Details

analyze105.0ms (2.3%)

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
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	7×	body	80	nan
0.0ms	5×	body	80	invalid

simplify186.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (183.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)))
0.2b	(.f64 (/.f64 1.0 (sqrt.f64 (.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)
0.3b	(/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
0.4b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

rewrite63.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64` `times-frac_binary64`
24×	`add-cube-cbrt_binary64` `associate-l_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
8×	`associate-*r/_binary64` `sqrt-prod_binary64`
6×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `flip-+_binary64` `associate-l/_binary64`
2×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64`

Counts

4 → 114

Calls

4 calls:

17.0ms	(/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
15.0ms	(.f64 (/.f64 1.0 (sqrt.f64 (.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)
14.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)))
14.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

series63.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 (/.f64 1.0 (sqrt.f64 (.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)
18.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 (/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))) rand)))
12.0ms	(/.f64 1.0 (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
8.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4974	2418
1	4974	2418

prune299.0ms (6.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 0.0b

Counts

127 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))
0.1b	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 1.0 (/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
0.4b	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
8×	`associate-*r/_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`sqrt-prod_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `difference-of-squares_binary64` `frac-times_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 102

Calls

4 calls:

11.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 1.0 (/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))))))
11.0ms	(/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
10.0ms	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))
8.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))

series51.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (.f64 1.0 (/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))))))
18.0ms	(/.f64 rand (sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))))
8.0ms	(sqrt.f64 (*.f64 9.0 (-.f64 a (/.f64 1.0 3.0))))
5.0ms	(*.f64 9.0 (-.f64 a (/.f64 1.0 3.0)))

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5053	2006

prune289.0ms (6.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 0.0b

Counts

122 → 7

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b

(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

0.1b

(*.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))

0.3b

(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))

rewrite59.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

403×	`times-frac_binary64`
310×	`add-sqr-sqrt_binary64`
234×	`sqrt-prod_binary64`
232×	`*-un-lft-identity_binary64`
182×	`add-cube-cbrt_binary64`
50×	`difference-of-squares_binary64`
25×	`distribute-lft-out--_binary64`
22×	`associate-/l*_binary64`
11×	`div-inv_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/r*_binary64`
6×	`pow1_binary64` `associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`frac-times_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `add-log-exp_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 295

Calls

3 calls:

18.0ms

(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))

14.0ms

(*.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))

7.0ms

(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

series51.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

24.0ms

(*.f64 (-.f64 a (/.f64 1.0 3.0)) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))

22.0ms

(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))

5.0ms

(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

simplify107.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4985	7011
1	4985	7011

prune842.0ms (18.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	306	5	311

Merged error: 0b

Counts

311 → 5

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))
0.1b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))
0.3b	(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))
0.4b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))))))

rewrite87.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

404×	`times-frac_binary64`
321×	`add-sqr-sqrt_binary64`
247×	`sqrt-prod_binary64`
238×	`*-un-lft-identity_binary64`
186×	`add-cube-cbrt_binary64`
52×	`difference-of-squares_binary64`
46×	`sqrt-div_binary64`
32×	`frac-times_binary64`
26×	`distribute-lft-out--_binary64`
23×	`flip3--_binary64` `flip--_binary64`
22×	`associate-/l*_binary64`
18×	`associate-l_binary64`
16×	`associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
11×	`div-inv_binary64`
10×	`associate-*l/_binary64`
9×	`associate-/r*_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/r/_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 353

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))))))
18.0ms	(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))
13.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))
7.0ms	(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

series95.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))))))
29.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (.f64 (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))) (+.f64 1.0 (*.f64 1.0 (/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))))))
21.0ms	(/.f64 (/.f64 rand (sqrt.f64 9.0)) (sqrt.f64 (-.f64 a (/.f64 1.0 3.0))))
5.0ms	(sqrt.f64 (-.f64 a (/.f64 1.0 3.0)))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5058	9323

prune1.3s (27.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	365	5	370

Merged error: 0b

Counts

370 → 5

regimes125.0ms (2.7%)

Accuracy

Total 0.1b remaining (75.3%)

Threshold costs 0.1b (75.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	21
1	34	21

end0.0ms (0%)

sample620.0ms (13.5%)

Algorithm

1×

intervals

Results

447.0ms	8000×	body	80	valid
14.0ms	267×	body	80	invalid
13.0ms	257×	body	80	nan

Details

analyze105.0ms (2.3%)

sample22.0ms (0.5%)

simplify186.0ms (4.1%)

prune9.0ms (0.2%)

localize18.0ms (0.4%)

rewrite63.0ms (1.4%)

series63.0ms (1.4%)

simplify59.0ms (1.3%)

prune299.0ms (6.5%)

localize12.0ms (0.3%)

rewrite43.0ms (0.9%)

series51.0ms (1.1%)

simplify38.0ms (0.8%)

prune289.0ms (6.3%)

localize10.0ms (0.2%)

rewrite59.0ms (1.3%)

series51.0ms (1.1%)

simplify107.0ms (2.3%)

prune842.0ms (18.3%)

localize12.0ms (0.3%)

rewrite87.0ms (1.9%)

series95.0ms (2.1%)

simplify71.0ms (1.6%)

prune1.3s (27.3%)

regimes125.0ms (2.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample620.0ms (13.5%)

Profiling