Details

analyze610.0ms (8.3%)

Algorithm

1×

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)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	38×	body	2048	valid
7.0ms	155×	body	128	valid
5.0ms	27×	body	1024	valid
3.0ms	13×	body	4096	valid
1.0ms	36×	body	128	nan
1.0ms	12×	body	512	valid
1.0ms	11×	body	256	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify172.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune6.0ms (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)

localize10.0ms (0.1%)

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)
1.0b	(-.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)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms (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:

12.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series578.0ms (7.9%)

Counts

4 → 67

Calls

4 calls:

189.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
128.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)

Compiler

Compiled 1712 to 1386 computations (19% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5012	2999

prune149.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	10	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Error

4.4b

Counts

154 → 10

Compiler

Compiled 2792 to 600 computations (78.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
1.0b	(-.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)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite48.0ms (0.7%)

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:

14.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series545.0ms (7.4%)

Counts

4 → 67

Calls

4 calls:

172.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
129.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
123.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)

Compiler

Compiled 1864 to 1538 computations (17.5% saved)

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4961	5990
1	4961	5990

prune176.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	230	11	241

Error

4.4b

Counts

241 → 11

Compiler

Compiled 5228 to 1179 computations (77.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
1.0b	(-.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)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite112.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

789×	`times-frac_binary64`
494×	`add-sqr-sqrt_binary64`
407×	`*-un-lft-identity_binary64`
321×	`add-cube-cbrt_binary64`
86×	`difference-of-squares_binary64`
46×	`sqrt-prod_binary64`
44×	`add-exp-log_binary64`
43×	`distribute-lft-out--_binary64`
40×	`div-inv_binary64`
32×	`div-exp_binary64`
29×	`associate-/r/_binary64`
24×	`associate-/r*_binary64`
17×	`flip3--_binary64` `flip--_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
5×	`pow1_binary64`
4×	`cancel-sign-sub-inv_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 425

Calls

4 calls:

25.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series571.0ms (7.8%)

Counts

4 → 67

Calls

4 calls:

188.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
132.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
127.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
124.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2016 to 1690 computations (16.2% saved)

simplify216.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

492 → 492

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5012	18660

prune505.0ms (6.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	491	1	492
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	492	11	503

Error

4.4b

Counts

503 → 11

Compiler

Compiled 13791 to 3694 computations (73.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series533.0ms (7.2%)

Counts

4 → 64

Calls

4 calls:

138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
126.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3176 to 2224 computations (30% saved)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5089	2186

prune109.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	128	11	139

Error

4.4b

Counts

139 → 11

Compiler

Compiled 3736 to 606 computations (83.8% saved)

regimes798.0ms (10.9%)

Accuracy

Total 5.3b remaining (48.8%)

Threshold costs 0b (0%)

Compiler

Compiled 3580 to 2318 computations (35.3% saved)

bsearch76.0ms (1%)

Steps

Iters	Range		Point
11	1.4996567207304356e-167	2.1758290880961906e-142	2.142371076687032e-142
12	-4.659684812883713e+193	-4.559874932742751e+148	-1.5888046213400475e+149

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	44
1	60	44

end0.0ms (0%)

sample1.7s (23.5%)

Algorithm

1×

intervals

Results

235.0ms	5231×	body	128	valid
223.0ms	1066×	body	2048	valid
119.0ms	732×	body	1024	valid
107.0ms	421×	body	4096	valid
41.0ms	347×	body	512	valid
36.0ms	814×	body	128	nan
16.0ms	203×	body	256	valid
10.0ms	225×	body	128	invalid

Compiler

Compiled 931 to 605 computations (35% saved)

Details

analyze610.0ms (8.3%)

sample43.0ms (0.6%)

simplify172.0ms (2.3%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite46.0ms (0.6%)

series578.0ms (7.9%)

simplify74.0ms (1%)

prune149.0ms (2%)

localize10.0ms (0.1%)

rewrite48.0ms (0.7%)

series545.0ms (7.4%)

simplify114.0ms (1.6%)

prune176.0ms (2.4%)

localize11.0ms (0.2%)

rewrite112.0ms (1.5%)

series571.0ms (7.8%)

simplify216.0ms (2.9%)

prune505.0ms (6.9%)

localize11.0ms (0.2%)

rewrite31.0ms (0.4%)

series533.0ms (7.2%)

simplify65.0ms (0.9%)

prune109.0ms (1.5%)

regimes798.0ms (10.9%)

bsearch76.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.7s (23.5%)

Profiling