Details

analyze41.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

sample18.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	2×	body	80	invalid

simplify43.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	799	14
1	799	14

prune5.0ms (0.2%)

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

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (.f64 x 9.0))) (/.f64 y (.f64 3.0 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3.0 (sqrt.f64 x)))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.3b	(/.f64 1.0 (*.f64 x 9.0))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
2×	`associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

12.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (.f64 x 9.0))) (/.f64 y (.f64 3.0 (sqrt.f64 x))))
8.0ms	(/.f64 1.0 (*.f64 x 9.0))
5.0ms	(/.f64 y (*.f64 3.0 (sqrt.f64 x)))
5.0ms	(*.f64 3.0 (sqrt.f64 x))

series32.0ms (1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 y (*.f64 3.0 (sqrt.f64 x)))
11.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (.f64 x 9.0))) (/.f64 y (.f64 3.0 (sqrt.f64 x))))
5.0ms	(*.f64 3.0 (sqrt.f64 x))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify58.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4981	999
1	4981	999

prune164.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	86	9	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	9	96

Merged error: 0.0b

Counts

96 → 9

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y 3.0) (sqrt.f64 x)))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(/.f64 (/.f64 y 3.0) (sqrt.f64 x))

rewrite56.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`
16×	`associate-/l*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`div-inv_binary64`
8×	`add-log-exp_binary64`
7×	`associate-/r*_binary64`
5×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64`
3×	`pow1_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate--l+_binary64`

Counts

3 → 156

Calls

3 calls:

34.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y 3.0) (sqrt.f64 x)))
8.0ms	(/.f64 (/.f64 y 3.0) (sqrt.f64 x))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))

series25.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 (/.f64 y 3.0) (sqrt.f64 x))
11.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y 3.0) (sqrt.f64 x)))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4965	2300
1	4965	2300

prune235.0ms (7.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Merged error: 0.0b

Counts

174 → 8

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0))))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(/.f64 (sqrt.f64 x) (/.f64 y 3.0))
0.3b	(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0)))

rewrite161.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

943×	`times-frac_binary64`
482×	`add-sqr-sqrt_binary64`
456×	`*-un-lft-identity_binary64`
443×	`add-cube-cbrt_binary64`
202×	`sqrt-prod_binary64`
97×	`associate-/r*_binary64`
40×	`div-inv_binary64`
35×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
12×	`associate-/l*_binary64`
11×	`cbrt-undiv_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
6×	`associate-/r/_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64`
3×	`diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate--l-_binary64` `cbrt-unprod_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `associate--l+_binary64`

Counts

4 → 524

Calls

4 calls:

92.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0))))
20.0ms	(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0)))
8.0ms	(/.f64 (sqrt.f64 x) (/.f64 y 3.0))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))

series54.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0)))
17.0ms	(/.f64 (sqrt.f64 x) (/.f64 y 3.0))
12.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 y 3.0))))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify112.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4979	8274
1	4979	8274

prune1.1s (33.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	535	1	536
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	536	8	544

Merged error: 0.0b

Counts

544 → 8

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y (sqrt.f64 x)) 3.0))
0.3b	(/.f64 y (sqrt.f64 x))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(/.f64 (/.f64 y (sqrt.f64 x)) 3.0)

rewrite62.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`times-frac_binary64`
109×	`add-sqr-sqrt_binary64`
101×	`*-un-lft-identity_binary64`
96×	`add-cube-cbrt_binary64`
49×	`sqrt-prod_binary64`
28×	`associate-/l*_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r*_binary64`
9×	`add-log-exp_binary64`
7×	`div-inv_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64` `difference-of-squares_binary64`
3×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate--l+_binary64`

Counts

4 → 188

Calls

4 calls:

35.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y (sqrt.f64 x)) 3.0))
9.0ms	(/.f64 (/.f64 y (sqrt.f64 x)) 3.0)
5.0ms	(/.f64 1.0 (*.f64 x 9.0))
4.0ms	(/.f64 y (sqrt.f64 x))

series36.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (/.f64 y (sqrt.f64 x)) 3.0)
12.0ms	(-.f64 (-.f64 1.0 (/.f64 1.0 (*.f64 x 9.0))) (/.f64 (/.f64 y (sqrt.f64 x)) 3.0))
9.0ms	(/.f64 y (sqrt.f64 x))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4966	2505
1	4966	2505

prune244.0ms (7.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Merged error: 0.0b

Counts

208 → 8

regimes99.0ms (3%)

Accuracy

Total 0.2b remaining (87.6%)

Threshold costs 0.2b (87.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	14
1	52	14

end0.0ms (0%)

sample492.0ms (15.2%)

Algorithm

1×

intervals

Results

353.0ms	8000×	body	80	valid
5.0ms	113×	body	80	invalid

Details

analyze41.0ms (1.2%)

sample18.0ms (0.6%)

simplify43.0ms (1.3%)

prune5.0ms (0.2%)

localize9.0ms (0.3%)

rewrite33.0ms (1%)

series32.0ms (1%)

simplify58.0ms (1.8%)

prune164.0ms (5.1%)

localize9.0ms (0.3%)

rewrite56.0ms (1.7%)

series25.0ms (0.8%)

simplify67.0ms (2.1%)

prune235.0ms (7.2%)

localize11.0ms (0.3%)

rewrite161.0ms (5%)

series54.0ms (1.7%)

simplify112.0ms (3.5%)

prune1.1s (33.6%)

localize10.0ms (0.3%)

rewrite62.0ms (1.9%)

series36.0ms (1.1%)

simplify74.0ms (2.3%)

prune244.0ms (7.5%)

regimes99.0ms (3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample492.0ms (15.2%)

Profiling