Details

analyze40.0ms (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)

sample44.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	48×	body	2048	valid
12.0ms	53×	body	1024	valid
4.0ms	39×	body	512	valid
3.0ms	97×	body	128	valid
1.0ms	19×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify221.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

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: 29.4b

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))
3.9b	(-.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))

series73.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
23.0ms	(exp.f64 (*.f64 a x))

simplify49.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4985	374
1	4985	374

prune36.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 3.7b

Counts

32 → 6

Compiler

Compiled 422 to 217 computations (48.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.7b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.6b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.1b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

11.0ms	(.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 x (.f64 1/6 (pow.f64 a 3)))
6.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series539.0ms (13%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
177.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
87.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
84.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4975	1832
1	4975	1832

prune106.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0.4b

Counts

92 → 6

Compiler

Compiled 2291 to 1358 computations (40.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.6b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
1.7b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
6.6b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite42.0ms (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:

13.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
6.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
4.0ms	(*.f64 x 1/6)

series407.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
146.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
68.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
25.0ms	(*.f64 x 1/6)

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5618	1933

prune106.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Merged error: 0.4b

Counts

108 → 6

Compiler

Compiled 2442 to 1415 computations (42.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
0.3b	(*.f64 x 1/6)
0.6b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
9.5b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1446`
12×	`pow1_binary64_1483` `add-exp-log_binary64_1460`
11×	`add-cube-cbrt_binary64_1457` `add-cbrt-cube_binary64_1458` `*-un-lft-identity_binary64_1425`
9×	`log-prod_binary64_1508`
6×	`unpow-prod-down_binary64_1501` `associate-r_binary64_1367`
4×	`pow-pow_binary64_1494` `unpow-prod-up_binary64_1500` `associate-l_binary64_1368` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `add-log-exp_binary64_1461` `pow-prod-down_binary64_1493`
3×	`distribute-lft-in_binary64_1376` `exp-prod_binary64_1474` `distribute-rgt-in_binary64_1377` `rem-log-exp_binary64_1463`
2×	`unswap-sqr_binary64_1393` `pow-to-exp_binary64_1491` `associate-r/_binary64_1369` `pow-exp_binary64_1490` `sqr-pow_binary64_1397` `-commutative_binary64_1358`
1×	`pow-unpow_binary64_1499` `flip3-+_binary64_1428` `flip-+_binary64_1399` `log-pow_binary64_1511`

Counts

4 → 81

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
5.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
4.0ms	(*.f64 x 1/6)
4.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))

series366.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
110.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
64.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
20.0ms	(*.f64 x 1/6)

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5003	1747

prune102.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Merged error: 0.4b

Counts

99 → 6

Compiler

Compiled 2247 to 1276 computations (43.2% saved)

regimes265.0ms (6.4%)

Compiler: Compiled 1726 to 1275 computations (26.1% saved)

bsearch1.0ms (0%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	57
1	37	57

end0.0ms (0%)

sample1.5s (35.5%)

Algorithm

1×

intervals

Results

483.0ms	1483×	body	2048	valid
275.0ms	1701×	body	1024	valid
101.0ms	1093×	body	512	valid
83.0ms	3111×	body	128	valid
35.0ms	612×	body	256	valid
5.0ms	145×	body	128	invalid

Compiler

Compiled 349 to 250 computations (28.4% saved)

Details

analyze40.0ms (1%)

sample44.0ms (1%)

simplify221.0ms (5.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite8.0ms (0.2%)

series73.0ms (1.8%)

simplify49.0ms (1.2%)

prune36.0ms (0.9%)

localize15.0ms (0.4%)

rewrite39.0ms (0.9%)

series539.0ms (13%)

simplify41.0ms (1%)

prune106.0ms (2.6%)

localize10.0ms (0.3%)

rewrite42.0ms (1%)

series407.0ms (9.8%)

simplify43.0ms (1%)

prune106.0ms (2.5%)

localize13.0ms (0.3%)

rewrite29.0ms (0.7%)

series366.0ms (8.8%)

simplify76.0ms (1.8%)

prune102.0ms (2.4%)

regimes265.0ms (6.4%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.5s (35.5%)

Profiling