Details

analyze1.9s (9.4%)

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)

sample150.0ms (0.7%)

Algorithm

1×

intervals

Results

47.0ms	256×	body	128	valid
45.0ms	283×	body	128	nan
29.0ms	153×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify199.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5205	41

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 26.1b

Counts

2 → 1

Compiler

Compiled 116 to 100 computations (13.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.5b	(/.f64 (.f64 M D) (.f64 d 2))
9.3b	(sqrt.f64 (/.f64 d h))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.9b	(sqrt.f64 (/.f64 d l))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`add-exp-log_binary64_1493`
42×	`prod-exp_binary64_1504`
31×	`add-sqr-sqrt_binary64_1477`
30×	`times-frac_binary64_1461`
28×	`add-cbrt-cube_binary64_1491`
26×	`sqrt-prod_binary64_1471`
25×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
20×	`div-exp_binary64_1506`
13×	`associate-r_binary64_1395`
10×	`cbrt-unprod_binary64_1488` `pow-exp_binary64_1523`
8×	`pow1_binary64_1516`
6×	`cbrt-undiv_binary64_1489`
4×	`rem-sqrt-square_binary64_1468` `add-log-exp_binary64_1494` `div-inv_binary64_1452`
2×	`sqrt-pow1_binary64_1473` `sqrt-div_binary64_1472` `pow-to-exp_binary64_1524` `pow1/2_binary64_1535`
1×	`associate-r/_binary64_1397` `clear-num_binary64_1454` `associate-/r_binary64_1399` `-commutative_binary64_1386` `frac-2neg_binary64_1466` `associate-/l_binary64_1400` `associate-l_binary64_1396` `pow-prod-down_binary64_1526`

Counts

4 → 115

Calls

4 calls:

12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

series363.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
75.0ms	(sqrt.f64 (/.f64 d l))
72.0ms	(sqrt.f64 (/.f64 d h))
44.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5222	2151

prune1.2s (6.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	106	21	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	21	128

Merged error: 11.1b

Counts

128 → 21

Compiler

Compiled 25198 to 18483 computations (26.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
5.5b	(/.f64 (.f64 M D) (.f64 d 2))
9.3b	(sqrt.f64 (/.f64 d h))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite69.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64_1493`
48×	`prod-exp_binary64_1504`
37×	`add-cbrt-cube_binary64_1491`
22×	`add-sqr-sqrt_binary64_1477`
20×	`div-exp_binary64_1506` `times-frac_binary64_1461`
19×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
16×	`associate-r_binary64_1395` `pow1_binary64_1516` `cbrt-unprod_binary64_1488`
13×	`sqrt-prod_binary64_1471` `sqrt-div_binary64_1472`
12×	`associate-*r/_binary64_1397`
10×	`pow-exp_binary64_1523`
9×	`frac-times_binary64_1465`
7×	`pow-prod-down_binary64_1526`
6×	`cbrt-undiv_binary64_1489` `associate-*l/_binary64_1398`
4×	`add-log-exp_binary64_1494` `flip--_binary64_1430` `flip3--_binary64_1459`
3×	`div-inv_binary64_1452`
2×	`distribute-rgt-in_binary64_1405` `rem-sqrt-square_binary64_1468` `-commutative_binary64_1386` `pow-to-exp_binary64_1524` `cancel-sign-sub-inv_binary64_1421` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `associate-l*_binary64_1396`
1×	`sqrt-pow1_binary64_1473` `clear-num_binary64_1454` `associate-/r_binary64_1399` `frac-2neg_binary64_1466` `associate-/l_binary64_1400` `pow1/2_binary64_1535`

Counts

4 → 126

Calls

4 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d h))

series1.7s (8.2%)

Counts

4 → 12

Calls

4 calls:

1.4s	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
159.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
77.0ms	(sqrt.f64 (/.f64 d h))
46.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify103.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5076	4534

prune1.3s (6.3%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	125	13	138
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	131	28	159

