Details

analyze22.0ms (1.5%)

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 10 to 8 computations (20% saved)

sample15.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify10.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

rewrite62.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`

Counts

3 → 71

Calls

3 calls:

7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 962 to 749 computations (22.1% saved)

series28.0ms (1.9%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 441 to 345 computations (21.8% saved)

simplify86.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

377×	`sub-neg_binary64`
341×	`associate-/r*_binary64`
327×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

89 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1318
1	254	1240
2	594	1219
3	1586	1202
4	4129	1202
5	4864	1202

prune21.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Error

Counts

45 → 4

Alt Table

Status	Error	Program
▶	20.4b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	39.9b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
	35.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

Compiler

Compiled 439 to 339 computations (22.8% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

rewrite15.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

4.0ms

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

Compiler

Compiled 301 to 227 computations (24.6% saved)

series9.0ms (0.6%)

Error

Counts

1 → 6

Calls

1 calls:

8.0ms

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

Compiler

Compiled 94 to 75 computations (20.2% saved)

simplify76.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

564×	`unsub-neg_binary64`
468×	`associate-l_binary64`
347×	`associate-r_binary64`
344×	`unswap-sqr_binary64`
285×	`times-frac_binary64`

Counts

28 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	370
1	148	328
2	479	328
3	1526	328
4	3025	328
5	4560	328
6	5294	328

prune8.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	16	4	20

Error

Counts

20 → 4

Alt Table

Status	Error	Program
✓	20.4b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	39.9b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	35.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

Compiler

Compiled 176 to 133 computations (24.4% saved)

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
34.7b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

rewrite110.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

142×	`*-un-lft-identity_binary64`
91×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
68×	`distribute-lft-out_binary64`
57×	`add-cube-cbrt_binary64`

Counts

4 → 187

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
8.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

Compiler

Compiled 2476 to 2008 computations (18.9% saved)

series53.0ms (3.6%)

Error

Counts

4 → 24

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
12.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
11.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

Compiler

Compiled 767 to 635 computations (17.2% saved)

simplify159.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/l*_binary64`
444×	`log-div_binary64`
346×	`unswap-sqr_binary64`
262×	`associate-/l/_binary64`
184×	`associate-/r/_binary64`

Counts

211 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	4430
1	496	4042
2	1471	3945
3	4516	3945
4	5136	3945

prune39.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	162	4	166

Error

Counts

166 → 4

Alt Table

Status	Error	Program
✓	20.4b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	39.9b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	35.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

Compiler

Compiled 1110 to 875 computations (21.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
4.5b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite27.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`sqrt-prod_binary64`
7×	`cancel-sign-sub-inv_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 41

Calls

2 calls:

5.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))
2.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 508 to 445 computations (12.4% saved)

series17.0ms (1.1%)

Error

Counts

2 → 12

Calls

2 calls:

6.0ms	(-.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 309 to 261 computations (15.5% saved)

simplify104.0ms (7%)

Algorithm

1×	egg-herbie

Rules

538×	`unsub-neg_binary64`
421×	`neg-mul-1_binary64`
367×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
281×	`distribute-rgt-in_binary64`

Counts

53 → 29

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	636
1	191	610
2	417	595
3	1263	586
4	3107	562
5	4668	562
6	4813	562
7	4939	562

prune12.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	29	4	33

Error

Counts

33 → 4

Alt Table

Status	Error	Program
	20.4b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))
	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	39.9b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
	35.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

Compiler

Compiled 285 to 239 computations (16.1% saved)

regimes89.0ms (6%)

Accuracy

Total 0.2b remaining (97.7%)

Threshold costs 0.2b (97.7%)

Compiler

Compiled 1166 to 906 computations (22.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	13	15
2	12	15

end0.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample495.0ms (33.3%)

Algorithm

1×

intervals

Results

283.0ms	7998×	body	128	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 60 to 49 computations (18.3% saved)

Details

analyze22.0ms (1.5%)

sample15.0ms (1%)

simplify10.0ms (0.7%)

prune1.0ms (0.1%)

localize5.0ms (0.4%)

rewrite62.0ms (4.2%)

series28.0ms (1.9%)

simplify86.0ms (5.8%)

prune21.0ms (1.4%)

localize4.0ms (0.3%)

rewrite15.0ms (1%)

series9.0ms (0.6%)

simplify76.0ms (5.1%)

prune8.0ms (0.6%)

localize8.0ms (0.5%)

rewrite110.0ms (7.4%)

series53.0ms (3.6%)

simplify159.0ms (10.7%)

prune39.0ms (2.6%)

localize5.0ms (0.3%)

rewrite27.0ms (1.8%)

series17.0ms (1.1%)

simplify104.0ms (7%)

prune12.0ms (0.8%)

regimes89.0ms (6%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample495.0ms (33.3%)

Profiling