Details

analyze2.0s (9.8%)

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)

sample163.0ms (0.8%)

Algorithm

1×

intervals

Results

47.0ms	256×	body	128	valid
44.0ms	304×	body	128	nan
39.0ms	190×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify198.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune5.0ms (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: 27.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.6b	(sqrt.f64 (/.f64 d l))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.3b	(sqrt.f64 (/.f64 d h))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1485`
41×	`prod-exp_binary64_1496`
32×	`add-sqr-sqrt_binary64_1469`
29×	`times-frac_binary64_1453`
26×	`add-cube-cbrt_binary64_1482` `sqrt-prod_binary64_1463` `*-un-lft-identity_binary64_1447`
21×	`add-cbrt-cube_binary64_1483`
16×	`associate-r_binary64_1387` `div-exp_binary64_1498`
14×	`sqrt-div_binary64_1464`
13×	`pow1_binary64_1508`
10×	`pow-exp_binary64_1515`
9×	`cbrt-unprod_binary64_1480` `frac-times_binary64_1457`
6×	`associate-r/_binary64_1389` `associate-l/_binary64_1390`
4×	`flip--_binary64_1422` `flip3--_binary64_1451` `pow-prod-down_binary64_1518` `rem-sqrt-square_binary64_1460` `add-log-exp_binary64_1486`
3×	`div-inv_binary64_1444`
2×	`sqrt-pow1_binary64_1465` `sub-neg_binary64_1440` `distribute-rgt-in_binary64_1397` `associate-l_binary64_1388` `*-commutative_binary64_1378` `distribute-lft-in_binary64_1396` `cbrt-undiv_binary64_1481` `cancel-sign-sub-inv_binary64_1413` `pow1/2_binary64_1527` `pow-to-exp_binary64_1516`

Counts

4 → 127

Calls

4 calls:

19.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
4.0ms	(sqrt.f64 (/.f64 d h))
4.0ms	(sqrt.f64 (/.f64 d l))

series878.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

570.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
149.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
80.0ms	(sqrt.f64 (/.f64 d h))
78.0ms	(sqrt.f64 (/.f64 d l))

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4954	3595
1	4954	3595

prune269.0ms (1.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	118	21	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	21	140

Merged error: 13.6b

Counts

140 → 21

Compiler

Compiled 5411 to 2699 computations (50.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.3b	(/.f64 (.f64 M D) (.f64 d 2))
7.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
13.6b	(sqrt.f64 (/.f64 d l))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite70.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64_1485`
48×	`prod-exp_binary64_1496`
37×	`add-cbrt-cube_binary64_1483`
22×	`add-sqr-sqrt_binary64_1469`
20×	`times-frac_binary64_1453` `div-exp_binary64_1498`
19×	`add-cube-cbrt_binary64_1482` `*-un-lft-identity_binary64_1447`
16×	`associate-r_binary64_1387` `cbrt-unprod_binary64_1480` `pow1_binary64_1508`
13×	`sqrt-prod_binary64_1463` `sqrt-div_binary64_1464`
12×	`associate-*r/_binary64_1389`
10×	`pow-exp_binary64_1515`
9×	`frac-times_binary64_1457`
7×	`pow-prod-down_binary64_1518`
6×	`cbrt-undiv_binary64_1481` `associate-*l/_binary64_1390`
4×	`flip--_binary64_1422` `flip3--_binary64_1451` `add-log-exp_binary64_1486`
3×	`div-inv_binary64_1444`
2×	`sub-neg_binary64_1440` `distribute-rgt-in_binary64_1397` `associate-l_binary64_1388` `*-commutative_binary64_1378` `distribute-lft-in_binary64_1396` `cancel-sign-sub-inv_binary64_1413` `rem-sqrt-square_binary64_1460` `pow-to-exp_binary64_1516`
1×	`frac-2neg_binary64_1458` `sqrt-pow1_binary64_1465` `clear-num_binary64_1446` `associate-/r_binary64_1391` `associate-/l_binary64_1392` `pow1/2_binary64_1527`

Counts

4 → 126

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
13.0ms	(.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 l))

series2.2s (10.9%)

Counts

4 → 12

Calls

4 calls:

1.9s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
174.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
77.0ms	(sqrt.f64 (/.f64 d l))
44.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify98.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4960	4485
1	4960	4485

