Details

analyze1.8s (14.1%)

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)

sample89.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	30×	body	2048	valid
14.0ms	162×	body	128	valid
10.0ms	19×	body	4096	valid
8.0ms	23×	body	1024	valid
4.0ms	15×	body	512	valid
2.0ms	29×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify139.0ms (1.1%)

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

34.9b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize28.0ms (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)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite239.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

34.6b

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` `flip--_binary64` `cancel-sign-sub-inv_binary64`
3×	`associate-/r*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_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)
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
11.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2014 to 333 computations (83.5% saved)

series1.0s (8.1%)

Error

5.9b

Counts

4 → 63

Calls

4 calls:

326.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
222.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
205.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
193.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2421 to 1744 computations (28% saved)

simplify148.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5125	2853

prune222.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	10	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	11	150

Error

5.6b

Counts

150 → 11

Compiler

Compiled 2751 to 607 computations (77.9% saved)

localize19.0ms (0.1%)

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)))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite358.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

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` `flip--_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 164

Calls

4 calls:

25.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 4825 to 1174 computations (75.7% saved)

series989.0ms (7.7%)

Error

5.6b

Counts

4 → 63

Calls

4 calls:

295.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
212.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
209.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
192.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2663 to 1989 computations (25.3% saved)

simplify179.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5054	5844

prune319.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	229	9	238

Error

5.6b

Counts

238 → 9

Compiler

Compiled 5098 to 1146 computations (77.5% saved)

localize7.0ms (0.1%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series1.0ms (0%)

Error: 5.6b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune11.0ms (0.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	2	2
Total	9	9

Error

5.6b

Counts

9 → 9

Compiler

Compiled 97 to 72 computations (25.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 (.f64 a c) (.f64 b_2 b_2))
5.6b	(/.f64 (-.f64 (.f64 b_2 b_2) (+.f64 (.f64 a c) (*.f64 b_2 b_2))) a)
20.1b	(-.f64 (.f64 b_2 b_2) (+.f64 (.f64 a c) (*.f64 b_2 b_2)))
23.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite174.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

21×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `difference-of-squares_binary64`
4×	`associate-/l*_binary64`
3×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
2×	`sqrt-div_binary64` `sum-log_binary64` `diff-log_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sub-neg_binary64` `associate--r+_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 b_2 b_2) (+.f64 (.f64 a c) (*.f64 b_2 b_2))) a)
11.0ms	(-.f64 (.f64 b_2 b_2) (+.f64 (.f64 a c) (*.f64 b_2 b_2)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
7.0ms	(+.f64 (.f64 a c) (.f64 b_2 b_2))

Compiler

Compiled 2748 to 371 computations (86.5% saved)

series710.0ms (5.5%)

Error

5.5b

Counts

4 → 55

Calls

4 calls:

221.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
213.0ms	(+.f64 (.f64 a c) (.f64 b_2 b_2))
111.0ms	(-.f64 (.f64 b_2 b_2) (+.f64 (.f64 a c) (*.f64 b_2 b_2)))
89.0ms	(/.f64 (-.f64 (.f64 b_2 b_2) (+.f64 (.f64 a c) (*.f64 b_2 b_2))) a)

Compiler

Compiled 3244 to 1597 computations (50.8% saved)

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5202	1828

prune179.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	2	3	5
Picked	1	0	1
Done	0	3	3
Total	133	8	141

Error

5.5b

Counts

141 → 8

Compiler

Compiled 3365 to 463 computations (86.2% saved)

regimes1.6s (12.7%)

Accuracy

Total 1.1b remaining (16.8%)

Threshold costs 0b (0%)

Compiler

Compiled 6904 to 4098 computations (40.6% saved)

bsearch169.0ms (1.3%)

Steps

Iters	Range	Point
8	1.735129888743692e+97	3.429390838977963e+101	1.1291300979796327e+98
9	-1.9480591979902562e-303	6.332890319204513e-308	-1.6792010575006621e-307
10	-2.6997952728725967e+101	-4.0928987339401984e+89	-1.361732391767175e+95

Iters

Range

Point

1.735129888743692e+97

3.429390838977963e+101

1.1291300979796327e+98

-1.9480591979902562e-303

6.332890319204513e-308

-1.6792010575006621e-307

-2.6997952728725967e+101

-4.0928987339401984e+89

-1.361732391767175e+95

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	72
1	86	72

end0.0ms (0%)

sample4.2s (32.8%)

Algorithm

1×

intervals

Results

421.0ms	1092×	body	2048	valid
413.0ms	5208×	body	128	valid
204.0ms	696×	body	1024	valid
199.0ms	424×	body	4096	valid
87.0ms	393×	body	512	valid
62.0ms	757×	body	128	nan
28.0ms	187×	body	256	valid
21.0ms	270×	body	128	invalid

Compiler

Compiled 1780 to 1056 computations (40.7% saved)

Details

analyze1.8s (14.1%)

sample89.0ms (0.7%)

simplify139.0ms (1.1%)

prune11.0ms (0.1%)

localize28.0ms (0.2%)

rewrite239.0ms (1.9%)

series1.0s (8.1%)

simplify148.0ms (1.2%)

prune222.0ms (1.7%)

localize19.0ms (0.1%)

rewrite358.0ms (2.8%)

series989.0ms (7.7%)

simplify179.0ms (1.4%)

prune319.0ms (2.5%)

localize7.0ms (0.1%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify11.0ms (0.1%)

prune11.0ms (0.1%)

localize23.0ms (0.2%)

rewrite174.0ms (1.4%)

series710.0ms (5.5%)

simplify112.0ms (0.9%)

prune179.0ms (1.4%)

regimes1.6s (12.7%)

bsearch169.0ms (1.3%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample4.2s (32.8%)

Profiling