Details

analyze1.9s (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample145.0ms (0.7%)

Algorithm

1×

intervals

Results

46.0ms	256×	body	128	valid
38.0ms	265×	body	128	nan
29.0ms	152×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify198.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune9.0ms (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: 24.5b

Counts

2 → 2

Compiler

Compiled 151 to 131 computations (13.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
10.8b	(pow.f64 (/.f64 d h) (/.f64 1 2))
12.2b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
12.4b	(pow.f64 (/.f64 d l) (/.f64 1 2))

rewrite88.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

331×	`add-exp-log_binary64_1493`
179×	`prod-exp_binary64_1504`
99×	`div-exp_binary64_1506`
60×	`pow-exp_binary64_1523`
45×	`times-frac_binary64_1461`
40×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
30×	`add-cbrt-cube_binary64_1491`
26×	`unpow-prod-down_binary64_1534` `pow-unpow_binary64_1532`
18×	`pow-to-exp_binary64_1524`
16×	`associate-r_binary64_1395`
14×	`1-exp_binary64_1499` `rec-exp_binary64_1505`
13×	`cbrt-unprod_binary64_1488`
10×	`pow1_binary64_1516`
5×	`cbrt-undiv_binary64_1489` `div-inv_binary64_1452`
4×	`add-log-exp_binary64_1494`
3×	`associate-r/_binary64_1397` `associate-l/_binary64_1398`
2×	`distribute-rgt-in_binary64_1405` `-commutative_binary64_1386` `pow-pow_binary64_1527` `sqr-pow_binary64_1427` `cancel-sign-sub-inv_binary64_1421` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `associate-l*_binary64_1396` `pow-prod-down_binary64_1526`
1×	`frac-times_binary64_1465` `flip--_binary64_1430` `flip3--_binary64_1459`

Counts

4 → 204

Calls

4 calls:

21.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
19.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
7.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
7.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))

series883.0ms (4%)

Counts

4 → 12

Calls

4 calls:

541.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1 2)) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
142.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
100.0ms	(pow.f64 (/.f64 d h) (/.f64 1 2))
100.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4987	5019
1	4987	5019

prune1.8s (8.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	193	23	216
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	23	218

Merged error: 11.8b

Counts

218 → 23

Compiler

Compiled 36425 to 27814 computations (23.6% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
12.2b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
12.4b	(pow.f64 (/.f64 d l) (/.f64 1 2))

rewrite92.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`add-exp-log_binary64_1493`
171×	`prod-exp_binary64_1504`
96×	`div-exp_binary64_1506`
46×	`add-cbrt-cube_binary64_1491` `pow-exp_binary64_1523`
28×	`times-frac_binary64_1461`
26×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
20×	`cbrt-unprod_binary64_1488`
16×	`associate-r_binary64_1395`
14×	`1-exp_binary64_1499` `rec-exp_binary64_1505`
13×	`unpow-prod-down_binary64_1534` `pow-unpow_binary64_1532`
11×	`pow-to-exp_binary64_1524`
9×	`pow1_binary64_1516` `cbrt-undiv_binary64_1489`
7×	`associate-*l/_binary64_1398`
6×	`associate-*r/_binary64_1397`
4×	`add-log-exp_binary64_1494` `div-inv_binary64_1452`
3×	`sqrt-div_binary64_1472` `frac-times_binary64_1465`
2×	`distribute-rgt-in_binary64_1405` `-commutative_binary64_1386` `flip--_binary64_1430` `cancel-sign-sub-inv_binary64_1421` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `flip3--_binary64_1459` `associate-l*_binary64_1396` `pow-prod-down_binary64_1526`
1×	`clear-num_binary64_1454` `associate-/r_binary64_1399` `pow-pow_binary64_1527` `sqr-pow_binary64_1427` `frac-2neg_binary64_1466` `associate-/l_binary64_1400`

Counts

4 → 183

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
16.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
10.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))

series2.2s (9.7%)

Counts

4 → 12

Calls

4 calls:

1.8s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (pow.f64 (/.f64 d l) (/.f64 1 2))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 h l))))
157.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
100.0ms	(pow.f64 (/.f64 d l) (/.f64 1 2))
46.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify113.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	5605
1	4975	5605

prune1.4s (6.4%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	186	9	195
Fresh	3	19	22
Picked	1	0	1
Done	0	0	0
Total	190	28	218

