Details

analyze326.0ms (7.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1432	36
1	1432	36
0	2	2
1	2	2

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

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	497	18
1	497	18

prune4.0ms (0.1%)

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

Error

0.2b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_11672` `add-exp-log_binary64_11710`
21×	`add-sqr-sqrt_binary64_11694`
16×	`add-cbrt-cube_binary64_11708`
15×	`add-cube-cbrt_binary64_11707`
14×	`cancel-sign-sub-inv_binary64_11638`
12×	`times-frac_binary64_11678`
9×	`pow1_binary64_11733` `add-log-exp_binary64_11711`
8×	`associate--l+_binary64_11609`
6×	`associate-r_binary64_11612` `div-exp_binary64_11723` `associate-/l*_binary64_11617`
5×	`distribute-lft-out--_binary64_11624` `prod-exp_binary64_11721` `div-inv_binary64_11669`
4×	`cbrt-undiv_binary64_11706` `sqrt-prod_binary64_11688`
3×	`cbrt-unprod_binary64_11705` `associate-l_binary64_11613` `diff-log_binary64_11764`
2×	`clear-num_binary64_11671` `1-exp_binary64_11716` `pow-flip_binary64_11746` `frac-sub_binary64_11681` `associate-/r*_binary64_11616` `flip3--_binary64_11676` `unswap-sqr_binary64_11640` `frac-2neg_binary64_11683` `flip--_binary64_11647` `pow-prod-down_binary64_11743` `rec-exp_binary64_11722` `sub-neg_binary64_11665`
1×	`inv-pow_binary64_11757` `associate--l-_binary64_11610` `difference-of-squares_binary64_11641` `*-commutative_binary64_11603`

Counts

4 → 105

Calls

4 calls:

18.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
4.0ms	(/.f64 1 (*.f64 x 9))

series104.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
32.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
16.0ms	(*.f64 3 (sqrt.f64 x))
13.0ms	(/.f64 1 (*.f64 x 9))

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5119	1611

prune152.0ms (3.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	107	12	119

Error

0.0b

Counts

119 → 12

Compiler

Compiled 2293 to 1652 computations (28% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))

rewrite90.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

285×	`times-frac_binary64_11678`
169×	`add-sqr-sqrt_binary64_11694`
160×	`*-un-lft-identity_binary64_11672`
153×	`add-cube-cbrt_binary64_11707`
89×	`cancel-sign-sub-inv_binary64_11638`
83×	`sqrt-prod_binary64_11688`
19×	`add-exp-log_binary64_11710`
18×	`div-inv_binary64_11669`
16×	`associate-/l*_binary64_11617`
13×	`add-cbrt-cube_binary64_11708`
8×	`add-log-exp_binary64_11711` `associate--l+_binary64_11609`
7×	`div-exp_binary64_11723` `associate-/r*_binary64_11616`
6×	`pow1_binary64_11733`
5×	`cbrt-undiv_binary64_11706` `distribute-lft-out--_binary64_11624` `difference-of-squares_binary64_11641`
3×	`prod-exp_binary64_11721` `diff-log_binary64_11764`
2×	`clear-num_binary64_11671` `1-exp_binary64_11716` `pow-flip_binary64_11746` `frac-sub_binary64_11681` `flip3--_binary64_11676` `frac-2neg_binary64_11683` `flip--_binary64_11647` `rec-exp_binary64_11722` `sub-neg_binary64_11665`
1×	`cbrt-unprod_binary64_11705` `inv-pow_binary64_11757` `associate--l-_binary64_11610` `associate-/l/_binary64_11619` `pow-prod-down_binary64_11743`

Counts

3 → 253

Calls

3 calls:

46.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
7.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
4.0ms	(/.f64 1 (*.f64 x 9))

series83.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

40.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
32.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify116.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5132	5666

prune339.0ms (7.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	263	11	274

Error

0.0b

Counts

274 → 11

Compiler

Compiled 5916 to 3877 computations (34.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(/.f64 y (sqrt.f64 x))
0.3b	(/.f64 3 (/.f64 y (sqrt.f64 x)))
1.1b	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))

rewrite110.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

852×	`times-frac_binary64_11678`
416×	`add-cube-cbrt_binary64_11707` `add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
156×	`sqrt-prod_binary64_11688`
100×	`associate-/r*_binary64_11616`
43×	`add-exp-log_binary64_11710`
25×	`add-cbrt-cube_binary64_11708`
24×	`div-inv_binary64_11669`
23×	`div-exp_binary64_11723`
12×	`cbrt-undiv_binary64_11706` `associate-/l*_binary64_11617`
8×	`pow1_binary64_11733`
6×	`associate-/r/_binary64_11618`
5×	`1-exp_binary64_11716` `rec-exp_binary64_11722`
4×	`clear-num_binary64_11671` `add-log-exp_binary64_11711` `frac-2neg_binary64_11683`
3×	`pow-flip_binary64_11746` `prod-exp_binary64_11721`
2×	`inv-pow_binary64_11757`
1×	`cbrt-unprod_binary64_11705` `pow-prod-down_binary64_11743`

