Details

analyze3.0ms (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 (1.3%)

Algorithm

1×

intervals

Results

19.0ms	134×	body	1024	valid
5.0ms	61×	body	512	valid
3.0ms	256×	pre	128	true
2.0ms	9×	body	2048	valid
2.0ms	29×	body	256	valid
1.0ms	23×	body	128	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify175.0ms (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: 58.1b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

4.6b	(-.f64 (exp.f64 x) 1)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1477`
5×	`*-un-lft-identity_binary64_1455`
3×	`add-log-exp_binary64_1494` `cancel-sign-sub-inv_binary64_1421`
2×	`difference-of-squares_binary64_1424` `add-cube-cbrt_binary64_1490`
1×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459` `difference-of-sqr-1_binary64_1425` `add-exp-log_binary64_1493`

Counts

1 → 18

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)

simplify100.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4841	199
1	4841	199

prune59.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	2	22

Merged error: 0.1b

Counts

22 → 2

Compiler

Compiled 551 to 429 computations (22.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.4b	(*.f64 x 1/6)

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1477` `pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
9×	`associate-l_binary64_1396`
8×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
7×	`associate-r_binary64_1395`
6×	`associate-*r/_binary64_1397`
5×	`prod-exp_binary64_1504` `distribute-rgt-in_binary64_1405` `distribute-lft-in_binary64_1404` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
3×	`add-log-exp_binary64_1494` `*-commutative_binary64_1386`
2×	`flip-+_binary64_1429` `flip3-+_binary64_1458` `unswap-sqr_binary64_1423`

Counts

3 → 64

Calls

3 calls:

7.0ms	(.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)

series196.0ms (6.8%)

Counts

3 → 9

Calls

3 calls:

97.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
74.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
25.0ms	(*.f64 x 1/6)

simplify68.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4998	823
1	4998	823

prune58.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Merged error: 0.1b

Counts

75 → 2

Compiler

Compiled 1116 to 760 computations (31.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
4.6b	(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_1455`
15×	`add-sqr-sqrt_binary64_1477`
10×	`add-cube-cbrt_binary64_1490`
8×	`sqrt-pow1_binary64_1473` `pow1_binary64_1516`
7×	`sqrt-prod_binary64_1471` `flip-+_binary64_1429` `flip3-+_binary64_1458`
6×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `exp-prod_binary64_1507` `add-exp-log_binary64_1493`
5×	`associate-l_binary64_1396`
4×	`distribute-lft-out_binary64_1406` `associate-r_binary64_1395` `frac-times_binary64_1465`
2×	`associate-r/_binary64_1397` `rem-sqrt-square_binary64_1468` `pow1/2_binary64_1535` `associate-l/_binary64_1398`
1×	`prod-exp_binary64_1504` `distribute-rgt-in_binary64_1405` `*-commutative_binary64_1386` `distribute-lft-in_binary64_1404` `cbrt-unprod_binary64_1488` `sum-log_binary64_1546` `+-commutative_binary64_1385` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 75

Calls

4 calls:

12.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
5.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
2.0ms	(sqrt.f64 (exp.f64 x))
2.0ms	(sqrt.f64 (exp.f64 x))

series165.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
36.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
26.0ms	(sqrt.f64 (exp.f64 x))
22.0ms	(sqrt.f64 (exp.f64 x))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5168	990

prune103.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

Compiler

Compiled 1618 to 905 computations (44.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
0.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))))
0.4b	(*.f64 x 1/48)

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1477`
14×	`pow1_binary64_1516` `*-un-lft-identity_binary64_1455`
13×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
11×	`add-cube-cbrt_binary64_1490`
9×	`associate-r_binary64_1395` `associate-l_binary64_1396`
7×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
5×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
4×	`sqrt-pow1_binary64_1473` `associate-*r/_binary64_1397` `sqrt-prod_binary64_1471` `add-log-exp_binary64_1494` `frac-times_binary64_1465`
3×	`*-commutative_binary64_1386` `exp-prod_binary64_1507` `unswap-sqr_binary64_1423`
2×	`distribute-lft-out_binary64_1406` `distribute-rgt-in_binary64_1405` `distribute-lft-in_binary64_1404` `associate-*l/_binary64_1398`
1×	`rem-sqrt-square_binary64_1468` `pow1/2_binary64_1535`

Counts

4 → 87

Calls

4 calls:

12.0ms	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))))
8.0ms	(.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
4.0ms	(*.f64 x 1/48)
2.0ms	(sqrt.f64 (exp.f64 x))

series207.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
62.0ms	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))))
25.0ms	(*.f64 x 1/48)
23.0ms	(sqrt.f64 (exp.f64 x))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4953	1806
1	4953	1806

prune137.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	98	5	103

Merged error: 0.0b

Counts

103 → 5

Compiler

Compiled 2785 to 1788 computations (35.8% saved)

regimes34.0ms (1.2%)

Compiler: Compiled 278 to 201 computations (27.7% 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%)

sample1.3s (43.9%)

Algorithm

1×

intervals

Results

579.0ms	3966×	body	1024	valid
156.0ms	1986×	body	512	valid
104.0ms	8001×	pre	128	true
66.0ms	417×	body	2048	valid
53.0ms	1051×	body	256	valid
15.0ms	580×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 147 to 108 computations (26.5% saved)

Details

analyze3.0ms (0.1%)

sample37.0ms (1.3%)

simplify175.0ms (6%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite6.0ms (0.2%)

series17.0ms (0.6%)

simplify100.0ms (3.5%)

prune59.0ms (2%)

localize6.0ms (0.2%)

rewrite22.0ms (0.8%)

series196.0ms (6.8%)

simplify68.0ms (2.4%)

prune58.0ms (2%)

localize8.0ms (0.3%)

rewrite27.0ms (0.9%)

series165.0ms (5.7%)

simplify66.0ms (2.3%)

prune103.0ms (3.6%)

localize12.0ms (0.4%)

rewrite37.0ms (1.3%)

series207.0ms (7.2%)

simplify66.0ms (2.3%)

prune137.0ms (4.8%)

regimes34.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (43.9%)

Profiling