prune263.0ms (1.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	134	25	159

Merged error: 11.8b

Counts

159 → 25

Compiler

Compiled 6934 to 2826 computations (59.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
6.3b	(/.f64 (.f64 M D) (.f64 d 2))
7.3b	(.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))))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite81.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1485`
55×	`prod-exp_binary64_1496`
46×	`add-cbrt-cube_binary64_1483`
24×	`pow1_binary64_1508`
23×	`cbrt-unprod_binary64_1480`
20×	`div-exp_binary64_1498`
18×	`associate-*r/_binary64_1389`
16×	`associate-r_binary64_1387`
14×	`pow-prod-down_binary64_1518`
13×	`add-cube-cbrt_binary64_1482` `add-sqr-sqrt_binary64_1469` `*-un-lft-identity_binary64_1447`
12×	`sqrt-div_binary64_1464`
10×	`times-frac_binary64_1453` `pow-exp_binary64_1515`
9×	`frac-times_binary64_1457`
6×	`cbrt-undiv_binary64_1481` `associate-*l/_binary64_1390`
4×	`flip--_binary64_1422` `flip3--_binary64_1451` `add-log-exp_binary64_1486`
3×	`cbrt-prod_binary64_1478`
2×	`sub-neg_binary64_1440` `distribute-rgt-in_binary64_1397` `associate-l_binary64_1388` `*-commutative_binary64_1378` `distribute-lft-in_binary64_1396` `cancel-sign-sub-inv_binary64_1413` `div-inv_binary64_1444` `pow-to-exp_binary64_1516`
1×	`frac-2neg_binary64_1458` `clear-num_binary64_1446` `associate-/r_binary64_1391` `associate-/l_binary64_1392` `pow1/3_binary64_1529`

Counts

4 → 118

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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.0ms	(.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))
2.0ms	(cbrt.f64 h)

series2.7s (13.2%)

Counts

4 → 12

Calls

4 calls:

2.3s	(.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))))
179.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
171.0ms	(cbrt.f64 h)
45.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4995	5236
1	4995	5236

prune274.0ms (1.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	125	5	130
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	129	26	155

Merged error: 9.4b

Counts

155 → 26

Compiler

Compiled 7805 to 2770 computations (64.5% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 (.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))))
3.4b	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (.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)))))
6.3b	(/.f64 (.f64 M D) (.f64 d 2))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite106.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-exp-log_binary64_1485`
60×	`prod-exp_binary64_1496`
54×	`add-cbrt-cube_binary64_1483`
32×	`pow1_binary64_1508`
28×	`cbrt-unprod_binary64_1480`
27×	`associate-*r/_binary64_1389`
20×	`div-exp_binary64_1498`
19×	`pow-prod-down_binary64_1518`
17×	`associate-r_binary64_1387`
15×	`sqrt-div_binary64_1464`
12×	`add-cube-cbrt_binary64_1482` `add-sqr-sqrt_binary64_1469` `*-un-lft-identity_binary64_1447`
11×	`frac-times_binary64_1457`
10×	`distribute-rgt-in_binary64_1397` `times-frac_binary64_1453` `pow-exp_binary64_1515` `distribute-lft-in_binary64_1396`
6×	`flip--_binary64_1422` `sub-neg_binary64_1440` `flip3--_binary64_1451` `cbrt-undiv_binary64_1481` `cancel-sign-sub-inv_binary64_1413`
4×	`add-log-exp_binary64_1486` `associate-*l/_binary64_1390`
3×	`associate-l_binary64_1388` `*-commutative_binary64_1378`
2×	`div-inv_binary64_1444` `pow-to-exp_binary64_1516`
1×	`frac-2neg_binary64_1458` `clear-num_binary64_1446` `associate-/r_binary64_1391` `associate-/l_binary64_1392`

Counts

4 → 139

Calls

4 calls:

33.0ms	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (.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)))))
19.0ms	(.f64 (.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))))
13.0ms	(.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))

series3.5s (17.4%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (.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)))))
1.1s	(.f64 (.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))))
162.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
43.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify114.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5070	7320

prune260.0ms (1.3%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	2	23	25
Picked	0	1	1
Done	0	0	0
Total	150	27	177

Merged error: 9.4b

Counts

177 → 27

Compiler

Compiled 8160 to 2498 computations (69.4% saved)

regimes688.0ms (3.4%)

Compiler: Compiled 7048 to 4982 computations (29.3% saved)

bsearch580.0ms (2.9%)

Steps

Iters	Range		Point
8	2.9194797110079602e-266	9.960153937922263e-263	9.81519393445088e-263
9	-7.073942624481071e-217	-1.3783558644650406e-222	-5.932714166424622e-217

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	199
1	118	199

end0.0ms (0%)

sample5.4s (26.8%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.3s	8357×	body	128	nan
932.0ms	4839×	body	128	invalid

Compiler

Compiled 1332 to 921 computations (30.9% saved)

Details

analyze2.0s (9.8%)

sample163.0ms (0.8%)

simplify198.0ms (1%)

prune5.0ms (0%)

localize21.0ms (0.1%)

rewrite57.0ms (0.3%)

series878.0ms (4.4%)

simplify84.0ms (0.4%)

prune269.0ms (1.3%)

localize28.0ms (0.1%)

rewrite70.0ms (0.3%)

series2.2s (10.9%)

simplify98.0ms (0.5%)

prune263.0ms (1.3%)

localize31.0ms (0.2%)

rewrite81.0ms (0.4%)

series2.7s (13.2%)

simplify101.0ms (0.5%)

prune274.0ms (1.4%)

localize34.0ms (0.2%)

rewrite106.0ms (0.5%)

series3.5s (17.4%)

simplify114.0ms (0.6%)

prune260.0ms (1.3%)

regimes688.0ms (3.4%)

bsearch580.0ms (2.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.4s (26.8%)

Profiling