	9	6

prune2.0ms (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: 58.9b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

5.5b	(-.f64 (exp.f64 x) 1)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1446`
4×	`*-un-lft-identity_binary64_1425`
3×	`add-log-exp_binary64_1461`
2×	`difference-of-squares_binary64_1394`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `add-cube-cbrt_binary64_1457` `distribute-lft-out--_binary64_1379` `sub-neg_binary64_1418` `difference-of-sqr-1_binary64_1395` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `flip3--_binary64_1429` `add-exp-log_binary64_1460`

Counts

1 → 15

Calls

1 calls:

5.0ms

(-.f64 (exp.f64 x) 1)

series17.0ms (0.6%)

Counts

1 → 3

Calls

1 calls:

17.0ms

(-.f64 (exp.f64 x) 1)

simplify98.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4892	196
1	4892	196

prune24.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	16	3	19

Merged error: 0.0b

Counts

19 → 3

Compiler

Compiled 182 to 118 computations (35.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0b	(+.f64 1/2 (*.f64 x 1/6))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.3b	(*.f64 x 1/6)

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1446` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460`
9×	`add-cube-cbrt_binary64_1457` `associate-l_binary64_1368` `*-un-lft-identity_binary64_1425`
7×	`associate-r_binary64_1367`
6×	`associate-*r/_binary64_1369` `add-log-exp_binary64_1461`
5×	`distribute-lft-in_binary64_1376` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `distribute-rgt-in_binary64_1377` `pow-prod-down_binary64_1493`
3×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `*-commutative_binary64_1358`
2×	`unswap-sqr_binary64_1393`
1×	`sum-log_binary64_1513` `+-commutative_binary64_1357`

Counts

4 → 75

Calls

4 calls:

8.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)
3.0ms	(+.f64 1/2 (*.f64 x 1/6))

series229.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
83.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
40.0ms	(+.f64 1/2 (*.f64 x 1/6))
21.0ms	(*.f64 x 1/6)

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5343	968

prune70.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

Compiler

Compiled 1332 to 914 computations (31.4% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (exp.f64 x) 1))
0.0b	(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1)))
5.5b	(-.f64 (exp.f64 x) 1)
5.5b	(-.f64 (exp.f64 x) 1)

rewrite45.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64_1446`
49×	`sqrt-prod_binary64_1440`
42×	`*-un-lft-identity_binary64_1425`
20×	`pow1_binary64_1483`
16×	`difference-of-squares_binary64_1394` `swap-sqr_binary64_1392`
14×	`sqrt-div_binary64_1441`
13×	`add-cube-cbrt_binary64_1457`
10×	`associate-l_binary64_1368` `associate-r_binary64_1367`
9×	`flip--_binary64_1400` `distribute-lft-out--_binary64_1379` `pow1/2_binary64_1502` `difference-of-sqr-1_binary64_1395` `sqrt-pow1_binary64_1442` `flip3--_binary64_1429`
8×	`add-log-exp_binary64_1461`
6×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
5×	`pow-prod-up_binary64_1492`
4×	`unswap-sqr_binary64_1393` `frac-times_binary64_1435`
3×	`pow-sqr_binary64_1398` `pow-prod-down_binary64_1493`
2×	`diff-log_binary64_1514` `sub-neg_binary64_1418` `associate-r/_binary64_1369` `associate-l/_binary64_1370`
1×	`prod-exp_binary64_1471` `pow-plus_binary64_1485` `cbrt-unprod_binary64_1455` `rem-square-sqrt_binary64_1437` `pow2_binary64_1503` `sqrt-unprod_binary64_1444` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 122

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1)))
5.0ms	(sqrt.f64 (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)
5.0ms	(-.f64 (exp.f64 x) 1)

series96.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt.f64 (-.f64 (exp.f64 x) 1))
19.0ms	(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1)))
16.0ms	(-.f64 (exp.f64 x) 1)
15.0ms	(-.f64 (exp.f64 x) 1)

simplify74.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4978	1635
1	4978	1635

prune106.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	134	3	137

Merged error: 0.0b

Counts

137 → 3

Compiler

Compiled 1859 to 1227 computations (34% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
0.0b	(.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))))
5.5b	(-.f64 (exp.f64 x) 1)
5.5b	(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite62.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-div_binary64_1441`
32×	`frac-times_binary64_1435`
25×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
24×	`add-sqr-sqrt_binary64_1446`
22×	`*-un-lft-identity_binary64_1425`
16×	`associate-*r/_binary64_1369`
15×	`associate-l_binary64_1368`
13×	`pow1_binary64_1483`
10×	`flip--_binary64_1400` `sqrt-prod_binary64_1440` `associate-*l/_binary64_1370` `flip3--_binary64_1429`
9×	`add-cube-cbrt_binary64_1457`
8×	`associate-r_binary64_1367` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
6×	`pow-prod-down_binary64_1493`
4×	`distribute-lft-out_binary64_1378` `sqrt-pow1_binary64_1442` `difference-of-squares_binary64_1394`
3×	`unswap-sqr_binary64_1393`
2×	`distribute-lft-out--_binary64_1379` `prod-exp_binary64_1471` `pow1/2_binary64_1502` `cbrt-unprod_binary64_1455` `difference-of-sqr-1_binary64_1395` `*-commutative_binary64_1358`
1×	`distribute-lft-in_binary64_1376` `diff-log_binary64_1514` `sub-neg_binary64_1418` `sqrt-unprod_binary64_1444` `distribute-rgt-in_binary64_1377` `sum-log_binary64_1513` `+-commutative_binary64_1357`

Counts

4 → 115

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))))
15.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
5.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 1)

series351.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))))
83.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
33.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
15.0ms	(-.f64 (exp.f64 x) 1)

simplify91.0ms (3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5456	2553

prune141.0ms (4.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	3	130

Merged error: 0.0b

Counts

130 → 3

Compiler

Compiled 2864 to 1715 computations (40.1% saved)

regimes28.0ms (0.9%)

Compiler: Compiled 147 to 118 computations (19.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

end0.0ms (0%)

sample1.2s (40.4%)

Algorithm

1×

intervals

Results

587.0ms	4067×	body	1024	valid
158.0ms	2031×	body	512	valid
105.0ms	8000×	pre	128	true
58.0ms	365×	body	2048	valid
46.0ms	957×	body	256	valid
15.0ms	580×	body	128	valid

Compiler

Compiled 66 to 52 computations (21.2% saved)

Details

analyze4.0ms (0.1%)

sample37.0ms (1.2%)

simplify166.0ms (5.6%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite6.0ms (0.2%)

series17.0ms (0.6%)

simplify98.0ms (3.3%)

prune24.0ms (0.8%)

localize9.0ms (0.3%)

rewrite27.0ms (0.9%)

series229.0ms (7.7%)

simplify79.0ms (2.6%)

prune70.0ms (2.3%)

localize5.0ms (0.2%)

rewrite45.0ms (1.5%)

series96.0ms (3.2%)

simplify74.0ms (2.5%)

prune106.0ms (3.5%)

localize10.0ms (0.3%)

rewrite62.0ms (2.1%)

series351.0ms (11.7%)

simplify91.0ms (3%)

prune141.0ms (4.7%)

regimes28.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (40.4%)

Profiling