Details

analyze108.0ms (1.9%)

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%	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)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify202.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4981	40
1	4981	40

prune5.0ms (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: 0.3b

Counts

2 → 2

Compiler

Compiled 80 to 61 computations (23.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.2b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
18×	`associate-*r/_binary64_1369`
16×	`pow1_binary64_1483`
13×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `add-sqr-sqrt_binary64_1446`
10×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
8×	`flip--_binary64_1400` `sqrt-div_binary64_1441` `associate-r_binary64_1367` `associate-/r/_binary64_1373` `flip3--_binary64_1429`
7×	`associate-l_binary64_1368` `pow-prod-down_binary64_1493`
4×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456` `add-log-exp_binary64_1461` `frac-times_binary64_1435`
3×	`times-frac_binary64_1431` `associate-/l_binary64_1372` `-commutative_binary64_1358`
2×	`unswap-sqr_binary64_1393` `associate-/l/_binary64_1374` `associate-*l/_binary64_1370`
1×	`frac-2neg_binary64_1436` `associate-/r*_binary64_1371` `clear-num_binary64_1424` `div-sub_binary64_1430` `sqrt-prod_binary64_1440` `div-inv_binary64_1422`

Counts

4 → 94

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
10.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
6.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series624.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

368.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
191.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
40.0ms	(.f64 5 (.f64 v v))
25.0ms	(*.f64 PI.f64 t)

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4995	2769
1	4995	2769

prune182.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 0.1b

Counts

108 → 9

Compiler

Compiled 4073 to 2525 computations (38% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
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)))))
0.4b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite53.0ms (1%)

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`
14×	`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×	`unswap-sqr_binary64_1393` `associate-/l/_binary64_1374`
1×	`frac-2neg_binary64_1436` `associate-/r*_binary64_1371` `clear-num_binary64_1424` `div-sub_binary64_1430` `div-inv_binary64_1422`

Counts

4 → 109

Calls

4 calls:

16.0ms	(/.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))))
6.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series615.0ms (11%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(/.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)))))
238.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
35.0ms	(.f64 5 (.f64 v v))
27.0ms	(*.f64 PI.f64 t)

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4976	3590
1	4976	3590

prune210.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0.0b

Counts

130 → 6

Compiler

Compiled 4434 to 2771 computations (37.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 5)
0.2b	(*.f64 PI.f64 t)
0.4b	(/.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)))))

rewrite59.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1431`
51×	`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×	`sqrt-div_binary64_1441` `associate-r_binary64_1367`
4×	`associate-l_binary64_1368` `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` `unswap-sqr_binary64_1393` `clear-num_binary64_1424` `associate-r/_binary64_1369` `flip3--_binary64_1429` `-commutative_binary64_1358`

Counts

4 → 156

Calls

4 calls:

17.0ms	(/.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))))
8.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 (.f64 v v) 5)
4.0ms	(*.f64 PI.f64 t)

series494.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(/.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))))
132.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
33.0ms	(.f64 (.f64 v v) 5)
27.0ms	(*.f64 PI.f64 t)

simplify114.0ms (2%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4937	6117
1	4937	6117

prune333.0ms (6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	168	6	174

Merged error: 0b

Counts

174 → 6

Compiler

Compiled 6487 to 4154 computations (36% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 5)
0.2b	(*.f64 PI.f64 t)
0.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
1.0b	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite83.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`sqrt-prod_binary64_1440`
82×	`times-frac_binary64_1431`
80×	`add-sqr-sqrt_binary64_1446`
63×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
46×	`associate-l_binary64_1368`
45×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
18×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `associate-r_binary64_1367`
13×	`pow1_binary64_1483`
11×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
7×	`unswap-sqr_binary64_1393`
6×	`associate-/r_binary64_1371` `sqrt-div_binary64_1441` `associate-/r/_binary64_1373` `associate-/l_binary64_1372`
5×	`pow-prod-down_binary64_1493`
4×	`add-log-exp_binary64_1461`
3×	`associate-r/_binary64_1369` `div-inv_binary64_1422` `-commutative_binary64_1358`
2×	`flip--_binary64_1400` `flip3-+_binary64_1428` `flip-+_binary64_1399` `associate-/l/_binary64_1374` `flip3--_binary64_1429`
1×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `sqrt-undiv_binary64_1445` `associate-*l/_binary64_1370` `frac-times_binary64_1435`

Counts

4 → 189

Calls

4 calls:

31.0ms	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
12.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
6.0ms	(.f64 (.f64 v v) 5)
4.0ms	(*.f64 PI.f64 t)

series476.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
116.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
32.0ms	(.f64 (.f64 v v) 5)
25.0ms	(*.f64 PI.f64 t)

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5199	7956

prune504.0ms (9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	201	6	207

Merged error: 0b

Counts

207 → 6

Compiler

Compiled 9352 to 6076 computations (35% saved)

regimes76.0ms (1.4%)

Compiler: Compiled 868 to 670 computations (22.8% 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%)

sample1.1s (18.9%)

Algorithm

1×

intervals

Results

513.0ms	8000×	body	128	valid
0.0ms	7×	body	128	nan

Compiler

Compiled 268 to 206 computations (23.1% saved)

Details

analyze108.0ms (1.9%)

sample23.0ms (0.4%)

simplify202.0ms (3.6%)

prune5.0ms (0.1%)

localize15.0ms (0.3%)

rewrite49.0ms (0.9%)

series624.0ms (11.2%)

simplify69.0ms (1.2%)

prune182.0ms (3.3%)

localize15.0ms (0.3%)

rewrite53.0ms (1%)

series615.0ms (11%)

simplify80.0ms (1.4%)

prune210.0ms (3.8%)

localize15.0ms (0.3%)

rewrite59.0ms (1.1%)

series494.0ms (8.9%)

simplify114.0ms (2%)

prune333.0ms (6%)

localize18.0ms (0.3%)

rewrite83.0ms (1.5%)

series476.0ms (8.5%)

simplify100.0ms (1.8%)

prune504.0ms (9%)

regimes76.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (18.9%)

Profiling