Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify431.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (261.0ms)

Iter	Nodes	Cost
0	5111	37

prune7.0ms (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: 0.8b

Counts

2 → 2

Compiler

Compiled 145 to 102 computations (29.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
7.2b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite112.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1455`
34×	`distribute-lft-out_binary64_1406` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
24×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
21×	`associate-r_binary64_1395` `add-sqr-sqrt_binary64_1477`
18×	`associate-/r/_binary64_1401`
16×	`frac-times_binary64_1465`
15×	`add-cube-cbrt_binary64_1490`
14×	`times-frac_binary64_1461`
13×	`pow1_binary64_1516`
11×	`swap-sqr_binary64_1422`
10×	`prod-exp_binary64_1504` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `cbrt-unprod_binary64_1488` `associate-*l/_binary64_1398`
9×	`associate-l_binary64_1396`
8×	`associate-*r/_binary64_1397`
7×	`associate-/l/_binary64_1402`
6×	`associate-/r*_binary64_1399`
5×	`associate-/l*_binary64_1400`
4×	`add-log-exp_binary64_1494`
3×	`div-inv_binary64_1452` `unswap-sqr_binary64_1423`
2×	`clear-num_binary64_1454` `*-commutative_binary64_1386` `frac-2neg_binary64_1466` `pow-prod-down_binary64_1526`
1×	`distribute-rgt-in_binary64_1405` `pow-plus_binary64_1518` `pow2_binary64_1536` `distribute-lft-in_binary64_1404` `pow-prod-up_binary64_1525` `pow-sqr_binary64_1428`

Counts

4 → 158

Calls

4 calls:

32.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
18.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series711.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
251.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
111.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
33.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4982	3959
1	4982	3959

prune647.0ms (8.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	7	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 13155 to 9440 computations (28.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
0.0b	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

rewrite120.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64_1455`
89×	`times-frac_binary64_1461`
82×	`distribute-lft-out_binary64_1406`
60×	`add-sqr-sqrt_binary64_1477`
48×	`add-cube-cbrt_binary64_1490`
38×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
26×	`associate-r_binary64_1395` `associate-l_binary64_1396`
15×	`div-exp_binary64_1506` `associate-/r*_binary64_1399` `cbrt-undiv_binary64_1489`
10×	`associate-/r/_binary64_1401`
9×	`associate-/l*_binary64_1400`
8×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
7×	`flip-+_binary64_1429` `associate-/l/_binary64_1402` `flip3-+_binary64_1458`
6×	`pow1_binary64_1516`
5×	`div-inv_binary64_1452`
4×	`add-log-exp_binary64_1494` `unswap-sqr_binary64_1423`
3×	`clear-num_binary64_1454` `frac-2neg_binary64_1466`
2×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `associate-l/_binary64_1398`
1×	`*-commutative_binary64_1386` `pow-prod-down_binary64_1526`

Counts

4 → 202

Calls

4 calls:

36.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

series512.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
180.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
60.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
49.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify107.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4953	5499
1	4953	5499

prune434.0ms (5.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	214	7	221

Merged error: 0b

Counts

221 → 7

Compiler

Compiled 8627 to 5641 computations (34.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
0.1b	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))

rewrite221.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

808×	`*-un-lft-identity_binary64_1455`
627×	`times-frac_binary64_1461`
352×	`sqrt-prod_binary64_1471`
307×	`distribute-lft-out_binary64_1406`
265×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490`
58×	`associate-/r*_binary64_1399`
42×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
23×	`associate-/r/_binary64_1401`
21×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
20×	`sqrt-div_binary64_1472`
17×	`associate-/l*_binary64_1400`
14×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
12×	`div-inv_binary64_1452`
9×	`associate-/l/_binary64_1402`
6×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
4×	`pow1_binary64_1516` `clear-num_binary64_1454` `add-log-exp_binary64_1494` `frac-2neg_binary64_1466`
1×	`associate-r/_binary64_1397` `frac-times_binary64_1465` `associate-l/_binary64_1398`

Counts

4 → 500

Calls

4 calls:

57.0ms	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
27.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
14.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series399.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
79.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))
51.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
49.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify188.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4978	16829
1	4978	16829

prune1.6s (21.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	512	0	512
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	512	7	519

Merged error: 0b

Counts

519 → 7

Compiler

Compiled 20557 to 13776 computations (33% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 beta 1))
0.2b	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
7.2b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite125.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64_1455`
58×	`add-sqr-sqrt_binary64_1477`
56×	`add-exp-log_binary64_1493`
50×	`cbrt-prod_binary64_1486`
49×	`associate-r_binary64_1395`
47×	`times-frac_binary64_1461`
40×	`add-cbrt-cube_binary64_1491`
37×	`distribute-lft-out_binary64_1406`
34×	`add-cube-cbrt_binary64_1490`
24×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
22×	`associate-l_binary64_1396`
18×	`pow1_binary64_1516`
14×	`cbrt-div_binary64_1487` `div-exp_binary64_1506` `frac-times_binary64_1465` `cbrt-undiv_binary64_1489`
13×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
10×	`unswap-sqr_binary64_1423`
9×	`associate-*r/_binary64_1397` `swap-sqr_binary64_1422`
8×	`associate-*l/_binary64_1398`
7×	`pow1/3_binary64_1537`
6×	`pow-prod-down_binary64_1526`
4×	`associate-/r/_binary64_1401` `add-log-exp_binary64_1494`
3×	`*-commutative_binary64_1386`
2×	`div-inv_binary64_1452` `pow-prod-up_binary64_1525` `pow-sqr_binary64_1428`
1×	`pow-plus_binary64_1518` `pow2_binary64_1536`

Counts

4 → 189

Calls

4 calls:

41.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
34.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
17.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
3.0ms	(cbrt.f64 (+.f64 beta 1))

series418.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
110.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
52.0ms	(cbrt.f64 (+.f64 beta 1))
45.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5304	5176

prune387.0ms (5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	201	7	208

Merged error: 0b

Counts

208 → 7

Compiler

Compiled 7728 to 5214 computations (32.5% saved)

regimes40.0ms (0.5%)

Compiler: Compiled 436 to 330 computations (24.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample960.0ms (12.4%)

Algorithm

1×

intervals

Results

467.0ms	8000×	body	128	valid
139.0ms	8000×	pre	128	true

Compiler

Compiled 283 to 210 computations (25.8% saved)

Details

analyze5.0ms (0.1%)

sample28.0ms (0.4%)

simplify431.0ms (5.6%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

rewrite112.0ms (1.4%)

series711.0ms (9.2%)

simplify87.0ms (1.1%)

prune647.0ms (8.4%)

localize15.0ms (0.2%)

rewrite120.0ms (1.6%)

series512.0ms (6.6%)

simplify107.0ms (1.4%)

prune434.0ms (5.6%)

localize16.0ms (0.2%)

rewrite221.0ms (2.9%)

series399.0ms (5.2%)

simplify188.0ms (2.4%)

prune1.6s (21.2%)

localize20.0ms (0.3%)

rewrite125.0ms (1.6%)

series418.0ms (5.4%)

simplify83.0ms (1.1%)

prune387.0ms (5%)

regimes40.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample960.0ms (12.4%)

Profiling