Details

analyze12.0ms (0.6%)

Algorithm

1×

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

sample21.0ms (1.1%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

valid

simplify465.0ms (23.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	786	11
1	786	11

prune6.0ms (0.3%)

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 (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1.0 x) (+.f64 1.0 x))))
0.0b	(sqrt.f64 (/.f64 (-.f64 1.0 x) (+.f64 1.0 x)))
0.0b	(/.f64 (-.f64 1.0 x) (+.f64 1.0 x))

rewrite34.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
41×	`times-frac_binary64`
26×	`sqrt-prod_binary64`
24×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`
9×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 91

Calls

3 calls:

19.0ms	(/.f64 (-.f64 1.0 x) (+.f64 1.0 x))
8.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 x) (+.f64 1.0 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1.0 x) (+.f64 1.0 x))))

series24.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(/.f64 (-.f64 1.0 x) (+.f64 1.0 x))
7.0ms	(sqrt.f64 (/.f64 (-.f64 1.0 x) (+.f64 1.0 x)))
4.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1.0 x) (+.f64 1.0 x))))

simplify38.0ms (2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5097	1256

prune133.0ms (6.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1.0 x))
0.0b	(/.f64 1 (sqrt.f64 (+.f64 1.0 x)))
0.0b	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 x)))
0.0b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1.0 x))) (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 x))))

rewrite71.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`add-sqr-sqrt_binary64`
147×	`*-un-lft-identity_binary64`
134×	`times-frac_binary64`
87×	`sqrt-prod_binary64`
73×	`add-cube-cbrt_binary64`
41×	`associate-r_binary64`
32×	`add-exp-log_binary64`
27×	`associate-l_binary64`
20×	`add-cbrt-cube_binary64`
19×	`distribute-lft-out_binary64`
15×	`unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
14×	`associate-/r*_binary64`
11×	`div-exp_binary64`
10×	`sqrt-div_binary64`
9×	`pow1_binary64`
8×	`associate-/r/_binary64` `prod-exp_binary64` `associate-/l*_binary64`
6×	`cbrt-undiv_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `div-inv_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `pow-flip_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 238

Calls

4 calls:

36.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1.0 x))) (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 x))))
10.0ms	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1.0 x)))
6.0ms	(sqrt.f64 (+.f64 1.0 x))

series25.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 x)))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 1.0 x)))
5.0ms	(sqrt.f64 (+.f64 1.0 x))
4.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1.0 x))) (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 x))))

simplify47.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4967	3365
1	4967	3365

prune479.0ms (24.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	250	2	252

Merged error: 0b

Counts

252 → 2

regimes106.0ms (5.4%)

Accuracy

Total 0.0b remaining (41.7%)

Threshold costs 0.0b (41.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	19
1	26	19

end0.0ms (0%)

sample478.0ms (24.4%)

Algorithm

1×

intervals

Results

378.0ms

8000×

body

valid

Details

analyze12.0ms (0.6%)

sample21.0ms (1.1%)

simplify465.0ms (23.7%)

prune6.0ms (0.3%)

localize9.0ms (0.5%)

rewrite34.0ms (1.7%)

series24.0ms (1.2%)

simplify38.0ms (2%)

prune133.0ms (6.8%)

localize11.0ms (0.5%)

rewrite71.0ms (3.6%)

series25.0ms (1.3%)

simplify47.0ms (2.4%)

prune479.0ms (24.4%)

regimes106.0ms (5.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample478.0ms (24.4%)

Profiling