Details

analyze261.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample49.0ms

Algorithm

intervals

Results

16.0ms	114×	body	2048	nan
12.0ms	74×	body	1024	nan
10.0ms	256×	body	128	valid
2.0ms	22×	body	512	nan
1.0ms	10×	body	256	nan
0.0ms	12×	body	128	nan

simplify171.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	5001	14

prune1.0ms

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: 32.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
30.7b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

2 → 30

Calls

2 calls:

8.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series107.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
45.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify51.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4904	536
1	4904	536

prune28.0ms

Filtered

29 candidates to 36 candidates (-24.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	1	37

Merged error: 0b

Counts

37 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))))
0.2b	(/.f64 1/8 (pow.f64 x 3))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`add-log-exp_binary64`
12×	`associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-exp-log_binary64`
6×	`distribute-lft-out_binary64`
5×	`add-cbrt-cube_binary64` `sum-log_binary64`
4×	`sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow1_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-+r-_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `associate-+r+_binary64` `pow-exp_binary64`

Counts

3 → 97

Calls

3 calls:

30.0ms	(+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))
38.0ms	(+.f64 x (-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series196.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))
48.0ms	(+.f64 x (-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))))
51.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5649	1591

prune73.0ms

Filtered

62 candidates to 106 candidates (-71.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	1	107

Merged error: 0b

Counts

107 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	21
1	54	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

612.0ms	4091×	body	2048	nan
317.0ms	8000×	body	128	valid
239.0ms	2052×	body	1024	nan
89.0ms	1033×	body	512	nan
33.0ms	536×	body	256	nan
14.0ms	473×	body	128	nan
1.0ms	7×	body	4096	nan

Details

analyze261.0ms

sample49.0ms

simplify171.0ms

prune1.0ms

localize7.0ms

rewrite15.0ms

series107.0ms

simplify51.0ms

prune28.0ms

localize10.0ms

rewrite84.0ms

series196.0ms

simplify49.0ms

prune73.0ms

simplify2.0ms

end0.0ms

sample1.5s

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