Details

analyze66.0ms (1.9%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	235×	body	128	valid
2.0ms	5×	body	1024	valid
2.0ms	12×	body	256	valid
1.0ms	4×	body	512	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify169.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	96	14
1	96	14

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: 0.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1425`
8×	`log-prod_binary64_1508`
6×	`add-log-exp_binary64_1461`
5×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446`
4×	`associate--l+_binary64_1364` `log-div_binary64_1509` `pow1_binary64_1483` `add-exp-log_binary64_1460`
3×	`flip3-+_binary64_1428` `distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `flip-+_binary64_1399`
2×	`associate--l-_binary64_1365`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `sub-neg_binary64_1418` `sum-log_binary64_1513` `log-pow_binary64_1511` `+-commutative_binary64_1357` `rem-log-exp_binary64_1463` `flip3--_binary64_1429`

Counts

3 → 44

Calls

3 calls:

7.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series164.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

79.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
75.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
11.0ms	(+.f64 1 (exp.f64 x))

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5012	761

prune54.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	4	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.5b

Counts

54 → 4

Compiler

Compiled 826 to 476 computations (42.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))
0.7b	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
0.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1425`
14×	`cbrt-prod_binary64_1453`
11×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446`
10×	`pow1_binary64_1483`
8×	`unpow-prod-down_binary64_1501` `cube-prod_binary64_1450`
6×	`add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
5×	`add-cbrt-cube_binary64_1458` `log-pow_binary64_1511`
4×	`log-prod_binary64_1508`
3×	`pow-unpow_binary64_1499`
2×	`flip3-+_binary64_1428` `distribute-lft-out_binary64_1378` `unpow3_binary64_1488` `cube-mult_binary64_1452` `flip-+_binary64_1399` `log-div_binary64_1509` `sqr-pow_binary64_1397`
1×	`pow-pow_binary64_1494` `pow-to-exp_binary64_1491` `pow-exp_binary64_1490` `rem-cube-cbrt_binary64_1447` `pow1/3_binary64_1504` `sum-log_binary64_1513` `+-commutative_binary64_1357` `rem-log-exp_binary64_1463` `rem-cbrt-cube_binary64_1448`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+.f64 1 (exp.f64 x))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
3.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))

series299.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
84.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
78.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
9.0ms	(+.f64 1 (exp.f64 x))

simplify87.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4882	1105
1	4882	1105

prune82.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Merged error: 0.4b

Counts

91 → 5

Compiler

Compiled 1443 to 929 computations (35.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.5b	(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
0.7b	(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite49.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64_1483`
34×	`sqrt-prod_binary64_1440`
32×	`*-un-lft-identity_binary64_1425`
28×	`sqrt-div_binary64_1441` `add-sqr-sqrt_binary64_1446`
18×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442`
14×	`add-cube-cbrt_binary64_1457` `flip3-+_binary64_1428` `flip-+_binary64_1399` `log-pow_binary64_1511`
11×	`swap-sqr_binary64_1392`
10×	`pow-prod-up_binary64_1492`
9×	`add-exp-log_binary64_1460`
8×	`distribute-lft-out_binary64_1378` `log-div_binary64_1509` `frac-times_binary64_1435`
7×	`associate-l_binary64_1368` `associate-r_binary64_1367`
6×	`add-cbrt-cube_binary64_1458` `pow-sqr_binary64_1398` `pow-prod-down_binary64_1493`
4×	`unswap-sqr_binary64_1393` `associate-r/_binary64_1369` `associate-l/_binary64_1370` `add-log-exp_binary64_1461`
2×	`prod-exp_binary64_1471` `pow-plus_binary64_1485` `pow2_binary64_1503` `rem-log-exp_binary64_1463` `rem-sqrt-square_binary64_1438`
1×	`cbrt-unprod_binary64_1455` `rem-square-sqrt_binary64_1437` `sqrt-unprod_binary64_1444` `log-prod_binary64_1508` `*-commutative_binary64_1358`

Counts

4 → 126

Calls

4 calls:

16.0ms	(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
12.0ms	(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series168.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
38.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
34.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
14.0ms	(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))

simplify110.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4882	1734
1	4882	1734

prune139.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	139	4	143

Merged error: 0.4b

Counts

143 → 4

Compiler

Compiled 2520 to 1553 computations (38.4% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))))
0.2b	(.f64 (.f64 x x) (+.f64 3/4 (*.f64 3/8 (log.f64 2))))
0.8b	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
9.6b	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))))))

rewrite55.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64_1369`
15×	`pow1_binary64_1483`
14×	`add-sqr-sqrt_binary64_1446`
13×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
12×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
9×	`add-cube-cbrt_binary64_1457` `associate-l_binary64_1368` `associate-r_binary64_1367` `*-un-lft-identity_binary64_1425`
8×	`frac-add_binary64_1433`
6×	`cbrt-div_binary64_1454`
5×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `pow-prod-down_binary64_1493`
4×	`add-log-exp_binary64_1461`
3×	`distribute-lft-in_binary64_1376` `unswap-sqr_binary64_1393` `distribute-rgt-in_binary64_1377` `*-commutative_binary64_1358`
2×	`log-pow_binary64_1511`
1×	`cbrt-prod_binary64_1453` `pow1/3_binary64_1504`

Counts

4 → 88

Calls

4 calls:

14.0ms	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))))))
14.0ms	(.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))))
8.0ms	(.f64 (.f64 x x) (+.f64 3/4 (*.f64 3/8 (log.f64 2))))
7.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))

series593.0ms (17.1%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
198.0ms	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))))))
111.0ms	(.f64 (.f64 x x) (+.f64 3/4 (*.f64 3/8 (log.f64 2))))
71.0ms	(.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))))

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5256	3545

prune240.0ms (6.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	100	4	104

Merged error: 0.4b

Counts

104 → 4

Compiler

Compiled 4105 to 3289 computations (19.9% saved)

regimes35.0ms (1%)

Compiler: Compiled 314 to 288 computations (8.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	19
1	40	19

end0.0ms (0%)

sample919.0ms (26.5%)

Algorithm

1×

intervals

Results

371.0ms	7388×	body	128	valid
87.0ms	206×	body	1024	valid
54.0ms	236×	body	512	valid
21.0ms	167×	body	256	valid
4.0ms	3×	body	2048	valid
2.0ms	40×	body	128	invalid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 203 to 182 computations (10.3% saved)

Details

analyze66.0ms (1.9%)

sample23.0ms (0.7%)

simplify169.0ms (4.9%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite18.0ms (0.5%)

series164.0ms (4.7%)

simplify61.0ms (1.8%)

prune54.0ms (1.6%)

localize9.0ms (0.3%)

rewrite19.0ms (0.6%)

series299.0ms (8.6%)

simplify87.0ms (2.5%)

prune82.0ms (2.4%)

localize9.0ms (0.3%)

rewrite49.0ms (1.4%)

series168.0ms (4.8%)

simplify110.0ms (3.2%)

prune139.0ms (4%)

localize17.0ms (0.5%)

rewrite55.0ms (1.6%)

series593.0ms (17.1%)

simplify65.0ms (1.9%)

prune240.0ms (6.9%)

regimes35.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample919.0ms (26.5%)

Profiling