Details

analyze41.0ms (1.1%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample39.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	53×	body	2048	valid
7.0ms	48×	body	1024	valid
3.0ms	32×	body	512	valid
3.0ms	98×	body	128	valid
1.0ms	25×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify226.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4815	9
1	4815	9

prune2.0ms (0%)

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: 27.5b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.5b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1446` `add-log-exp_binary64_1461`
5×	`*-un-lft-identity_binary64_1425`
2×	`add-cube-cbrt_binary64_1457` `add-cbrt-cube_binary64_1458` `difference-of-squares_binary64_1394` `pow1_binary64_1483` `add-exp-log_binary64_1460`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `distribute-lft-out--_binary64_1379` `exp-to-pow_binary64_1484` `sub-neg_binary64_1418` `difference-of-sqr-1_binary64_1395` `exp-prod_binary64_1474` `rem-exp-log_binary64_1462` `flip3--_binary64_1429`

Counts

2 → 25

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series70.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

46.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
24.0ms	(exp.f64 (*.f64 a x))

simplify48.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4985	374
1	4985	374

prune33.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	5	32

Merged error: 4.9b

Counts

32 → 5

Compiler

Compiled 400 to 203 computations (49.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 1/6 (pow.f64 a 3))
5.9b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.3b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.9b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_1460`
20×	`add-sqr-sqrt_binary64_1446`
16×	`associate-r_binary64_1367`
13×	`add-cbrt-cube_binary64_1458`
11×	`add-cube-cbrt_binary64_1457` `prod-exp_binary64_1471` `*-un-lft-identity_binary64_1425`
9×	`associate-l_binary64_1368`
8×	`pow1_binary64_1483`
6×	`add-log-exp_binary64_1461`
5×	`unswap-sqr_binary64_1393` `cbrt-unprod_binary64_1455`
4×	`unpow-prod-down_binary64_1501` `cube-prod_binary64_1450`
3×	`*-commutative_binary64_1358`
2×	`flip3-+_binary64_1428` `pow-to-exp_binary64_1491` `associate-*r/_binary64_1369` `pow-exp_binary64_1490` `flip-+_binary64_1399` `sqr-pow_binary64_1397` `pow-prod-down_binary64_1493`
1×	`distribute-lft-in_binary64_1376` `unpow3_binary64_1488` `distribute-rgt-in_binary64_1377` `sum-log_binary64_1513` `cube-mult_binary64_1452` `+-commutative_binary64_1357`

Counts

4 → 83

Calls

4 calls:

10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
7.0ms	(*.f64 1/6 (pow.f64 a 3))
6.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))

series393.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
83.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
77.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
49.0ms	(*.f64 1/6 (pow.f64 a 3))

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4929	1404
1	4929	1404

prune111.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	95	5	100

Merged error: 2.5b

Counts

100 → 5

Compiler

Compiled 2314 to 1402 computations (39.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))))
0.4b	(*.f64 x 1/6)
0.7b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
6.3b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460`
15×	`add-sqr-sqrt_binary64_1446`
11×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `pow-prod-down_binary64_1493`
10×	`add-cube-cbrt_binary64_1457` `associate-l_binary64_1368` `associate-r_binary64_1367` `*-un-lft-identity_binary64_1425`
8×	`associate-*r/_binary64_1369`
6×	`distribute-lft-in_binary64_1376` `distribute-rgt-in_binary64_1377`
4×	`add-log-exp_binary64_1461` `*-commutative_binary64_1358`
3×	`unswap-sqr_binary64_1393` `flip3-+_binary64_1428` `flip-+_binary64_1399`

Counts

4 → 90

Calls

4 calls:

11.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))))
4.0ms	(*.f64 x 1/6)

series406.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))))
154.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
72.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
25.0ms	(*.f64 x 1/6)

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5607	1933

prune106.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 2.5b

Counts

107 → 6

Compiler

Compiled 2412 to 1393 computations (42.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.7b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
6.3b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460`
9×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `add-sqr-sqrt_binary64_1446` `pow-prod-down_binary64_1493`
8×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
6×	`associate-*r/_binary64_1369` `cbrt-prod_binary64_1453`
5×	`distribute-lft-in_binary64_1376` `distribute-rgt-in_binary64_1377`
4×	`associate-l_binary64_1368` `associate-r_binary64_1367` `add-log-exp_binary64_1461`
2×	`flip3-+_binary64_1428` `pow1/3_binary64_1504` `flip-+_binary64_1399` `*-commutative_binary64_1358`
1×	`unswap-sqr_binary64_1393`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series512.0ms (13.2%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt.f64 x)
148.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
138.0ms	(cbrt.f64 x)
67.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4979	1264
1	4979	1264

prune90.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Merged error: 2.5b

Counts

90 → 6

Compiler

Compiled 2397 to 1130 computations (52.9% saved)

regimes139.0ms (3.6%)

Compiler: Compiled 594 to 437 computations (26.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	47
1	41	47

end0.0ms (0%)

sample1.3s (33.8%)

Algorithm

1×

intervals

Results

473.0ms	1438×	body	2048	valid
278.0ms	1708×	body	1024	valid
104.0ms	1132×	body	512	valid
88.0ms	3083×	body	128	valid
40.0ms	639×	body	256	valid
4.0ms	118×	body	128	invalid

Compiler

Compiled 162 to 115 computations (29% saved)

Details

analyze41.0ms (1.1%)

sample39.0ms (1%)

simplify226.0ms (5.8%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite8.0ms (0.2%)

series70.0ms (1.8%)

simplify48.0ms (1.2%)

prune33.0ms (0.9%)

localize12.0ms (0.3%)

rewrite42.0ms (1.1%)

series393.0ms (10.1%)

simplify86.0ms (2.2%)

prune111.0ms (2.8%)

localize13.0ms (0.3%)

rewrite37.0ms (1%)

series406.0ms (10.4%)

simplify44.0ms (1.1%)

prune106.0ms (2.7%)

localize15.0ms (0.4%)

rewrite29.0ms (0.7%)

series512.0ms (13.2%)

simplify66.0ms (1.7%)

prune90.0ms (2.3%)

regimes139.0ms (3.6%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (33.8%)

Profiling