Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample89.0ms

Algorithm

intervals

Results

53.0ms	119×	body	1280	valid
19.0ms	75×	body	640	valid
5.0ms	35×	body	320	valid
2.0ms	22×	body	160	valid
0.0ms	5×	body	80	valid

simplify149.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	5283	12

prune4.0ms

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: 58.9b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
6.6b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_574`
52×	`add-sqr-sqrt_binary64_559`
48×	`times-frac_binary64_569`
30×	`log-prod_binary64_492`
25×	`add-cube-cbrt_binary64_545`
18×	`difference-of-squares_binary64_603`
13×	`distribute-lft-out_binary64_618`
9×	`distribute-lft-out--_binary64_619`
7×	`add-exp-log_binary64_538`
6×	`associate-/l*_binary64_638`
4×	`add-cbrt-cube_binary64_546` `associate-/r/_binary64_639` `associate-/r*_binary64_637`
3×	`pow1_binary64_520`
2×	`div-inv_binary64_575` `associate-/l/_binary64_640` `div-exp_binary64_527` `flip3-+_binary64_572` `flip-+_binary64_599` `rem-log-exp_binary64_537` `add-log-exp_binary64_539`
1×	`flip3--_binary64_573` `log-div_binary64_493` `frac-2neg_binary64_567` `clear-num_binary64_577` `log-pow_binary64_495` `flip--_binary64_600` `div-sub_binary64_568` `cbrt-undiv_binary64_544`

Counts

2 → 92

Calls

2 calls:

8.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
8.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

series39.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
29.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

simplify61.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4967	1896
1	4967	1896

prune225.0ms

Filtered

60 candidates to 98 candidates (-63.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Merged error: 0.0b

Counts

99 → 3

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 eps 5) -2/5)
0.1b	(*.f64 (pow.f64 eps 3) 2/3)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_559`
19×	`associate-l_binary64_634`
12×	`add-exp-log_binary64_538`
9×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
8×	`unpow-prod-down_binary64_509`
7×	`unswap-sqr_binary64_602`
6×	`add-cbrt-cube_binary64_546` `associate-r_binary64_633` `prod-exp_binary64_525`
4×	`sqr-pow_binary64_606` `cube-prod_binary64_547`
2×	`pow-to-exp_binary64_499` `pow1_binary64_520` `pow-exp_binary64_498` `cbrt-unprod_binary64_543` `*-commutative_binary64_642` `add-log-exp_binary64_539`
1×	`unpow3_binary64_518` `cube-mult_binary64_549`

Counts

2 → 56

Calls

2 calls:

5.0ms	(*.f64 (pow.f64 eps 5) -2/5)
6.0ms	(*.f64 (pow.f64 eps 3) 2/3)

series54.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(*.f64 (pow.f64 eps 5) -2/5)
24.0ms	(*.f64 (pow.f64 eps 3) 2/3)

simplify77.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5972	601

prune240.0ms

Filtered

42 candidates to 62 candidates (-47.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Merged error: 0.0b

Counts

65 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 eps))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
6.6b	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
6.7b	(log.f64 (sqrt.f64 (-.f64 1 eps)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64_574`
79×	`add-sqr-sqrt_binary64_559`
72×	`times-frac_binary64_569`
66×	`sqrt-prod_binary64_553`
51×	`log-prod_binary64_492`
45×	`add-cube-cbrt_binary64_545`
22×	`difference-of-squares_binary64_603`
19×	`distribute-lft-out_binary64_618`
11×	`distribute-lft-out--_binary64_619`
10×	`add-exp-log_binary64_538`
9×	`associate-/l*_binary64_638`
8×	`pow1_binary64_520`
6×	`add-cbrt-cube_binary64_546` `sqrt-div_binary64_554`
4×	`associate-/r/_binary64_639` `log-pow_binary64_495` `associate-/r*_binary64_637` `add-log-exp_binary64_539`
3×	`flip3--_binary64_573` `log-div_binary64_493` `rem-log-exp_binary64_537` `flip--_binary64_600`
2×	`div-inv_binary64_575` `associate-/l/_binary64_640` `sqrt-pow1_binary64_555` `div-exp_binary64_527` `flip3-+_binary64_572` `flip-+_binary64_599` `pow1/2_binary64_510`
1×	`rem-sqrt-square_binary64_562` `frac-2neg_binary64_567` `clear-num_binary64_577` `cbrt-undiv_binary64_544`

Counts

4 → 158

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 1 eps))
9.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
10.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
11.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (-.f64 1 eps))
27.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
41.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
25.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))

simplify107.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5048	3778

prune47.0ms

Filtered: 103 candidates to 170 candidates (-65.0%)

Details

analyze4.0ms

sample89.0ms

simplify149.0ms

prune4.0ms

localize12.0ms

rewrite20.0ms

series39.0ms

simplify61.0ms

prune225.0ms

localize19.0ms

rewrite12.0ms

series54.0ms

simplify77.0ms

prune240.0ms

localize13.0ms

rewrite40.0ms

series108.0ms

simplify107.0ms

prune47.0ms

Profiling