Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

sample17.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify359.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (346.0ms)

Iter	Nodes	Cost
0	7545	20

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: 0.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
28×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`distribute-lft-out_binary64` `associate-/l*_binary64`
7×	`div-inv_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `distribute-rgt-out_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `distribute-rgt1-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 90

Calls

3 calls:

6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
21.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

series91.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
21.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
29.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

simplify87.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4909	1928
1	4909	1928

prune86.0ms

Filtered

75 candidates to 99 candidates (-32.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	1	100

Merged error: 0b

Counts

100 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac_binary64`
120×	`*-un-lft-identity_binary64`
111×	`add-sqr-sqrt_binary64`
97×	`add-cube-cbrt_binary64`
65×	`sqrt-prod_binary64`
30×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64`
14×	`add-exp-log_binary64`
10×	`sqrt-div_binary64`
9×	`associate-/r/_binary64` `div-inv_binary64`
8×	`add-cbrt-cube_binary64`
7×	`distribute-lft-out_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`1-exp_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `frac-add_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 180

Calls

3 calls:

11.0ms	(/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
58.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))))

series98.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))))
23.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
29.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))))))

simplify159.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4932	4477
1	4932	4477

prune139.0ms

Filtered

110 candidates to 189 candidates (-71.8%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	189	1	190

Merged error: 0b

Counts

190 → 1

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample494.0ms

Algorithm

intervals

Results

401.0ms	8000×	body	80	valid
0.0ms	4×	body	80	nan

Details

analyze5.0ms

sample17.0ms

simplify359.0ms

prune1.0ms

localize9.0ms

rewrite34.0ms

series91.0ms

simplify87.0ms

prune86.0ms

localize10.0ms

rewrite82.0ms

series98.0ms

simplify159.0ms

prune139.0ms

simplify3.0ms

end0.0ms

sample494.0ms

Profiling