Details

analyze11.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample25.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	47×	body	1024	valid
6.0ms	141×	body	128	valid
5.0ms	44×	body	512	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify175.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 10.7b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (+.f64 x 1))
2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite102.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1455`
74×	`times-frac_binary64_1461`
72×	`add-sqr-sqrt_binary64_1477`
39×	`add-cube-cbrt_binary64_1490`
26×	`cancel-sign-sub-inv_binary64_1421`
18×	`distribute-lft-out--_binary64_1407`
17×	`distribute-lft-out_binary64_1406`
14×	`difference-of-squares_binary64_1424` `associate-+l+_binary64_1388`
12×	`add-exp-log_binary64_1493`
11×	`associate-/r*_binary64_1399` `add-log-exp_binary64_1494`
10×	`div-inv_binary64_1452`
8×	`add-cbrt-cube_binary64_1491`
6×	`pow1_binary64_1516` `associate-/l*_binary64_1400`
4×	`associate-/r/_binary64_1401` `div-exp_binary64_1506` `difference-of-sqr-1_binary64_1425`
3×	`flip--_binary64_1430` `frac-add_binary64_1463` `flip3--_binary64_1459`
2×	`inv-pow_binary64_1540` `flip-+_binary64_1429` `1-exp_binary64_1499` `clear-num_binary64_1454` `pow-flip_binary64_1529` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `sum-log_binary64_1546` `rec-exp_binary64_1505`
1×	`associate-+l-_binary64_1390` `+-commutative_binary64_1385`

Counts

4 → 161

Calls

4 calls:

46.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
26.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series168.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
29.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
19.0ms	(/.f64 1 (-.f64 x 1))
17.0ms	(/.f64 1 (+.f64 x 1))

simplify78.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4911	2799
1	4911	2799

prune536.0ms (17.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Merged error: 0.3b

Counts

174 → 4

Compiler

Compiled 9783 to 7987 computations (18.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
15.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite50.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-*r/_binary64_1397`
19×	`flip--_binary64_1430` `flip3--_binary64_1459`
16×	`add-sqr-sqrt_binary64_1477` `frac-add_binary64_1463`
13×	`*-un-lft-identity_binary64_1455`
12×	`frac-times_binary64_1465`
10×	`flip-+_binary64_1429` `flip3-+_binary64_1458` `associate-l_binary64_1396`
8×	`pow1_binary64_1516` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-cube-cbrt_binary64_1490` `add-exp-log_binary64_1493`
7×	`associate-r_binary64_1395`
6×	`distribute-rgt-in_binary64_1405` `distribute-lft-in_binary64_1404` `associate-*l/_binary64_1398`
5×	`cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448`
4×	`associate-+l+_binary64_1388`
2×	`prod-exp_binary64_1504` `difference-of-squares_binary64_1424` `*-commutative_binary64_1386` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423` `associate-+r+_binary64_1387`
1×	`distribute-lft-out_binary64_1406` `distribute-lft-out--_binary64_1407` `diff-log_binary64_1547` `sum-log_binary64_1546` `+-commutative_binary64_1385` `difference-of-sqr-1_binary64_1425`

Counts

4 → 102

Calls

4 calls:

13.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
11.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
7.0ms	(*.f64 x (+.f64 1 x))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series114.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(*.f64 x (+.f64 1 x))
28.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
24.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
8.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify78.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4988	3216
1	4988	3216

prune198.0ms (6.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	116	2	118

Merged error: 0.3b

Counts

118 → 2

Compiler

Compiled 4162 to 2818 computations (32.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 x 3) (neg.f64 x))
0.3b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_1455`
21×	`times-frac_binary64_1461`
14×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490`
10×	`distribute-lft-out_binary64_1406` `unpow3_binary64_1521` `distribute-rgt-out_binary64_1408`
7×	`associate-/r*_binary64_1399`
6×	`add-log-exp_binary64_1494`
5×	`neg-mul-1_binary64_1451` `distribute-rgt-neg-in_binary64_1413` `distribute-lft-neg-in_binary64_1412`
4×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`associate-/l*_binary64_1400`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `pow1_binary64_1516` `flip3-+_binary64_1458` `sum-log_binary64_1546`
1×	`neg-log_binary64_1548` `neg-sub0_binary64_1450` `unsub-neg_binary64_1449` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `associate-+r-_binary64_1389` `div-inv_binary64_1452` `+-commutative_binary64_1385`

Counts

2 → 63

Calls

2 calls:

16.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))
11.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))

series137.0ms (4.4%)

Counts

2 → 6

Calls

2 calls:

88.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))
49.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4894	964
1	4894	964

prune174.0ms (5.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

Compiler

Compiled 2546 to 2050 computations (19.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) -1)
0.1b	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary64_1461`
51×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
15×	`difference-of-sqr--1_binary64_1426`
13×	`associate-/l*_binary64_1400`
7×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
6×	`div-inv_binary64_1452`
4×	`associate-/r*_binary64_1399` `add-log-exp_binary64_1494`
3×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `pow1_binary64_1516` `flip3-+_binary64_1458`
1×	`associate-/l/_binary64_1402` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

2 → 98

Calls

2 calls:

11.0ms	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))
6.0ms	(+.f64 (*.f64 x x) -1)

series97.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(+.f64 (*.f64 x x) -1)
48.0ms	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5235	2363

prune114.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	104	5	109

Merged error: 0b

Counts

109 → 5

Compiler

Compiled 2083 to 1385 computations (33.5% saved)

regimes11.0ms (0.3%)

Compiler: Compiled 50 to 42 computations (16% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	9	13

end0.0ms (0%)

sample817.0ms (26.2%)

Algorithm

1×

intervals

Results

186.0ms	1266×	body	1024	valid
175.0ms	4491×	body	128	valid
168.0ms	1479×	body	512	valid
58.0ms	764×	body	256	valid

Compiler

Compiled 82 to 69 computations (15.9% saved)

Details

analyze11.0ms (0.4%)

sample25.0ms (0.8%)

simplify175.0ms (5.6%)

prune3.0ms (0.1%)

localize12.0ms (0.4%)

rewrite102.0ms (3.3%)

series168.0ms (5.4%)

simplify78.0ms (2.5%)

prune536.0ms (17.2%)

localize14.0ms (0.4%)

rewrite50.0ms (1.6%)

series114.0ms (3.7%)

simplify78.0ms (2.5%)

prune198.0ms (6.3%)

localize6.0ms (0.2%)

rewrite32.0ms (1%)

series137.0ms (4.4%)

simplify64.0ms (2.1%)

prune174.0ms (5.6%)

localize6.0ms (0.2%)

rewrite27.0ms (0.9%)

series97.0ms (3.1%)

simplify67.0ms (2.1%)

prune114.0ms (3.6%)

regimes11.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample817.0ms (26.2%)

Profiling