Details

analyze113.0ms (2%)

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify206.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4981	40
1	4981	40

prune8.0ms (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: 0.4b

Counts

2 → 2

Compiler

Compiled 80 to 61 computations (23.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 -6 v))
0.2b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
0.3b	(*.f64 PI.f64 t)
0.5b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
20×	`pow1_binary64_1483`
16×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-*r/_binary64_1369`
13×	`add-sqr-sqrt_binary64_1446`
12×	`associate-l_binary64_1368` `sqrt-div_binary64_1441`
11×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
10×	`pow-prod-down_binary64_1493`
8×	`associate-/r/_binary64_1373` `frac-times_binary64_1435`
7×	`flip--_binary64_1400` `flip3--_binary64_1429`
6×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
5×	`associate-r_binary64_1367`
4×	`distribute-lft-in_binary64_1376` `sub-neg_binary64_1418` `distribute-rgt-in_binary64_1377` `div-exp_binary64_1473` `associate-*l/_binary64_1370` `cbrt-undiv_binary64_1456` `add-log-exp_binary64_1461`
3×	`times-frac_binary64_1431` `sqrt-prod_binary64_1440` `associate-/l_binary64_1372` `-commutative_binary64_1358`
2×	`associate-/l/_binary64_1374`
1×	`frac-2neg_binary64_1436` `associate-/r*_binary64_1371` `unswap-sqr_binary64_1393` `clear-num_binary64_1424` `div-sub_binary64_1430` `div-inv_binary64_1422`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
14.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
5.0ms	(.f64 v (.f64 -6 v))
4.0ms	(*.f64 PI.f64 t)

series604.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

290.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
253.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
34.0ms	(.f64 v (.f64 -6 v))
27.0ms	(*.f64 PI.f64 t)

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4959	3576
1	4959	3576

prune227.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 0.0b

Counts

122 → 7

Compiler

Compiled 4467 to 2792 computations (37.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 v (.f64 v -6))
0.3b	(*.f64 PI.f64 t)
0.5b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1431`
50×	`add-sqr-sqrt_binary64_1446`
48×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
34×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
30×	`sqrt-prod_binary64_1440`
27×	`associate-/l*_binary64_1372`
11×	`pow1_binary64_1483`
10×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
8×	`associate-/r/_binary64_1373`
7×	`associate-/r*_binary64_1371`
6×	`associate-l_binary64_1368` `sqrt-div_binary64_1441`
4×	`associate-r_binary64_1367` `div-inv_binary64_1422` `add-log-exp_binary64_1461` `pow-prod-down_binary64_1493`
3×	`flip3-+_binary64_1428` `div-sub_binary64_1430` `flip-+_binary64_1399` `associate-/l/_binary64_1374`
2×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-r/_binary64_1369` `flip3--_binary64_1429` `-commutative_binary64_1358`
1×	`unswap-sqr_binary64_1393`

Counts

4 → 155

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
5.0ms	(.f64 v (.f64 v -6))
4.0ms	(*.f64 PI.f64 t)

series499.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

308.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
130.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
34.0ms	(.f64 v (.f64 v -6))
27.0ms	(*.f64 PI.f64 t)