Merged error: 10.0b

Counts

218 → 28

Compiler

Compiled 30885 to 21255 computations (31.2% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
4.6b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
12.2b	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))

rewrite93.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

305×	`add-exp-log_binary64_1493`
163×	`prod-exp_binary64_1504`
93×	`div-exp_binary64_1506`
55×	`add-cbrt-cube_binary64_1491`
40×	`pow-exp_binary64_1523`
27×	`cbrt-unprod_binary64_1488`
24×	`pow1_binary64_1516`
18×	`associate-*r/_binary64_1397`
16×	`associate-r_binary64_1395`
14×	`1-exp_binary64_1499` `rec-exp_binary64_1505` `pow-prod-down_binary64_1526`
13×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
12×	`sqrt-div_binary64_1472`
10×	`frac-times_binary64_1465` `times-frac_binary64_1461`
9×	`cbrt-undiv_binary64_1489` `associate-*l/_binary64_1398`
8×	`pow-to-exp_binary64_1524`
4×	`add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459`
3×	`cbrt-prod_binary64_1486`
2×	`distribute-rgt-in_binary64_1405` `-commutative_binary64_1386` `cancel-sign-sub-inv_binary64_1421` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `div-inv_binary64_1452` `associate-l*_binary64_1396`
1×	`pow1/3_binary64_1537` `clear-num_binary64_1454` `associate-/r_binary64_1399` `frac-2neg_binary64_1466` `associate-/l_binary64_1400`

Counts

4 → 164

Calls

4 calls:

36.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
16.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
1.0ms	(cbrt.f64 d)

series2.5s (11.2%)

Counts

4 → 12

Calls

4 calls:

2.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))))
171.0ms	(.f64 (.f64 (/.f64 1 2) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 h l))
153.0ms	(cbrt.f64 d)
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify102.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4985	6540
1	4985	6540

prune759.0ms (3.4%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	2	25	27
Picked	1	0	1
Done	0	0	0
Total	172	32	204

Merged error: 7.0b

Counts

204 → 32

Compiler

Compiled 18952 to 10285 computations (45.7% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))
4.6b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))))
6.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

rewrite91.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`add-exp-log_binary64_1493`
58×	`prod-exp_binary64_1504`
48×	`add-cbrt-cube_binary64_1491`
32×	`div-exp_binary64_1506`
22×	`pow1_binary64_1516` `cbrt-unprod_binary64_1488`
19×	`add-sqr-sqrt_binary64_1477`
17×	`associate-*r/_binary64_1397`
15×	`pow-exp_binary64_1523`
13×	`pow-prod-down_binary64_1526` `*-un-lft-identity_binary64_1455`
12×	`sqrt-div_binary64_1472`
11×	`associate-l_binary64_1396`
10×	`add-cube-cbrt_binary64_1490` `cancel-sign-sub-inv_binary64_1421`
9×	`associate-r_binary64_1395` `frac-times_binary64_1465`
8×	`cbrt-undiv_binary64_1489`
6×	`distribute-rgt-in_binary64_1405` `unpow-prod-down_binary64_1534` `distribute-lft-in_binary64_1404` `associate-*l/_binary64_1398`
5×	`div-inv_binary64_1452` `times-frac_binary64_1461`
4×	`add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459` `unswap-sqr_binary64_1423`
3×	`pow-to-exp_binary64_1524`
2×	`unpow2_binary64_1520` `difference-of-squares_binary64_1424` `clear-num_binary64_1454` `associate-/r_binary64_1399` `-commutative_binary64_1386` `sqr-pow_binary64_1427` `frac-2neg_binary64_1466` `associate-/l*_binary64_1400` `sub-neg_binary64_1448`
1×	`distribute-lft-out--_binary64_1407`

Counts

4 → 140

Calls

4 calls:

34.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))))
10.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))
8.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series2.5s (11.5%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))))
158.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (.f64 2 l))
151.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5028	6705

prune843.0ms (3.8%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	2	29	31
Picked	1	0	1
Done	0	0	0
Total	151	33	184

Merged error: 5.4b

Counts

184 → 33

Compiler

Compiled 21121 to 12068 computations (42.9% saved)

regimes592.0ms (2.7%)

Compiler: Compiled 8632 to 6320 computations (26.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	104	82
1	104	82

end0.0ms (0%)

sample5.5s (24.8%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.2s	8488×	body	128	nan
905.0ms	4793×	body	128	invalid

Compiler

Compiled 1523 to 1112 computations (27% saved)

Details

analyze1.9s (8.7%)

sample145.0ms (0.7%)

simplify198.0ms (0.9%)

prune9.0ms (0%)

localize29.0ms (0.1%)

rewrite88.0ms (0.4%)

series883.0ms (4%)

simplify104.0ms (0.5%)

prune1.8s (8.2%)

localize31.0ms (0.1%)

rewrite92.0ms (0.4%)

series2.2s (9.7%)

simplify113.0ms (0.5%)

prune1.4s (6.4%)

localize30.0ms (0.1%)

rewrite93.0ms (0.4%)

series2.5s (11.2%)

simplify102.0ms (0.5%)

prune759.0ms (3.4%)

localize31.0ms (0.1%)

rewrite91.0ms (0.4%)

series2.5s (11.5%)

simplify96.0ms (0.4%)

prune843.0ms (3.8%)

regimes592.0ms (2.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.5s (24.8%)

Profiling