Details

analyze319.0ms (6.2%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	183×	body	128	valid
6.0ms	22×	body	4096	valid
6.0ms	27×	body	2048	valid
2.0ms	11×	body	1024	valid
1.0ms	10×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify172.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0%)

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: 40.7b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.0b	(+.f64 (.f64 re re) (.f64 im im))
30.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_1516` `add-log-exp_binary64_1494`
7×	`*-un-lft-identity_binary64_1455`
6×	`add-sqr-sqrt_binary64_1477`
5×	`add-cube-cbrt_binary64_1490`
4×	`sqrt-prod_binary64_1471` `sqrt-div_binary64_1472` `flip-+_binary64_1429` `add-cbrt-cube_binary64_1491` `flip3-+_binary64_1458` `add-exp-log_binary64_1493`
3×	`sqrt-pow1_binary64_1473`
2×	`associate-*r/_binary64_1397` `pow1/2_binary64_1535` `sum-log_binary64_1546` `+-commutative_binary64_1385`
1×	`distribute-lft-out_binary64_1406` `rem-sqrt-square_binary64_1468` `pow-prod-down_binary64_1526`

Counts

4 → 51

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series361.0ms (7%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
52.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
42.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5005	1040

prune246.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 18.3b

Counts

64 → 8

Compiler

Compiled 4296 to 2639 computations (38.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_1477`
50×	`sqrt-prod_binary64_1471`
38×	`*-un-lft-identity_binary64_1455`
36×	`times-frac_binary64_1461`
26×	`add-cube-cbrt_binary64_1490`
12×	`difference-of-squares_binary64_1424`
11×	`pow1_binary64_1516`
9×	`associate-/r*_binary64_1399`
6×	`distribute-lft-out--_binary64_1407` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
4×	`sqrt-pow1_binary64_1473` `sqrt-div_binary64_1472` `associate-/l*_binary64_1400`
3×	`cancel-sign-sub-inv_binary64_1421` `pow-prod-down_binary64_1526`
2×	`associate-/r/_binary64_1401` `flip--_binary64_1430` `pow1/2_binary64_1535` `flip3--_binary64_1459`
1×	`rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `sqrt-undiv_binary64_1476` `div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `div-inv_binary64_1452`

Counts

4 → 108

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series330.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
59.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
45.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5246	3621

prune274.0ms (5.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	119	9	128

Merged error: 10.3b

Counts

128 → 9

Compiler

Compiled 6209 to 2986 computations (51.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.3b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
30.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite83.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_1471`
143×	`add-sqr-sqrt_binary64_1477`
112×	`times-frac_binary64_1461`
100×	`*-un-lft-identity_binary64_1455`
72×	`add-cube-cbrt_binary64_1490`
60×	`associate-r_binary64_1395`
28×	`difference-of-squares_binary64_1424`
14×	`distribute-lft-out--_binary64_1407`
11×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
9×	`associate-/r*_binary64_1399`
7×	`pow1_binary64_1516`
6×	`sqrt-div_binary64_1472` `add-log-exp_binary64_1494` `associate-/l*_binary64_1400`
5×	`unswap-sqr_binary64_1423`
4×	`associate-/r/_binary64_1401`
3×	`flip--_binary64_1430` `cancel-sign-sub-inv_binary64_1421` `flip3--_binary64_1459` `associate-l_binary64_1396`
2×	`prod-exp_binary64_1504` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452`
1×	`sqrt-pow1_binary64_1473` `associate-r/_binary64_1397` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `sqrt-undiv_binary64_1476` `clear-num_binary64_1454` `-commutative_binary64_1386` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `sub-neg_binary64_1448` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `pow-prod-down_binary64_1526`

Counts

4 → 198

Calls

4 calls:

28.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
14.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series450.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
145.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
55.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
48.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5001	6419

prune372.0ms (7.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	206	4	210
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	210	9	219

Merged error: 2.9b

Counts

219 → 9

Compiler

Compiled 8760 to 3868 computations (55.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.2b	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
30.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite59.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_1477`
60×	`sqrt-prod_binary64_1471`
42×	`*-un-lft-identity_binary64_1455`
38×	`times-frac_binary64_1461`
28×	`add-cube-cbrt_binary64_1490`
27×	`associate-r_binary64_1395`
14×	`difference-of-squares_binary64_1424`
8×	`pow1_binary64_1516`
7×	`distribute-lft-out--_binary64_1407`
6×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
4×	`associate-/r/_binary64_1401` `sqrt-div_binary64_1472`
3×	`rem-sqrt-square_binary64_1468` `flip--_binary64_1430` `cancel-sign-sub-inv_binary64_1421` `flip3--_binary64_1459` `associate-l_binary64_1396` `unswap-sqr_binary64_1423`
2×	`sqrt-pow1_binary64_1473` `pow1/2_binary64_1535` `div-inv_binary64_1452`
1×	`prod-exp_binary64_1504` `associate-r/_binary64_1397` `flip-+_binary64_1429` `-commutative_binary64_1386` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `pow-prod-down_binary64_1526`

Counts

4 → 113

Calls

4 calls:

21.0ms	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
12.0ms	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series471.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
156.0ms	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
56.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
49.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4947	3291
1	4947	3291

prune172.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	124	10	134

Merged error: 2.8b

Counts

134 → 10

Compiler

Compiled 4131 to 1870 computations (54.7% saved)

regimes148.0ms (2.9%)

Compiler: Compiled 530 to 452 computations (14.7% saved)

bsearch67.0ms (1.3%)

Steps

Iters	Range		Point
5	2.35752468746922e-18	5.376121288418778e-18	2.3897943661054227e-18
8	1.0024622983231318e-217	2.9117635137105902e-213	1.1339651548786607e-217
7	-1.3794740741452004e-299	-3.1837278662513398e-301	-6.527935055640734e-301
5	-2.445867495953277e+136	-7.828159777283928e+135	-2.3838929425074713e+136

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	115
1	86	115

end0.0ms (0%)

sample1.2s (22.5%)

Algorithm

1×

intervals

Results

290.0ms	6019×	body	128	valid
169.0ms	583×	body	4096	valid
149.0ms	645×	body	2048	valid
85.0ms	413×	body	1024	valid
29.0ms	215×	body	512	valid
11.0ms	125×	body	256	valid

Compiler

Compiled 288 to 226 computations (21.5% saved)

Details

analyze319.0ms (6.2%)

sample32.0ms (0.6%)

simplify172.0ms (3.4%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series361.0ms (7%)

simplify56.0ms (1.1%)

prune246.0ms (4.8%)

localize12.0ms (0.2%)

rewrite49.0ms (0.9%)

series330.0ms (6.4%)

simplify82.0ms (1.6%)

prune274.0ms (5.3%)

localize16.0ms (0.3%)

rewrite83.0ms (1.6%)

series450.0ms (8.8%)

simplify94.0ms (1.8%)

prune372.0ms (7.3%)

localize12.0ms (0.2%)

rewrite59.0ms (1.1%)

series471.0ms (9.2%)

simplify53.0ms (1%)

prune172.0ms (3.4%)

regimes148.0ms (2.9%)

bsearch67.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (22.5%)

Profiling