Merged error: 8.8b

Counts

159 → 28

Compiler

Compiled 28322 to 19022 computations (32.8% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
5.2b	(.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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
5.5b	(/.f64 (.f64 M D) (.f64 d 2))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite76.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1493`
55×	`prod-exp_binary64_1504`
46×	`add-cbrt-cube_binary64_1491`
24×	`pow1_binary64_1516`
23×	`cbrt-unprod_binary64_1488`
20×	`div-exp_binary64_1506`
18×	`associate-*r/_binary64_1397`
16×	`associate-r_binary64_1395`
14×	`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×	`pow-exp_binary64_1523` `times-frac_binary64_1461`
9×	`frac-times_binary64_1465`
6×	`cbrt-undiv_binary64_1489` `associate-*l/_binary64_1398`
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` `pow-to-exp_binary64_1524` `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 → 118

Calls

4 calls:

33.0ms	(.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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 d)

series2.5s (12.1%)

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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
173.0ms	(cbrt.f64 d)
151.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
39.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4995	5248
1	4995	5248

prune825.0ms (4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	4	23	27
Picked	1	0	1
Done	0	0	0
Total	129	29	158

Merged error: 7.8b

Counts

158 → 29

Compiler

Compiled 20083 to 11409 computations (43.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.2b	(.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 d 2)) 2)) h) l)))
5.5b	(/.f64 (.f64 M D) (.f64 d 2))
5.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
7.2b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)

rewrite89.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64_1493`
55×	`prod-exp_binary64_1504`
48×	`add-cbrt-cube_binary64_1491`
24×	`pow1_binary64_1516`
23×	`cbrt-unprod_binary64_1488`
21×	`div-exp_binary64_1506`
17×	`associate-*r/_binary64_1397`
15×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
14×	`cancel-sign-sub-inv_binary64_1421` `pow-prod-down_binary64_1526`
12×	`sqrt-div_binary64_1472` `add-cube-cbrt_binary64_1490`
10×	`pow-exp_binary64_1523` `times-frac_binary64_1461`
9×	`associate-r_binary64_1395` `frac-times_binary64_1465`
8×	`distribute-rgt-in_binary64_1405` `distribute-lft-in_binary64_1404`
7×	`cbrt-undiv_binary64_1489`
6×	`associate-*l/_binary64_1398`
4×	`associate-/r*_binary64_1399` `add-log-exp_binary64_1494` `flip--_binary64_1430` `div-inv_binary64_1452` `flip3--_binary64_1459`
2×	`difference-of-squares_binary64_1424` `clear-num_binary64_1454` `-commutative_binary64_1386` `pow-to-exp_binary64_1524` `frac-2neg_binary64_1466` `associate-/l_binary64_1400` `sub-neg_binary64_1448` `associate-l_binary64_1396`
1×	`distribute-lft-out--_binary64_1407`

Counts

4 → 130

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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
10.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series2.5s (12.2%)

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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
156.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
140.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5063	6969

prune918.0ms (4.5%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	1	27	28
Picked	0	1	1
Done	0	0	0
Total	138	33	171

Merged error: 6.8b

Counts

171 → 33

Compiler

Compiled 23034 to 12927 computations (43.9% saved)

regimes600.0ms (2.9%)

Compiler: Compiled 8242 to 5738 computations (30.4% saved)

bsearch103.0ms (0.5%)

Steps

Iters	Range		Point
6	3.7702626348561733e-51	2.5378994579081793e-50	2.1293566993651843e-50

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	152
1	118	152

end0.0ms (0%)

sample5.4s (26.5%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.2s	8374×	body	128	nan
918.0ms	4757×	body	128	invalid

Compiler

Compiled 1501 to 1029 computations (31.4% saved)

Details

analyze1.9s (9.4%)

sample150.0ms (0.7%)

simplify199.0ms (1%)

prune8.0ms (0%)

localize25.0ms (0.1%)

rewrite40.0ms (0.2%)

series363.0ms (1.8%)

simplify53.0ms (0.3%)

prune1.2s (6.1%)

localize26.0ms (0.1%)

rewrite69.0ms (0.3%)

series1.7s (8.2%)

simplify103.0ms (0.5%)

prune1.3s (6.3%)

localize31.0ms (0.2%)

rewrite76.0ms (0.4%)

series2.5s (12.1%)

simplify101.0ms (0.5%)

prune825.0ms (4%)

localize31.0ms (0.2%)

rewrite89.0ms (0.4%)

series2.5s (12.2%)

simplify117.0ms (0.6%)

prune918.0ms (4.5%)

regimes600.0ms (2.9%)

bsearch103.0ms (0.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.4s (26.5%)

Profiling