Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	68×	body	2048	valid
6.0ms	35×	body	1024	valid
5.0ms	133×	body	128	valid
2.0ms	15×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify162.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune7.0ms (0.1%)

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: 16.5b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1425`
22×	`add-sqr-sqrt_binary64_1446`
13×	`add-cube-cbrt_binary64_1457`
9×	`times-frac_binary64_1431`
8×	`sqrt-prod_binary64_1440` `add-log-exp_binary64_1461`
6×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
5×	`pow1_binary64_1483`
4×	`difference-of-squares_binary64_1394`
3×	`associate-/r_binary64_1371` `distribute-lft-out--_binary64_1379` `distribute-lft-out_binary64_1378` `associate-/l_binary64_1372`
2×	`flip3-+_binary64_1428` `sqrt-div_binary64_1441` `flip-+_binary64_1399`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `frac-2neg_binary64_1436` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `clear-num_binary64_1424` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `+-commutative_binary64_1357` `rem-sqrt-square_binary64_1438` `flip3--_binary64_1429` `cbrt-undiv_binary64_1456`

Counts

4 → 73

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
6.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

series327.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
108.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
60.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
41.0ms	(/.f64 1/2 (hypot.f64 1 x))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4940	1355
1	4940	1355

prune100.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Merged error: 16.0b

Counts

86 → 4

Compiler

Compiled 1405 to 1276 computations (9.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.3b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1425`
76×	`add-sqr-sqrt_binary64_1446`
44×	`times-frac_binary64_1431`
33×	`distribute-lft-out_binary64_1378`
20×	`sqrt-prod_binary64_1440`
19×	`add-cube-cbrt_binary64_1457`
16×	`difference-of-squares_binary64_1394`
8×	`distribute-lft-out--_binary64_1379` `add-log-exp_binary64_1461`
6×	`associate-/r_binary64_1371` `add-cbrt-cube_binary64_1458` `associate-/l_binary64_1372` `add-exp-log_binary64_1460`
5×	`pow1_binary64_1483`
3×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
2×	`flip--_binary64_1400` `sqrt-div_binary64_1441` `associate-/r/_binary64_1373` `associate-/l/_binary64_1374` `flip3--_binary64_1429`
1×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `pow1/2_binary64_1502` `sub-neg_binary64_1418` `clear-num_binary64_1424` `div-sub_binary64_1430` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `+-commutative_binary64_1357` `rem-sqrt-square_binary64_1438` `cbrt-undiv_binary64_1456`

Counts

4 → 109

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series606.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
106.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
105.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
70.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4974	3605
1	4974	3605

prune233.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	119	6	125

Merged error: 16.0b

Counts

125 → 6

Compiler

Compiled 3507 to 3157 computations (10% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
1.3b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite83.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-sqr-sqrt_binary64_1446`
86×	`*-un-lft-identity_binary64_1425`
82×	`times-frac_binary64_1431`
44×	`add-cube-cbrt_binary64_1457`
36×	`difference-of-squares_binary64_1394`
25×	`unpow-prod-down_binary64_1501` `cube-prod_binary64_1450`
15×	`distribute-lft-out_binary64_1378`
14×	`associate-/l*_binary64_1372`
11×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
7×	`associate-/r*_binary64_1371` `sqr-pow_binary64_1397`
6×	`distribute-lft-out--_binary64_1379` `add-log-exp_binary64_1461`
5×	`pow1_binary64_1483`
4×	`div-inv_binary64_1422` `associate-/l/_binary64_1374`
3×	`pow-unpow_binary64_1499` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
2×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `flip3-+_binary64_1428` `clear-num_binary64_1424` `pow-exp_binary64_1490` `rem-cube-cbrt_binary64_1447` `associate-/r/_binary64_1373` `flip-+_binary64_1399` `flip3--_binary64_1429`
1×	`diff-log_binary64_1514` `pow-pow_binary64_1494` `pow-to-exp_binary64_1491` `sub-neg_binary64_1418` `div-sub_binary64_1430` `unpow3_binary64_1488` `cube-div_binary64_1451` `cube-mult_binary64_1452`

Counts

4 → 168

Calls

4 calls:

31.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
13.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
9.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

series994.0ms (14.7%)

Counts

4 → 12

Calls

4 calls:

619.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
156.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
118.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
100.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5355	6100

prune700.0ms (10.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	180	6	186

Merged error: 15.7b

Counts

186 → 6

Compiler

Compiled 8432 to 7486 computations (11.2% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
0.2b	(/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3))
1.3b	(+.f64 1/8 (/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3)))

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_1425`
64×	`times-frac_binary64_1431`
48×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446`
19×	`associate-/r*_binary64_1371`
15×	`distribute-lft-out_binary64_1378`
13×	`add-exp-log_binary64_1460`
12×	`unpow-prod-down_binary64_1501` `cube-prod_binary64_1450`
11×	`associate-/l*_binary64_1372`
10×	`add-cbrt-cube_binary64_1458`
6×	`add-log-exp_binary64_1461`
5×	`div-exp_binary64_1473`
4×	`flip3-+_binary64_1428` `unpow3_binary64_1488` `cube-mult_binary64_1452` `flip-+_binary64_1399` `associate-/l/_binary64_1374` `pow1_binary64_1483` `sqr-pow_binary64_1397`
3×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `div-inv_binary64_1422` `cbrt-undiv_binary64_1456`
2×	`associate-/r/_binary64_1373`
1×	`pow-to-exp_binary64_1491` `pow-exp_binary64_1490` `sum-log_binary64_1513` `+-commutative_binary64_1357`

Counts

4 → 150

Calls

4 calls:

29.0ms	(/.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
13.0ms	(+.f64 1/8 (/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3)))
9.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
6.0ms	(/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3))

series969.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

591.0ms	(/.f64 (+.f64 1/8 (/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
155.0ms	(+.f64 1/8 (/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3)))
119.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
104.0ms	(/.f64 -1/8 (pow.f64 (hypot.f64 1 x) 3))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5089	4289

prune567.0ms (8.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	162	6	168

Merged error: 15.7b

Counts

168 → 6

Compiler

Compiled 6980 to 6183 computations (11.4% saved)

regimes59.0ms (0.9%)

Compiler: Compiled 488 to 448 computations (8.2% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	70
1	39	70

end0.0ms (0%)

sample1.4s (20.7%)

Algorithm

1×

intervals

Results

519.0ms	2159×	body	2048	valid
182.0ms	4108×	body	128	valid
179.0ms	985×	body	1024	valid
68.0ms	508×	body	512	valid
19.0ms	240×	body	256	valid

Compiler

Compiled 299 to 276 computations (7.7% saved)

Details

analyze2.0ms (0%)

sample36.0ms (0.5%)

simplify162.0ms (2.4%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite31.0ms (0.5%)

series327.0ms (4.8%)

simplify73.0ms (1.1%)

prune100.0ms (1.5%)

localize11.0ms (0.2%)

rewrite53.0ms (0.8%)

series606.0ms (8.9%)

simplify76.0ms (1.1%)

prune233.0ms (3.4%)

localize18.0ms (0.3%)

rewrite83.0ms (1.2%)

series994.0ms (14.7%)

simplify99.0ms (1.5%)

prune700.0ms (10.3%)

localize18.0ms (0.3%)

rewrite76.0ms (1.1%)

series969.0ms (14.3%)

simplify64.0ms (0.9%)

prune567.0ms (8.4%)

regimes59.0ms (0.9%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.4s (20.7%)

Profiling