Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify217.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4983	13
1	4983	13

prune6.0ms (0.2%)

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: 0.5b

Counts

2 → 2

Compiler

Compiled 77 to 58 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.6b	(/.f64 1 (*.f64 i i))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1477`
35×	`times-frac_binary64_1461`
33×	`*-un-lft-identity_binary64_1455`
17×	`add-cube-cbrt_binary64_1490`
15×	`add-exp-log_binary64_1493`
12×	`difference-of-squares_binary64_1424`
10×	`pow1_binary64_1516`
9×	`associate-/r*_binary64_1399` `add-cbrt-cube_binary64_1491`
8×	`distribute-lft-out--_binary64_1407`
6×	`pow-flip_binary64_1529` `associate-/l*_binary64_1400` `div-inv_binary64_1452`
5×	`div-exp_binary64_1506`
3×	`prod-exp_binary64_1504` `cbrt-undiv_binary64_1489`
2×	`associate-/r/_binary64_1401` `1-exp_binary64_1499` `clear-num_binary64_1454` `add-log-exp_binary64_1494` `frac-2neg_binary64_1466` `rec-exp_binary64_1505`
1×	`inv-pow_binary64_1540` `pow-plus_binary64_1518` `flip--_binary64_1430` `pow2_binary64_1536` `cbrt-unprod_binary64_1488` `flip3--_binary64_1459` `pow-prod-up_binary64_1525` `pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`

Counts

2 → 81

Calls

2 calls:

9.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(/.f64 1 (*.f64 i i))

series63.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

39.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
24.0ms	(/.f64 1 (*.f64 i i))

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5040	1212

prune159.0ms (4.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 0b

Counts

89 → 5

Compiler

Compiled 2474 to 2022 computations (18.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
0.1b	(/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i))))
0.1b	(/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i))))

rewrite47.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_1455`
65×	`add-sqr-sqrt_binary64_1477`
58×	`times-frac_binary64_1461`
39×	`add-cube-cbrt_binary64_1490`
21×	`associate-r_binary64_1395`
19×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
18×	`associate-l_binary64_1396`
9×	`associate-/r*_binary64_1399`
8×	`associate-/r/_binary64_1401`
7×	`distribute-lft-out_binary64_1406` `distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
6×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400`
5×	`pow1_binary64_1516`
4×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `unswap-sqr_binary64_1423`
3×	`add-log-exp_binary64_1494`
2×	`flip-+_binary64_1429` `clear-num_binary64_1454` `flip--_binary64_1430` `frac-2neg_binary64_1466` `flip3-+_binary64_1458` `flip3--_binary64_1459`
1×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `-commutative_binary64_1386` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526`

Counts

3 → 133

Calls

3 calls:

22.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
6.0ms	(/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i))))
6.0ms	(/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i))))

series283.0ms (8%)

Counts

3 → 9

Calls

3 calls:

142.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i)))))
75.0ms	(/.f64 1/2 (-.f64 2 (fabs.f64 (/.f64 1 i))))
66.0ms	(/.f64 1/2 (+.f64 2 (fabs.f64 (/.f64 1 i))))

simplify89.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5458	3252

prune229.0ms (6.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	142	5	147

Merged error: 0b

Counts

147 → 5

Compiler

Compiled 3597 to 3213 computations (10.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite72.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64_1477`
96×	`times-frac_binary64_1461` `*-un-lft-identity_binary64_1455`
47×	`add-cube-cbrt_binary64_1490`
30×	`associate-r_binary64_1395`
21×	`difference-of-squares_binary64_1424` `associate-l_binary64_1396`
19×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
18×	`div-inv_binary64_1452`
14×	`distribute-lft-out_binary64_1406` `distribute-lft-out--_binary64_1407`
13×	`associate-/r*_binary64_1399`
8×	`associate-/r/_binary64_1401`
6×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400`
5×	`pow1_binary64_1516`
4×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `unswap-sqr_binary64_1423`
3×	`add-log-exp_binary64_1494`
2×	`flip-+_binary64_1429` `clear-num_binary64_1454` `flip--_binary64_1430` `frac-2neg_binary64_1466` `flip3-+_binary64_1458` `flip3--_binary64_1459`
1×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `-commutative_binary64_1386` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526`

Counts

3 → 161

Calls

3 calls:

37.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
9.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series85.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

50.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
18.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
17.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

simplify94.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5149	3334

prune247.0ms (7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	170	5	175

Merged error: 0b

Counts

175 → 5

Compiler

Compiled 3953 to 3438 computations (13% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

0.1b

(/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i)))

0.2b

(/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i)))

rewrite93.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`add-sqr-sqrt_binary64_1477`
139×	`times-frac_binary64_1461`
116×	`*-un-lft-identity_binary64_1455`
55×	`add-cube-cbrt_binary64_1490`
54×	`associate-r_binary64_1395`
53×	`cbrt-prod_binary64_1486`
39×	`difference-of-squares_binary64_1424`
31×	`add-exp-log_binary64_1493`
26×	`distribute-lft-out--_binary64_1407`
21×	`add-cbrt-cube_binary64_1491`
20×	`div-inv_binary64_1452`
13×	`associate-/r*_binary64_1399`
11×	`associate-l_binary64_1396`
10×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
9×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
8×	`associate-/r/_binary64_1401`
7×	`associate-/l*_binary64_1400`
6×	`distribute-lft-out_binary64_1406` `unswap-sqr_binary64_1423`
5×	`pow1_binary64_1516`
3×	`add-log-exp_binary64_1494`
2×	`flip-+_binary64_1429` `clear-num_binary64_1454` `flip--_binary64_1430` `frac-2neg_binary64_1466` `flip3-+_binary64_1458` `flip3--_binary64_1459`
1×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `-commutative_binary64_1386` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526`

Counts

3 → 198

Calls

3 calls:

40.0ms

(*.f64 (/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

12.0ms

(/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i)))

11.0ms

(/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i)))

series174.0ms (4.9%)

Counts

3 → 9

Calls

3 calls:

98.0ms

(*.f64 (/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

44.0ms

(/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i)))

32.0ms

(/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i)))

simplify109.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4934	5210
1	4934	5210

prune421.0ms (11.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	207	5	212

Merged error: 0b

Counts

212 → 5

Compiler

Compiled 5675 to 5057 computations (10.9% saved)

regimes60.0ms (1.7%)

Compiler: Compiled 604 to 508 computations (15.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample931.0ms (26.3%)

Algorithm

1×

intervals

Results

400.0ms	8000×	body	128	valid
98.0ms	8000×	pre	128	true

Compiler

Compiled 320 to 271 computations (15.3% saved)

Details

analyze6.0ms (0.2%)

sample22.0ms (0.6%)

simplify217.0ms (6.1%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite21.0ms (0.6%)

series63.0ms (1.8%)

simplify75.0ms (2.1%)

prune159.0ms (4.5%)

localize10.0ms (0.3%)

rewrite47.0ms (1.3%)

series283.0ms (8%)

simplify89.0ms (2.5%)

prune229.0ms (6.5%)

localize8.0ms (0.2%)

rewrite72.0ms (2%)

series85.0ms (2.4%)

simplify94.0ms (2.7%)

prune247.0ms (7%)

localize13.0ms (0.4%)

rewrite93.0ms (2.6%)

series174.0ms (4.9%)

simplify109.0ms (3.1%)

prune421.0ms (11.9%)

regimes60.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample931.0ms (26.3%)

Profiling