Details

analyze601.0ms (10.3%)

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)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	46×	body	2048	valid
7.0ms	146×	body	128	valid
4.0ms	26×	body	1024	valid
4.0ms	15×	body	4096	valid
2.0ms	18×	body	512	valid
1.0ms	34×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify171.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

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

Merged error: 38.9b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series236.0ms (4.1%)

Counts

4 → 36

Calls

4 calls:

97.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
62.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
54.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5271	3211

prune131.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	11	133

Merged error: 10.1b

Counts

133 → 11

Compiler

Compiled 2908 to 624 computations (78.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.6b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.9b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 129

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
14.0ms	(/.f64 (.f64 a c) (-.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)))

series371.0ms (6.4%)

Counts

4 → 36

Calls

4 calls:

147.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
123.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
41.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5109	5015

prune151.0ms (2.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	6	3	9
Picked	1	0	1
Done	0	1	1
Total	163	13	176

Merged error: 8.4b

Counts

176 → 13

Compiler

Compiled 4536 to 900 computations (80.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.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))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms (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×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(/.f64 c (-.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	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series251.0ms (4.3%)

Counts

4 → 36

Calls

4 calls:

124.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
41.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5127	2924

prune100.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	7	4	11
Picked	0	1	1
Done	0	1	1
Total	127	7	134

Merged error: 7.4b

Counts

134 → 7

Compiler

Compiled 2830 to 805 computations (71.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
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))

series250.0ms (4.3%)

Counts

4 → 36

Calls

4 calls:

124.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
41.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5159	5630

prune150.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	191	8	199

Merged error: 7.4b

Counts

199 → 8

Compiler

Compiled 4638 to 972 computations (79% saved)

regimes770.0ms (13.2%)

Compiler: Compiled 5455 to 3050 computations (44.1% saved)

bsearch101.0ms (1.7%)

Steps

Iters	Range	Point
9	4.3769022778595943e+126	1.2317934582595504e+132	1.202936056126418e+131
10	-1.4570940629344822e-237	-1.2678616427067808e-254	-1.2914624728520754e-254
8	-6.552313714640706e+158	-1.23943341754481e+154	-1.3429027736351954e+154

Iters

Range

Point

4.3769022778595943e+126

1.2317934582595504e+132

1.202936056126418e+131

-1.4570940629344822e-237

-1.2678616427067808e-254

-1.2914624728520754e-254

-6.552313714640706e+158

-1.23943341754481e+154

-1.3429027736351954e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	91
1	130	91

end0.0ms (0%)

sample1.9s (33.4%)

Algorithm

1×

intervals

Results

239.0ms	1157×	body	2048	valid
228.0ms	5079×	body	128	valid
126.0ms	754×	body	1024	valid
111.0ms	417×	body	4096	valid
52.0ms	404×	body	512	valid
36.0ms	774×	body	128	nan
16.0ms	189×	body	256	valid
12.0ms	272×	body	128	invalid

Compiler

Compiled 1395 to 781 computations (44% saved)

Details

analyze601.0ms (10.3%)

sample44.0ms (0.8%)

simplify171.0ms (2.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite49.0ms (0.8%)

series236.0ms (4.1%)

simplify73.0ms (1.2%)

prune131.0ms (2.2%)

localize9.0ms (0.2%)

rewrite52.0ms (0.9%)

series371.0ms (6.4%)

simplify86.0ms (1.5%)

prune151.0ms (2.6%)

localize9.0ms (0.2%)

rewrite33.0ms (0.6%)

series251.0ms (4.3%)

simplify68.0ms (1.2%)

prune100.0ms (1.7%)

localize11.0ms (0.2%)

rewrite45.0ms (0.8%)

series250.0ms (4.3%)

simplify96.0ms (1.7%)

prune150.0ms (2.6%)

regimes770.0ms (13.2%)

bsearch101.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (33.4%)

Profiling