Details

analyze2.0ms (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

sample28.0ms (1.2%)

Algorithm

1×

intervals

Results

12.0ms	54×	body	1280	valid
5.0ms	46×	body	640	valid
4.0ms	130×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune4.0ms (0.2%)

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: 30.1b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1.0))

series19.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1.0))

simplify52.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune62.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.2b

Counts

41 → 4

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

rewrite24.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 71

Calls

3 calls:

10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1.0))

series25.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1.0))

simplify29.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5038	1051

prune125.0ms (5.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 0.0b

Counts

84 → 9

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x))))
0.3b	(cbrt.f64 (+.f64 1.0 x))
0.3b	(cbrt.f64 (+.f64 1.0 x))

rewrite28.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`cbrt-prod_binary64`
10×	`associate-r_binary64`
9×	`times-frac_binary64` `sqrt-prod_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`cbrt-div_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/.f64 1.0 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x)))) (sqrt.f64 x)))
8.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x))))
3.0ms	(cbrt.f64 (+.f64 1.0 x))
3.0ms	(cbrt.f64 (+.f64 1.0 x))

series102.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 1.0 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x)))) (sqrt.f64 x)))
15.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1.0 x))) (sqrt.f64 (cbrt.f64 (+.f64 1.0 x))))
8.0ms	(cbrt.f64 (+.f64 1.0 x))
8.0ms	(cbrt.f64 (+.f64 1.0 x))

simplify71.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4896	2095
1	4896	2095

prune197.0ms (8.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

rewrite85.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

297×	`*-un-lft-identity_binary64`
274×	`sqrt-prod_binary64`
157×	`times-frac_binary64`
119×	`add-sqr-sqrt_binary64`
116×	`distribute-lft-out_binary64`
88×	`add-cube-cbrt_binary64`
41×	`swap-sqr_binary64`
27×	`associate-r_binary64` `associate-l_binary64`
20×	`pow1_binary64`
14×	`associate-/r/_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64`
7×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64`
5×	`pow-prod-up_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 250

Calls

4 calls:

35.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
11.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
10.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))

series72.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
17.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))

simplify83.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4946	4249
1	4946	4249

prune482.0ms (21.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	4	3	7
Picked	1	0	1
Done	0	2	2
Total	264	8	272

Merged error: 0.0b

Counts

272 → 8

regimes46.0ms (2.1%)

Accuracy

Total 0.1b remaining (75.4%)

Threshold costs 0.1b (75.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms (0%)

sample644.0ms (28.8%)

Algorithm

1×

intervals

Results

236.0ms	1750×	body	1280	valid
129.0ms	1220×	body	640	valid
120.0ms	4106×	body	80	valid
47.0ms	608×	body	320	valid
16.0ms	316×	body	160	valid

Details

analyze2.0ms (0.1%)

sample28.0ms (1.2%)

simplify8.0ms (0.3%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

rewrite13.0ms (0.6%)

series19.0ms (0.8%)

simplify52.0ms (2.3%)

prune62.0ms (2.8%)

localize7.0ms (0.3%)

rewrite24.0ms (1.1%)

series25.0ms (1.1%)

simplify29.0ms (1.3%)

prune125.0ms (5.6%)

localize10.0ms (0.4%)

rewrite28.0ms (1.3%)

series102.0ms (4.6%)

simplify71.0ms (3.2%)

prune197.0ms (8.8%)

localize11.0ms (0.5%)

rewrite85.0ms (3.8%)

series72.0ms (3.2%)

simplify83.0ms (3.7%)

prune482.0ms (21.5%)

regimes46.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample644.0ms (28.8%)

Profiling