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4931	6101
1	4931	6101

prune326.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	169	5	174

Merged error: 0b

Counts

174 → 5

Compiler

Compiled 6420 to 4103 computations (36.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
0.3b	(*.f64 PI.f64 t)
0.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
1.0b	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite67.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log_binary64_1460`
52×	`add-sqr-sqrt_binary64_1446`
49×	`add-cbrt-cube_binary64_1458`
46×	`times-frac_binary64_1431`
40×	`*-un-lft-identity_binary64_1425`
38×	`add-cube-cbrt_binary64_1457`
32×	`prod-exp_binary64_1471`
27×	`associate-l_binary64_1368`
25×	`div-exp_binary64_1473`
23×	`sqrt-prod_binary64_1440`
18×	`cbrt-unprod_binary64_1455`
14×	`cbrt-undiv_binary64_1456`
12×	`associate-r_binary64_1367`
10×	`pow1_binary64_1483`
8×	`associate-/r/_binary64_1373`
7×	`associate-/r*_binary64_1371`
6×	`unswap-sqr_binary64_1393` `associate-/l*_binary64_1372`
5×	`associate-*r/_binary64_1369` `1-exp_binary64_1466` `rec-exp_binary64_1472`
4×	`sqrt-div_binary64_1441` `div-inv_binary64_1422` `add-log-exp_binary64_1461`
3×	`flip--_binary64_1400` `pow-flip_binary64_1496` `flip3--_binary64_1429`
2×	`frac-2neg_binary64_1436` `flip3-+_binary64_1428` `clear-num_binary64_1424` `flip-+_binary64_1399` `associate-/l/_binary64_1374` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`
1×	`inv-pow_binary64_1507` `pow1/2_binary64_1502` `div-sub_binary64_1430` `sqrt-pow1_binary64_1442` `associate-*l/_binary64_1370` `frac-times_binary64_1435`

Counts

4 → 167

Calls

4 calls:

24.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
11.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
4.0ms	(*.f64 PI.f64 t)

series534.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
124.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
81.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
25.0ms	(*.f64 PI.f64 t)

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4932	5762
1	4932	5762

prune317.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	179	5	184

Merged error: 0b

Counts

184 → 5

Compiler

Compiled 6574 to 4229 computations (35.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
1.0b	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`sqrt-prod_binary64_1440`
76×	`times-frac_binary64_1431`
70×	`add-sqr-sqrt_binary64_1446`
60×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
12×	`associate-/r*_binary64_1371`
10×	`sqrt-div_binary64_1441`
8×	`add-cbrt-cube_binary64_1458` `associate-/r/_binary64_1373` `add-exp-log_binary64_1460`
6×	`associate-/l*_binary64_1372` `pow1_binary64_1483` `rem-sqrt-square_binary64_1438`
4×	`flip3-+_binary64_1428` `div-inv_binary64_1422` `flip-+_binary64_1399` `associate-/l/_binary64_1374` `add-log-exp_binary64_1461`
2×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `pow1/2_binary64_1502` `clear-num_binary64_1424` `div-sub_binary64_1430` `sqrt-pow1_binary64_1442` `div-exp_binary64_1473` `flip3--_binary64_1429` `cbrt-undiv_binary64_1456`

Counts

4 → 162

Calls

4 calls:

11.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
9.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

series675.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
213.0ms	(sqrt.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))))
121.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
117.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5166	7128

prune649.0ms (11.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	174	5	179

Merged error: 0b

Counts

179 → 5

Compiler

Compiled 10348 to 7061 computations (31.8% saved)

regimes48.0ms (0.8%)

Compiler: Compiled 493 to 391 computations (20.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	40
1	62	40

end0.0ms (0%)

sample866.0ms (15%)

Algorithm

1×

intervals

Results

543.0ms	8000×	body	128	valid
1.0ms	17×	body	128	nan

Compiler

Compiled 216 to 169 computations (21.8% saved)

Details

analyze113.0ms (2%)

sample28.0ms (0.5%)

simplify206.0ms (3.6%)

prune8.0ms (0.1%)

localize16.0ms (0.3%)

rewrite54.0ms (0.9%)

series604.0ms (10.5%)

simplify80.0ms (1.4%)

prune227.0ms (3.9%)

localize16.0ms (0.3%)

rewrite58.0ms (1%)

series499.0ms (8.7%)

simplify97.0ms (1.7%)

prune326.0ms (5.7%)

localize19.0ms (0.3%)

rewrite67.0ms (1.2%)

series534.0ms (9.3%)

simplify96.0ms (1.7%)

prune317.0ms (5.5%)

localize19.0ms (0.3%)

rewrite64.0ms (1.1%)

series675.0ms (11.7%)

simplify81.0ms (1.4%)

prune649.0ms (11.2%)

regimes48.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample866.0ms (15%)

Profiling