Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample13.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify95.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

prune7.0ms (0.4%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite19.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_1442`
23×	`add-sqr-sqrt_binary64_1464`
20×	`distribute-lft-out_binary64_1393`
18×	`times-frac_binary64_1448`
13×	`add-cube-cbrt_binary64_1477`
10×	`sqrt-prod_binary64_1458`
6×	`associate-/r*_binary64_1386`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
3×	`associate-/l*_binary64_1387`
2×	`associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

2 → 55

Calls

2 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series37.0ms (2%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify76.0ms (4%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5820	1014

prune65.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Merged error: 0b

Counts

62 → 4

Compiler

Compiled 891 to 663 computations (25.6% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite43.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64_1442`
48×	`add-sqr-sqrt_binary64_1464`
38×	`times-frac_binary64_1448`
32×	`distribute-lft-out_binary64_1393`
25×	`add-cube-cbrt_binary64_1477`
24×	`associate-r_binary64_1382`
16×	`add-exp-log_binary64_1480` `sqrt-prod_binary64_1458`
10×	`add-cbrt-cube_binary64_1478`
6×	`associate-/r*_binary64_1386` `pow1_binary64_1503`
5×	`add-log-exp_binary64_1481`
4×	`associate-/r/_binary64_1388` `prod-exp_binary64_1491` `div-exp_binary64_1493`
3×	`associate-/l_binary64_1387` `associate-l*_binary64_1383` `flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `1-exp_binary64_1486` `rec-exp_binary64_1492`
1×	`associate-r/_binary64_1384` `inv-pow_binary64_1527` `sum-log_binary64_1533` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `un-div-inv_binary64_1440`

Counts

3 → 106

Calls

3 calls:

18.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series53.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

28.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
17.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify83.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5437	1705

prune111.0ms (5.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	115	4	119

Merged error: 0b

Counts

119 → 4

Compiler

Compiled 1801 to 1477 computations (18% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
0.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

rewrite48.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`*-un-lft-identity_binary64_1442`
156×	`times-frac_binary64_1448`
111×	`add-sqr-sqrt_binary64_1464`
77×	`add-cube-cbrt_binary64_1477`
68×	`distribute-lft-out_binary64_1393`
34×	`sqrt-prod_binary64_1458`
25×	`associate-/r*_binary64_1386`
16×	`add-exp-log_binary64_1480`
10×	`add-cbrt-cube_binary64_1478`
9×	`associate-/l*_binary64_1387`
8×	`div-exp_binary64_1493`
6×	`div-inv_binary64_1439`
5×	`add-log-exp_binary64_1481`
4×	`cbrt-undiv_binary64_1476` `pow1_binary64_1503`
2×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`inv-pow_binary64_1527` `sum-log_binary64_1533` `associate-/r/_binary64_1388` `+-commutative_binary64_1372` `pow-flip_binary64_1516`

Counts

3 → 167

Calls

3 calls:

13.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
11.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series56.0ms (3%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
20.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify109.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4922	3652
1	4922	3652

prune184.0ms (9.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	176	4	180

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 3020 to 2275 computations (24.7% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1464`
3×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `associate-l_binary64_1383` `add-exp-log_binary64_1480` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
2×	`associate-*r/_binary64_1384`
1×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

1 → 22

Calls

1 calls:

6.0ms

(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))

series9.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

9.0ms

(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))

simplify68.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5166	310

prune19.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	25	4	29

Merged error: 0b

Counts

29 → 4

Compiler

Compiled 302 to 227 computations (24.8% saved)

regimes68.0ms (3.6%)

Compiler: Compiled 540 to 448 computations (17% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample689.0ms (36.4%)

Algorithm

1×

intervals

Results

242.0ms	7996×	body	128	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 278 to 232 computations (16.5% saved)

Details

analyze3.0ms (0.2%)

sample13.0ms (0.7%)

simplify95.0ms (5%)

prune7.0ms (0.4%)

localize6.0ms (0.3%)

rewrite19.0ms (1%)

series37.0ms (2%)

simplify76.0ms (4%)

prune65.0ms (3.4%)

localize7.0ms (0.3%)

rewrite43.0ms (2.3%)

series53.0ms (2.8%)

simplify83.0ms (4.4%)

prune111.0ms (5.9%)

localize7.0ms (0.4%)

rewrite48.0ms (2.5%)

series56.0ms (3%)

simplify109.0ms (5.7%)

prune184.0ms (9.7%)

localize6.0ms (0.3%)

rewrite7.0ms (0.4%)

series9.0ms (0.5%)

simplify68.0ms (3.6%)

prune19.0ms (1%)

regimes68.0ms (3.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample689.0ms (36.4%)

Profiling