Details

analyze158.0ms (4.9%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 11 to 11 computations (0% saved)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	28×	body	128	nan
0.0ms	10×	body	128	invalid

Compiler

Compiled 21 to 24 computations (-14.3% saved)

simplify161.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune4.0ms (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: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
0.2b	(*.f64 y (sqrt.f64 z))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1446`
6×	`associate-r_binary64_1367`
5×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
4×	`sqrt-prod_binary64_1440` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
3×	`associate-l_binary64_1368`
2×	`unswap-sqr_binary64_1393`
1×	`prod-exp_binary64_1471` `flip3-+_binary64_1428` `cbrt-unprod_binary64_1455` `sum-log_binary64_1513` `flip-+_binary64_1399` `+-commutative_binary64_1357` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

2 → 33

Calls

2 calls:

5.0ms	(*.f64 y (sqrt.f64 z))
3.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

series120.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

64.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
56.0ms	(*.f64 y (sqrt.f64 z))

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5064	474

prune41.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Merged error: 0.0b

Counts

40 → 7

Compiler

Compiled 608 to 287 computations (52.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 z))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_1440`
25×	`add-sqr-sqrt_binary64_1446`
18×	`associate-r_binary64_1367`
15×	`add-cube-cbrt_binary64_1457` `pow1_binary64_1483` `*-un-lft-identity_binary64_1425`
11×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`sqrt-pow1_binary64_1442`
4×	`associate-l_binary64_1368` `prod-exp_binary64_1471` `pow1/2_binary64_1502` `cbrt-unprod_binary64_1455` `rem-sqrt-square_binary64_1438` `add-log-exp_binary64_1461` `pow-prod-down_binary64_1493`
3×	`unswap-sqr_binary64_1393`
2×	`*-commutative_binary64_1358`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
2.0ms	(sqrt.f64 (sqrt.f64 z))
2.0ms	(sqrt.f64 (sqrt.f64 z))

series343.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt.f64 (sqrt.f64 z))
97.0ms	(sqrt.f64 (sqrt.f64 z))
81.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
66.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4918	1032
1	4918	1032

prune89.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Merged error: 0b

Counts

107 → 7

Compiler

Compiled 1751 to 654 computations (62.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

rewrite55.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`sqrt-prod_binary64_1440`
33×	`associate-r_binary64_1367`
28×	`add-sqr-sqrt_binary64_1446`
23×	`pow1_binary64_1483`
20×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
19×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
10×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `pow-prod-down_binary64_1493`
9×	`sqrt-pow1_binary64_1442`
5×	`associate-l_binary64_1368`
4×	`add-log-exp_binary64_1461`
3×	`unswap-sqr_binary64_1393` `pow1/2_binary64_1502` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 108

Calls

4 calls:

18.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
14.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
4.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))

series385.0ms (12%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
106.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
82.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
67.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5401	1566

prune113.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	120	7	127

Merged error: 0b

Counts

127 → 7

Compiler

Compiled 2647 to 860 computations (67.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))
0.6b	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))
0.6b	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))
0.6b	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))

rewrite37.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`cbrt-prod_binary64_1453` `sqrt-prod_binary64_1440`
73×	`add-sqr-sqrt_binary64_1446`
29×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
18×	`swap-sqr_binary64_1392`
16×	`unswap-sqr_binary64_1393`
12×	`associate-l_binary64_1368` `associate-r_binary64_1367`
11×	`pow1_binary64_1483`
9×	`pow1/3_binary64_1504`
6×	`add-exp-log_binary64_1460`
4×	`add-cbrt-cube_binary64_1458` `add-log-exp_binary64_1461`
2×	`pow-sqr_binary64_1398` `pow-prod-up_binary64_1492` `pow-prod-down_binary64_1493`
1×	`prod-exp_binary64_1471` `pow-plus_binary64_1485` `cbrt-unprod_binary64_1455` `pow2_binary64_1503` `*-commutative_binary64_1358`

Counts

4 → 127

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))
3.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))
3.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))
3.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))

series411.0ms (12.8%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))
103.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))
99.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))
99.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 z)))

simplify59.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4959	2356
1	4959	2356

prune138.0ms (4.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	139	7	146

Merged error: 0b

Counts

146 → 7

Compiler

Compiled 4070 to 902 computations (77.8% saved)

regimes98.0ms (3.1%)

Compiler: Compiled 714 to 510 computations (28.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	12
1	12	12

end0.0ms (0%)

sample706.0ms (22%)

Algorithm

1×

intervals

Results

308.0ms	8000×	body	128	valid
36.0ms	1052×	body	128	nan
15.0ms	419×	body	128	invalid

Compiler

Compiled 133 to 99 computations (25.6% saved)

Details

analyze158.0ms (4.9%)

sample23.0ms (0.7%)

simplify161.0ms (5%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite11.0ms (0.3%)

series120.0ms (3.7%)

simplify57.0ms (1.8%)

prune41.0ms (1.3%)

localize9.0ms (0.3%)

rewrite29.0ms (0.9%)

series343.0ms (10.7%)

simplify61.0ms (1.9%)

prune89.0ms (2.8%)

localize11.0ms (0.3%)

rewrite55.0ms (1.7%)

series385.0ms (12%)

simplify63.0ms (2%)

prune113.0ms (3.5%)

localize12.0ms (0.4%)

rewrite37.0ms (1.2%)

series411.0ms (12.8%)

simplify59.0ms (1.9%)

prune138.0ms (4.3%)

regimes98.0ms (3.1%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample706.0ms (22%)

Profiling