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
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 (0.6%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify103.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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: 0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

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 (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_2465`
23×	`add-sqr-sqrt_binary64_2487`
20×	`distribute-lft-out_binary64_2416`
18×	`times-frac_binary64_2471`
13×	`add-cube-cbrt_binary64_2500`
10×	`sqrt-prod_binary64_2481`
6×	`associate-/r*_binary64_2409`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `pow1_binary64_2526` `associate-/r/_binary64_2411`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `frac-2neg_binary64_2476`

Counts

2 → 55

Calls

2 calls:

8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series58.0ms (2.9%)

Counts

2 → 12

Calls

2 calls:

37.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
21.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

Compiler

Compiled 194 to 166 computations (14.4% saved)

simplify75.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	6244	1014

prune63.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	5	68

Merged error: 0b

Counts

68 → 5

Compiler

Compiled 916 to 686 computations (25.1% saved)

localize6.0ms (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)))))

rewrite42.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64_2465`
48×	`add-sqr-sqrt_binary64_2487`
38×	`times-frac_binary64_2471`
32×	`distribute-lft-out_binary64_2416`
25×	`add-cube-cbrt_binary64_2500`
24×	`associate-r_binary64_2405`
16×	`sqrt-prod_binary64_2481` `add-exp-log_binary64_2503`
10×	`add-cbrt-cube_binary64_2501`
6×	`associate-/r*_binary64_2409` `pow1_binary64_2526`
5×	`add-log-exp_binary64_2504`
4×	`div-exp_binary64_2516` `associate-/r/_binary64_2411` `prod-exp_binary64_2514`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `associate-/l_binary64_2410` `associate-l*_binary64_2406`
2×	`rec-exp_binary64_2515` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `1-exp_binary64_2509` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `inv-pow_binary64_2550` `pow-flip_binary64_2539` `associate-r/_binary64_2407` `clear-num_binary64_2464` `un-div-inv_binary64_2463` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536`

Counts

3 → 106

Calls

3 calls:

15.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
8.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series83.0ms (4.1%)

Counts

3 → 18

Calls

3 calls:

37.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
28.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

Compiler

Compiled 324 to 278 computations (14.2% saved)

simplify89.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4894	1683
1	4894	1683

prune111.0ms (5.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	124	5	129

Merged error: 0b

Counts

129 → 5

Compiler

Compiled 1830 to 1509 computations (17.5% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 x (+.f64 -1/8 (.f64 x 1/16)))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 -1/8 (*.f64 x 1/16)))))

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2487`
6×	`-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `associate-r_binary64_2405` `associate-l*_binary64_2406`
4×	`associate-*r/_binary64_2407`
2×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `distribute-lft-in_binary64_2414` `*-commutative_binary64_2396` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`

Counts

2 → 44

Calls

2 calls:

6.0ms	(.f64 x (+.f64 -1/8 (.f64 x 1/16)))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 -1/8 (*.f64 x 1/16)))))

series66.0ms (3.3%)

Counts

2 → 9

Calls

2 calls:

41.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 -1/8 (*.f64 x 1/16)))))
25.0ms	(.f64 x (+.f64 -1/8 (.f64 x 1/16)))

Compiler

Compiled 168 to 150 computations (10.7% saved)

simplify62.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4972	779
1	4972	779

prune49.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	53	5	58

Merged error: 0b

Counts

58 → 5

Compiler

Compiled 878 to 656 computations (25.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite57.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`*-un-lft-identity_binary64_2465`
89×	`add-sqr-sqrt_binary64_2487`
76×	`times-frac_binary64_2471`
75×	`sqrt-prod_binary64_2481`
56×	`distribute-lft-out_binary64_2416`
45×	`add-cube-cbrt_binary64_2500`
42×	`associate-r_binary64_2405`
10×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`associate-/r_binary64_2409` `unswap-sqr_binary64_2433` `associate-/l_binary64_2410` `associate-l_binary64_2406`
5×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
4×	`associate-/r/_binary64_2411`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
2×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `associate-r/_binary64_2407` `clear-num_binary64_2464` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536`

Counts

3 → 144

Calls

3 calls:

25.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series102.0ms (5%)

Counts

3 → 14

Calls

3 calls:

46.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
38.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
17.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

Compiler

Compiled 378 to 301 computations (20.4% saved)

simplify100.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4916	2785
1	4916	2785

prune142.0ms (7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	158	5	163

Merged error: 0b

Counts

163 → 5

Compiler

Compiled 2836 to 1763 computations (37.8% saved)

regimes66.0ms (3.2%)

Compiler: Compiled 512 to 424 computations (17.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample682.0ms (33.6%)

Algorithm

1×

intervals

Results

244.0ms	7995×	body	128	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 264 to 220 computations (16.7% saved)

Details

analyze3.0ms (0.1%)

sample13.0ms (0.6%)

simplify103.0ms (5.1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite19.0ms (0.9%)

series58.0ms (2.9%)

simplify75.0ms (3.7%)

prune63.0ms (3.1%)

localize6.0ms (0.3%)

rewrite42.0ms (2.1%)

series83.0ms (4.1%)

simplify89.0ms (4.4%)

prune111.0ms (5.4%)

localize9.0ms (0.4%)

rewrite15.0ms (0.7%)

series66.0ms (3.3%)

simplify62.0ms (3.1%)

prune49.0ms (2.4%)

localize7.0ms (0.3%)

rewrite57.0ms (2.8%)

series102.0ms (5%)

simplify100.0ms (4.9%)

prune142.0ms (7%)

regimes66.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample682.0ms (33.6%)

Profiling