Details

analyze562.0ms (14.1%)

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%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 8 to 8 computations (0% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	36×	body	128	invalid

Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify166.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	160	14
1	160	14

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1461`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `add-cube-cbrt_binary64_1457` `sub-neg_binary64_1418` `add-sqr-sqrt_binary64_1446` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `flip3--_binary64_1429` `add-exp-log_binary64_1460` `*-un-lft-identity_binary64_1425`

Counts

1 → 11

Calls

1 calls:

5.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

series92.0ms (2.3%)

Counts

1 → 3

Calls

1 calls:

91.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6201	286

prune12.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.0b

Counts

15 → 3

Compiler

Compiled 202 to 59 computations (70.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
2.0b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
2.0b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1446`
24×	`sqrt-prod_binary64_1440`
21×	`pow1_binary64_1483`
16×	`sqrt-div_binary64_1441`
14×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
10×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442`
9×	`flip--_binary64_1400` `flip3--_binary64_1429`
8×	`swap-sqr_binary64_1392`
6×	`associate-l_binary64_1368` `associate-r_binary64_1367` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
5×	`pow-prod-up_binary64_1492`
4×	`unswap-sqr_binary64_1393` `frac-times_binary64_1435`
3×	`pow-sqr_binary64_1398` `pow-prod-down_binary64_1493`
2×	`associate-r/_binary64_1369` `associate-l/_binary64_1370` `rem-sqrt-square_binary64_1438`
1×	`diff-log_binary64_1514` `prod-exp_binary64_1471` `pow-plus_binary64_1485` `sub-neg_binary64_1418` `cbrt-unprod_binary64_1455` `rem-square-sqrt_binary64_1437` `pow2_binary64_1503` `sqrt-unprod_binary64_1444` `*-commutative_binary64_1358`

Counts

4 → 98

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
5.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series533.0ms (13.3%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
181.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
89.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
78.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify60.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5100	2569

prune81.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	109	4	113

Merged error: 0.0b

Counts

113 → 4

Compiler

Compiled 2327 to 441 computations (81% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.3b	(pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 3)
35.4b	(cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 3))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_1453`
9×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
6×	`unpow-prod-down_binary64_1501` `cube-prod_binary64_1450`
5×	`add-log-exp_binary64_1461`
4×	`add-cbrt-cube_binary64_1458` `cube-div_binary64_1451` `pow1_binary64_1483` `add-exp-log_binary64_1460`
3×	`flip--_binary64_1400` `pow-unpow_binary64_1499` `flip3--_binary64_1429`
2×	`cbrt-div_binary64_1454` `unpow3_binary64_1488` `cube-mult_binary64_1452` `sqr-pow_binary64_1397`
1×	`diff-log_binary64_1514` `pow-pow_binary64_1494` `pow-to-exp_binary64_1491` `sub-neg_binary64_1418` `pow-exp_binary64_1490` `rem-cube-cbrt_binary64_1447` `pow1/3_binary64_1504` `rem-cbrt-cube_binary64_1448`

Counts

3 → 59

Calls

3 calls:

7.0ms	(pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 3)
5.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 3))
4.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series471.0ms (11.8%)

Counts

3 → 9

Calls

3 calls:

308.0ms	(pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 3)
83.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 3))
80.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify52.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5244	1542

prune52.0ms (1.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

Compiler

Compiled 1085 to 382 computations (64.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2)
0.4b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2)) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
2.7b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
27.9b	(cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_1453`
30×	`add-sqr-sqrt_binary64_1446`
14×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
11×	`associate-l_binary64_1368` `unpow-prod-down_binary64_1501`
10×	`unswap-sqr_binary64_1393`
7×	`pow1_binary64_1483` `add-exp-log_binary64_1460`
6×	`unpow2_binary64_1487` `associate-r_binary64_1367`
5×	`sqr-pow_binary64_1397`
4×	`cbrt-div_binary64_1454` `add-cbrt-cube_binary64_1458` `pow1/3_binary64_1504` `add-log-exp_binary64_1461`
3×	`pow-unpow_binary64_1499`
2×	`flip--_binary64_1400` `associate-*r/_binary64_1369` `flip3--_binary64_1429` `pow-prod-down_binary64_1493`
1×	`pow-pow_binary64_1494` `prod-exp_binary64_1471` `pow-to-exp_binary64_1491` `cbrt-unprod_binary64_1455` `pow3_binary64_1505` `pow-exp_binary64_1490` `*-commutative_binary64_1358`

Counts

4 → 89

Calls

4 calls:

14.0ms	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2)) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
5.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2))
5.0ms	(pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2)
4.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series823.0ms (20.6%)

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2))
271.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
131.0ms	(pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2)
99.0ms	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)) 2)) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))

simplify109.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4936	3079
1	4936	3079

prune90.0ms (2.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	101	4	105

Merged error: 0.0b

Counts

105 → 4

Compiler

Compiled 2622 to 669 computations (74.5% saved)

regimes82.0ms (2%)

Compiler: Compiled 405 to 332 computations (18% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms (0%)

sample581.0ms (14.5%)

Algorithm

1×

intervals

Results

210.0ms	8000×	body	128	valid
37.0ms	1388×	body	128	invalid

Compiler

Compiled 68 to 57 computations (16.2% saved)

Details

analyze562.0ms (14.1%)

sample20.0ms (0.5%)

simplify166.0ms (4.2%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite6.0ms (0.1%)

series92.0ms (2.3%)

simplify67.0ms (1.7%)

prune12.0ms (0.3%)

localize8.0ms (0.2%)

rewrite41.0ms (1%)

series533.0ms (13.3%)

simplify60.0ms (1.5%)

prune81.0ms (2%)

localize8.0ms (0.2%)

rewrite22.0ms (0.5%)

series471.0ms (11.8%)

simplify52.0ms (1.3%)

prune52.0ms (1.3%)

localize11.0ms (0.3%)

rewrite39.0ms (1%)

series823.0ms (20.6%)

simplify109.0ms (2.7%)

prune90.0ms (2.3%)

regimes82.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample581.0ms (14.5%)

Profiling