Details

analyze1.9s (15.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	72
1	1992	72
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample74.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	159×	body	128	valid
14.0ms	33×	body	2048	valid
9.0ms	28×	body	1024	valid
7.0ms	13×	body	4096	valid
3.0ms	12×	body	512	valid
3.0ms	30×	body	128	nan
2.0ms	11×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune11.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.8b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite75.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
16.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
10.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series1.0s (8.7%)

Counts

4 → 69

Calls

4 calls:

329.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
268.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
228.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
223.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1725 to 1398 computations (19% saved)

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5250	3068

prune285.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	142	13	155
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	13	156

Error

4.4b

Counts

156 → 13

Compiler

Compiled 2874 to 653 computations (77.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite98.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
124×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
71×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
24×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 164

Calls

4 calls:

31.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series1.0s (8.4%)

Counts

4 → 69

Calls

4 calls:

321.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
261.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
227.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
201.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1879 to 1552 computations (17.4% saved)

simplify149.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5074	6059

prune338.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	234	12	246

Error

4.4b

Counts

246 → 12

Compiler

Compiled 5297 to 1212 computations (77.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
12.3b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) b_2)
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite64.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`difference-of-squares_binary64`

Counts

4 → 57

Calls

4 calls:

31.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) b_2)
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series1.1s (8.9%)

Counts

4 → 75

Calls

4 calls:

285.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) b_2)
271.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
265.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
248.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2886 to 2091 computations (27.5% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4994	2164
1	4994	2164

prune201.0ms (1.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	132	12	144

Error

4.4b

Counts

144 → 12

Compiler

Compiled 3427 to 783 computations (77.2% saved)

localize7.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms (0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	2	2
Total	12	12

Error

4.4b

Counts

12 → 12

Compiler

Compiled 0 to 0 computations (0% saved)

regimes1.9s (15.7%)

Accuracy

Total 4.3b remaining (44.2%)

Threshold costs 0b (0%)

Compiler

Compiled 3844 to 2378 computations (38.1% saved)

bsearch96.0ms (0.8%)

Steps

Iters	Range		Point
7	9.552551429944764e-107	1.810979747950746e-104	1.7698566509785747e-104
9	-2.8121047578881617e+159	-4.920445536489442e+152	-1.4123968497632831e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	53
1	65	53

end0.0ms (0%)

sample3.4s (28.1%)

Algorithm

1×

intervals

Results

452.0ms	1100×	body	2048	valid
447.0ms	5201×	body	128	valid
241.0ms	754×	body	1024	valid
201.0ms	399×	body	4096	valid
86.0ms	366×	body	512	valid
59.0ms	741×	body	128	nan
32.0ms	180×	body	256	valid
19.0ms	229×	body	128	invalid

Compiler

Compiled 1003 to 623 computations (37.9% saved)

Details

analyze1.9s (15.4%)

sample74.0ms (0.6%)

simplify139.0ms (1.2%)

prune11.0ms (0.1%)

localize19.0ms (0.2%)

rewrite75.0ms (0.6%)

series1.0s (8.7%)

simplify100.0ms (0.8%)

prune285.0ms (2.4%)

localize19.0ms (0.2%)

rewrite98.0ms (0.8%)

series1.0s (8.4%)

simplify149.0ms (1.2%)

prune338.0ms (2.8%)

localize21.0ms (0.2%)

rewrite64.0ms (0.5%)

series1.1s (8.9%)

simplify83.0ms (0.7%)

prune201.0ms (1.7%)

localize7.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

regimes1.9s (15.7%)

bsearch96.0ms (0.8%)

simplify6.0ms (0%)

end0.0ms (0%)

sample3.4s (28.1%)

Profiling