Counts

4 → 485

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
11.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
4.0ms	(/.f64 1 (*.f64 x 9))
4.0ms	(/.f64 y (sqrt.f64 x))

series122.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
37.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
32.0ms	(/.f64 y (sqrt.f64 x))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify177.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4946	11034
1	4946	11034

prune875.0ms (19%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	495	2	497
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	497	11	508

Error

0.0b

Counts

508 → 11

Compiler

Compiled 12698 to 7742 computations (39% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 -1 (.f64 (sqrt.f64 x) (/.f64 -3 y))))
0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 (sqrt.f64 x) (/.f64 -3 y))
1.1b	(/.f64 -1 (*.f64 (sqrt.f64 x) (/.f64 -3 y)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_11694`
29×	`add-exp-log_binary64_11710`
28×	`*-un-lft-identity_binary64_11672`
23×	`times-frac_binary64_11678` `add-cbrt-cube_binary64_11708`
21×	`add-cube-cbrt_binary64_11707`
15×	`cancel-sign-sub-inv_binary64_11638`
13×	`associate-r_binary64_11612`
9×	`pow1_binary64_11733` `div-exp_binary64_11723` `add-log-exp_binary64_11711`
8×	`associate--l+_binary64_11609`
7×	`cbrt-undiv_binary64_11706` `prod-exp_binary64_11721`
6×	`div-inv_binary64_11669` `associate-l_binary64_11613` `associate-/l*_binary64_11617`
5×	`cbrt-unprod_binary64_11705` `distribute-lft-out--_binary64_11624` `sqrt-prod_binary64_11688`
4×	`unswap-sqr_binary64_11640`
3×	`associate-*r/_binary64_11614` `diff-log_binary64_11764`
2×	`associate-/r/_binary64_11618` `clear-num_binary64_11671` `1-exp_binary64_11716` `pow-flip_binary64_11746` `frac-sub_binary64_11681` `associate-/r*_binary64_11616` `flip3--_binary64_11676` `frac-2neg_binary64_11683` `flip--_binary64_11647` `pow-prod-down_binary64_11743` `rec-exp_binary64_11722` `sub-neg_binary64_11665`
1×	`inv-pow_binary64_11757` `associate--l-_binary64_11610` `difference-of-squares_binary64_11641` `*-commutative_binary64_11603`

Counts

4 → 124

Calls

4 calls:

14.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 -1 (.f64 (sqrt.f64 x) (/.f64 -3 y))))
8.0ms	(*.f64 (sqrt.f64 x) (/.f64 -3 y))
7.0ms	(/.f64 -1 (*.f64 (sqrt.f64 x) (/.f64 -3 y)))
4.0ms	(/.f64 1 (*.f64 x 9))

series138.0ms (3%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(/.f64 -1 (*.f64 (sqrt.f64 x) (/.f64 -3 y)))
43.0ms	(*.f64 (sqrt.f64 x) (/.f64 -3 y))
31.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 -1 (.f64 (sqrt.f64 x) (/.f64 -3 y))))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4927	2008
1	4927	2008

prune148.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	136	11	147

Error

0.0b

Counts

147 → 11

Compiler

Compiled 2653 to 1930 computations (27.3% saved)

regimes220.0ms (4.8%)

Accuracy

Total 0.2b remaining (96.2%)

Threshold costs 0.2b (96.2%)

Compiler

Compiled 2408 to 2089 computations (13.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	24
1	41	24

end0.0ms (0%)

sample1.3s (28.2%)

Algorithm

1×

intervals

Results

342.0ms	8000×	body	128	valid
4.0ms	93×	body	128	invalid

Compiler

Compiled 837 to 729 computations (12.9% saved)

Details

analyze326.0ms (7.1%)

sample18.0ms (0.4%)

simplify32.0ms (0.7%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite40.0ms (0.9%)

series104.0ms (2.3%)

simplify51.0ms (1.1%)

prune152.0ms (3.3%)

localize9.0ms (0.2%)

rewrite90.0ms (2%)

series83.0ms (1.8%)

simplify116.0ms (2.5%)

prune339.0ms (7.4%)

localize11.0ms (0.2%)

rewrite110.0ms (2.4%)

series122.0ms (2.6%)

simplify177.0ms (3.8%)

prune875.0ms (19%)

localize11.0ms (0.2%)

rewrite44.0ms (1%)

series138.0ms (3%)

simplify73.0ms (1.6%)

prune148.0ms (3.2%)

regimes220.0ms (4.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (28.2%)

Profiling