Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	61×	body	1024	valid
4.0ms	140×	body	128	valid
3.0ms	37×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify170.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune3.0ms (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: 28.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_13241` `sqrt-prod_binary64_13235` `*-un-lft-identity_binary64_13220`
4×	`difference-of-squares_binary64_13189` `add-log-exp_binary64_13256`
3×	`pow1_binary64_13278` `distribute-lft-out--_binary64_13174` `add-cube-cbrt_binary64_13252`
2×	`sqrt-div_binary64_13236` `add-exp-log_binary64_13255` `distribute-lft-out_binary64_13173` `add-cbrt-cube_binary64_13253`
1×	`flip--_binary64_13195` `sqrt-pow1_binary64_13237` `flip-+_binary64_13194` `diff-log_binary64_13309` `rem-sqrt-square_binary64_13233` `flip3-+_binary64_13223` `sub-neg_binary64_13213` `pow1/2_binary64_13297` `flip3--_binary64_13224`

Counts

2 → 34

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series95.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

70.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify101.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4907	747
1	4907	747

prune44.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

Compiler

Compiled 629 to 416 computations (33.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_13220`
24×	`sqrt-prod_binary64_13235`
21×	`distribute-lft-out_binary64_13173`
18×	`times-frac_binary64_13226`
16×	`add-sqr-sqrt_binary64_13241`
15×	`add-cube-cbrt_binary64_13252`
7×	`add-exp-log_binary64_13255`
6×	`associate-/r*_binary64_13166`
5×	`pow1_binary64_13278` `add-log-exp_binary64_13256` `add-cbrt-cube_binary64_13253`
3×	`flip-+_binary64_13194` `associate-/l*_binary64_13167` `flip3-+_binary64_13223`
2×	`associate-/r/_binary64_13168` `sqrt-div_binary64_13236` `div-exp_binary64_13268`
1×	`clear-num_binary64_13219` `pow-flip_binary64_13291` `rec-exp_binary64_13267` `sum-log_binary64_13308` `sqrt-pow1_binary64_13237` `div-inv_binary64_13217` `+-commutative_binary64_13152` `rem-sqrt-square_binary64_13233` `frac-2neg_binary64_13231` `1-exp_binary64_13261` `cbrt-undiv_binary64_13251` `pow1/2_binary64_13297` `inv-pow_binary64_13302`

Counts

3 → 75

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series134.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
40.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5545	1516

prune94.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	80	7	87

Merged error: 0.0b

Counts

87 → 7

Compiler

Compiled 1449 to 1029 computations (29% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite134.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64_13220`
290×	`sqrt-prod_binary64_13235`
168×	`times-frac_binary64_13226`
136×	`add-sqr-sqrt_binary64_13241`
116×	`distribute-lft-out_binary64_13173`
88×	`add-cube-cbrt_binary64_13252`
43×	`swap-sqr_binary64_13187`
31×	`pow1_binary64_13278`
27×	`associate-r_binary64_13162` `associate-l_binary64_13163` `sqrt-pow1_binary64_13237`
16×	`unswap-sqr_binary64_13188`
14×	`associate-/r/_binary64_13168` `add-exp-log_binary64_13255`
12×	`associate-/r*_binary64_13166`
11×	`pow-flip_binary64_13291` `inv-pow_binary64_13302`
10×	`add-cbrt-cube_binary64_13253`
9×	`div-inv_binary64_13217` `pow-prod-up_binary64_13287` `pow1/2_binary64_13297`
7×	`flip-+_binary64_13194` `flip3-+_binary64_13223`
6×	`associate-/l*_binary64_13167`
5×	`sqrt-div_binary64_13236` `pow-prod-down_binary64_13288` `pow-sqr_binary64_13193`
4×	`add-log-exp_binary64_13256` `div-exp_binary64_13268`
3×	`rem-sqrt-square_binary64_13233`
2×	`clear-num_binary64_13219` `rec-exp_binary64_13267` `frac-2neg_binary64_13231` `1-exp_binary64_13261` `cbrt-undiv_binary64_13251`
1×	`frac-times_binary64_13230` `sqrt-unprod_binary64_13239` `associate-l/_binary64_13165` `prod-exp_binary64_13266` `pow2_binary64_13298` `associate-r/_binary64_13164` `pow-plus_binary64_13280` `cbrt-unprod_binary64_13250` `rem-square-sqrt_binary64_13232` `*-commutative_binary64_13153`

Counts

4 → 278

Calls

4 calls:

50.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
13.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series272.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
66.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
52.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify115.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5287	6672

prune517.0ms (13.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	286	4	290
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	289	8	297

Merged error: 0b

Counts

297 → 8

Compiler

Compiled 7366 to 5393 computations (26.8% saved)

localize199.0ms (5.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_13220`
28×	`sqrt-prod_binary64_13235`
13×	`distribute-lft-out_binary64_13173`
11×	`add-sqr-sqrt_binary64_13241`
9×	`unpow-prod-down_binary64_13296` `add-cube-cbrt_binary64_13252`
8×	`pow1_binary64_13278`
6×	`add-log-exp_binary64_13256`
5×	`add-exp-log_binary64_13255`
4×	`sqrt-div_binary64_13236` `add-cbrt-cube_binary64_13253`
3×	`pow-unpow_binary64_13294` `pow-pow_binary64_13289` `sqrt-pow1_binary64_13237` `flip-+_binary64_13194` `flip3-+_binary64_13223` `pow1/2_binary64_13297`
2×	`rem-sqrt-square_binary64_13233`
1×	`sqrt-pow2_binary64_13238` `sum-log_binary64_13308` `sqr-pow_binary64_13192` `pow-to-exp_binary64_13286` `pow-exp_binary64_13285` `+-commutative_binary64_13152`

Counts

4 → 74

Calls

4 calls:

13.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 x))

series254.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
77.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
22.0ms	(sqrt.f64 (+.f64 1 x))

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4955	1661
1	4955	1661

prune101.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	86	8	94

Merged error: 0b

Counts

94 → 8

Compiler

Compiled 1806 to 1382 computations (23.5% saved)

regimes129.0ms (3.3%)

Compiler: Compiled 1339 to 1097 computations (18.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.3s (33.5%)

Algorithm

1×

intervals

Results

225.0ms	2125×	body	1024	valid
127.0ms	4200×	body	128	valid
73.0ms	952×	body	512	valid
32.0ms	222×	body	2048	valid
26.0ms	501×	body	256	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 664 to 546 computations (17.8% saved)

Details

analyze3.0ms (0.1%)

sample20.0ms (0.5%)

simplify170.0ms (4.3%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series95.0ms (2.4%)

simplify101.0ms (2.6%)

prune44.0ms (1.1%)

localize7.0ms (0.2%)

rewrite30.0ms (0.8%)

series134.0ms (3.4%)

simplify68.0ms (1.7%)

prune94.0ms (2.4%)

localize9.0ms (0.2%)

rewrite134.0ms (3.4%)

series272.0ms (6.9%)

simplify115.0ms (2.9%)

prune517.0ms (13.2%)

localize199.0ms (5.1%)

rewrite40.0ms (1%)

series254.0ms (6.5%)

simplify43.0ms (1.1%)

prune101.0ms (2.6%)

regimes129.0ms (3.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (33.5%)

Profiling