Details

analyze2.0s (10.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4785	128
1	4785	128
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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample106.0ms (0.6%)

Algorithm

1×

intervals

Results

43.0ms	75×	body	1024	valid
18.0ms	117×	body	128	valid
16.0ms	43×	body	512	valid
5.0ms	21×	body	256	valid
2.0ms	19×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify133.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune10.0ms (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

Error

12.8b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
5.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite252.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

10.7b

Rules

44×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`prod-exp_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 115

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series1.5s (7.9%)

Error

0.2b

Counts

4 → 51

Calls

4 calls:

576.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
347.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
283.0ms	(/.f64 x (tan.f64 B))
150.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4362 to 3161 computations (27.5% saved)

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4923	3898
1	4923	3898

prune299.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	154	12	166
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	12	168

Error

0.0b

Counts

168 → 12

Compiler

Compiled 5105 to 2541 computations (50.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
17.5b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite291.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
25×	`unpow-prod-down_binary64` `associate-r_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-l_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`pow-pow_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 138

Calls

4 calls:

15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
6.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 4662 to 2467 computations (47.1% saved)

series1.8s (9.7%)

Error

0.0b

Counts

4 → 61

Calls

4 calls:

543.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
513.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
317.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
280.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 5581 to 4106 computations (26.4% saved)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4964	6120
1	4964	6120

prune364.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	198	13	211

Error

0.0b

Counts

211 → 13

Compiler

Compiled 6730 to 3633 computations (46% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 F)
0.6b	(cbrt.f64 F)
1.8b	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
17.5b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite211.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

44×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
22×	`associate-r_binary64`
18×	`add-exp-log_binary64` `cbrt-prod_binary64`
9×	`unpow-prod-down_binary64` `unswap-sqr_binary64`
8×	`add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`prod-exp_binary64`
5×	`pow1_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `pow1/3_binary64`
1×	`pow-pow_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
6.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)

Compiler

Compiled 3793 to 1676 computations (55.8% saved)

series1.4s (7.6%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

761.0ms	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
326.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
114.0ms	(cbrt.f64 F)
107.0ms	(cbrt.f64 F)

Compiler

Compiled 4333 to 3185 computations (26.5% saved)

simplify98.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4924	3610
1	4924	3610

prune257.0ms (1.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	128	15	143

Error

0.0b

Counts

143 → 15

Compiler

Compiled 5317 to 2530 computations (52.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
5.1b	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
17.5b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
17.5b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

rewrite492.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

72×	`add-exp-log_binary64`
58×	`add-sqr-sqrt_binary64`
47×	`prod-exp_binary64`
44×	`unpow-prod-down_binary64`
28×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
23×	`associate-l_binary64`
18×	`add-cbrt-cube_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unswap-sqr_binary64`
12×	`sqr-pow_binary64` `swap-sqr_binary64`
11×	`associate-r_binary64`
10×	`div-exp_binary64` `times-frac_binary64`
8×	`pow1_binary64`
7×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `*-commutative_binary64`
1×	`associate-*l/_binary64` `div-inv_binary64` `pow2_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`

Counts

4 → 150

Calls

4 calls:

24.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
19.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
6.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
6.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

Compiler

Compiled 7593 to 4488 computations (40.9% saved)

series1.2s (6.7%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

568.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
196.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
179.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
174.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

Compiler

Compiled 5742 to 4200 computations (26.9% saved)

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4951	6731
1	4951	6731

prune442.0ms (2.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	210	15	225

Error

0.0b

Counts

225 → 15

Compiler

Compiled 7833 to 4388 computations (44% saved)

regimes1.4s (7.8%)

Accuracy

Total 0.2b remaining (94.5%)

Threshold costs 0.2b (94.5%)

Compiler

Compiled 12896 to 9780 computations (24.2% saved)

bsearch156.0ms (0.8%)

Steps

Iters	Range		Point
8	6452015.598640546	17838438981.706886	107624428.82360403
9	-2.5818420275574264e+65	-2.790998873094731e+60	-2.3713589216342914e+61

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	50	68
1	50	68

end0.0ms (0%)

sample5.6s (30.4%)

Algorithm

1×

intervals

Results

1.3s	2249×	body	1024	valid
535.0ms	4084×	body	128	valid
422.0ms	1080×	body	512	valid
151.0ms	585×	body	256	valid
82.0ms	663×	body	128	invalid
14.0ms	136×	body	128	nan
2.0ms	2×	body	2048	valid

Compiler

Compiled 3281 to 2484 computations (24.3% saved)

Details

analyze2.0s (10.8%)

sample106.0ms (0.6%)

simplify133.0ms (0.7%)

prune10.0ms (0.1%)

localize25.0ms (0.1%)

rewrite252.0ms (1.4%)

series1.5s (7.9%)

simplify100.0ms (0.5%)

prune299.0ms (1.6%)

localize18.0ms (0.1%)

rewrite291.0ms (1.6%)

series1.8s (9.7%)

simplify103.0ms (0.6%)

prune364.0ms (2%)

localize23.0ms (0.1%)

rewrite211.0ms (1.2%)

series1.4s (7.6%)

simplify98.0ms (0.5%)

prune257.0ms (1.4%)

localize23.0ms (0.1%)

rewrite492.0ms (2.7%)

series1.2s (6.7%)

simplify90.0ms (0.5%)

prune442.0ms (2.4%)

regimes1.4s (7.8%)

bsearch156.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.6s (30.4%)

Profiling