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)

sample19.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	59×	body	1024	valid
4.0ms	142×	body	128	valid
2.0ms	31×	body	512	valid
1.0ms	19×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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: 28.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_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 → 40

Calls

2 calls:

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

series107.0ms (3.8%)

Counts

2 → 6

Calls

2 calls:

80.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5010	794

prune68.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 0.1b

Counts

47 → 4

Compiler

Compiled 989 to 689 computations (30.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (1.2%)

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` `add-exp-log_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_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` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 74

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))

series126.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify69.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4942	1501
1	4942	1501

prune245.0ms (8.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	80	7	87

Merged error: 0.0b

Counts

87 → 7

Compiler

Compiled 3889 to 2979 computations (23.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite94.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64`
74×	`*-un-lft-identity_binary64`
37×	`pow1_binary64`
32×	`distribute-lft-out_binary64` `add-sqr-sqrt_binary64`
28×	`sqrt-div_binary64`
18×	`pow1/2_binary64` `sqrt-pow1_binary64`
16×	`add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
14×	`flip3-+_binary64` `add-exp-log_binary64` `pow-flip_binary64` `flip-+_binary64`
11×	`add-cbrt-cube_binary64`
10×	`pow-prod-up_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
3×	`prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `rec-exp_binary64` `div-exp_binary64` `pow2_binary64`
1×	`associate-/r_binary64` `rem-square-sqrt_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqr-abs_binary64` `-commutative_binary64`

Counts

4 → 153

Calls

4 calls:

30.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
27.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series278.0ms (10%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
78.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
71.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
50.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify101.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4871	2990
1	4871	2990

prune239.0ms (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 4031 to 2880 computations (28.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.3b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite49.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64`
36×	`sqrt-prod_binary64`
30×	`distribute-lft-out_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
10×	`swap-sqr_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
4×	`frac-times_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

23.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.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))
4.0ms	(sqrt.f64 (+.f64 1 x))

series157.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
39.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
30.0ms	(sqrt.f64 (+.f64 1 x))
25.0ms	(sqrt.f64 (+.f64 1 x))

simplify64.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4935	1899
1	4935	1899

prune208.0ms (7.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	106	7	113

Merged error: 0b

Counts

113 → 7

Compiler

Compiled 3593 to 2572 computations (28.4% saved)

regimes18.0ms (0.7%)

Compiler: Compiled 147 to 115 computations (21.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

end0.0ms (0%)

sample770.0ms (27.7%)

Algorithm

1×

intervals

Results

207.0ms	2014×	body	1024	valid
124.0ms	4245×	body	128	valid
78.0ms	1013×	body	512	valid
30.0ms	233×	body	2048	valid
25.0ms	495×	body	256	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 171 to 137 computations (19.9% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.7%)

simplify11.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite17.0ms (0.6%)

series107.0ms (3.8%)

simplify65.0ms (2.3%)

prune68.0ms (2.5%)

localize6.0ms (0.2%)

rewrite33.0ms (1.2%)

series126.0ms (4.5%)

simplify69.0ms (2.5%)

prune245.0ms (8.8%)

localize9.0ms (0.3%)

rewrite94.0ms (3.4%)

series278.0ms (10%)

simplify101.0ms (3.6%)

prune239.0ms (8.6%)

localize14.0ms (0.5%)

rewrite49.0ms (1.8%)

series157.0ms (5.7%)

simplify64.0ms (2.3%)

prune208.0ms (7.5%)

regimes18.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample770.0ms (27.7%)

Profiling