Details

analyze3.3s (11.5%)

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
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)

sample196.0ms (0.7%)

Algorithm

1×

intervals

Results

83.0ms	65×	body	1024	valid
32.0ms	43×	body	512	valid
30.0ms	128×	body	128	valid
9.0ms	19×	body	256	valid
4.0ms	18×	body	128	invalid
2.0ms	1×	body	2048	valid
1.0ms	5×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify426.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (244.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune16.0ms (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

14.8b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize51.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 F (sin.f64 B))
6.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite417.0ms (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:

29.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
19.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
7.0ms	(/.f64 F (sin.f64 B))
7.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series1.7s (6%)

Error

0.1b

Counts

4 → 46

Calls

4 calls:

658.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
403.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
371.0ms	(/.f64 x (tan.f64 B))
155.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3903 to 2829 computations (27.5% saved)

simplify170.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4969	3736
1	4969	3736

prune431.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	147	14	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	14	163

Error

0.0b

Counts

163 → 14

Compiler

Compiled 4998 to 2496 computations (50.1% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
16.7b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite286.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 93

Calls

4 calls:

24.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
20.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))
12.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
7.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 2798 to 1468 computations (47.5% saved)

series1.8s (6.3%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

638.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2)) (sin.f64 B))
366.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
333.0ms	(/.f64 x (tan.f64 B))
329.0ms	(.f64 F (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2))

Compiler

Compiled 4452 to 3313 computations (25.6% saved)

simplify172.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4981	3753
1	4981	3753

prune413.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	147	12	159

Error

0.0b

Counts

159 → 12

Compiler

Compiled 4525 to 2467 computations (45.5% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.3b	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)))
0.4b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2))
16.7b	(pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)

rewrite787.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

189×	`times-frac_binary64`
112×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
51×	`unpow-prod-down_binary64`
35×	`associate-/r*_binary64`
22×	`add-exp-log_binary64`
17×	`sqr-pow_binary64`
13×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
5×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `frac-2neg_binary64` `clear-num_binary64`
2×	`associate-/r/_binary64`
1×	`pow-pow_binary64` `tan-quot_binary64`

Counts

4 → 210

Calls

4 calls:

25.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)))
19.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2))
12.0ms	(pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)
7.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 7827 to 4098 computations (47.6% saved)

series1.9s (6.5%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

618.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)))
440.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2))
342.0ms	(/.f64 x (tan.f64 B))
315.0ms	(pow.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))) -1/2)

Compiler

Compiled 4945 to 3510 computations (29% saved)

simplify271.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4943	9798
1	4943	9798

prune1.0s (3.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	265	2	267
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	266	13	279

Error

0.0b

Counts

279 → 13

Compiler

Compiled 9489 to 4841 computations (49% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(*.f64 F (/.f64 1 (sin.f64 B)))
6.5b	(.f64 (.f64 F (/.f64 1 (sin.f64 B))) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2))
16.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite408.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 117

Calls

4 calls:

31.0ms	(.f64 (.f64 F (/.f64 1 (sin.f64 B))) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2))
16.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
16.0ms	(*.f64 F (/.f64 1 (sin.f64 B)))
11.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 3654 to 2010 computations (45% saved)

series1.7s (5.9%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

669.0ms	(.f64 (.f64 F (/.f64 1 (sin.f64 B))) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2))
372.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
366.0ms	(/.f64 x (tan.f64 B))
176.0ms	(*.f64 F (/.f64 1 (sin.f64 B)))

Compiler

Compiled 4009 to 2957 computations (26.2% saved)

simplify171.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4908	3381
1	4908	3381

prune398.0ms (1.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	163	13	176

Error

0.0b

Counts

176 → 13

Compiler

Compiled 4687 to 2468 computations (47.3% saved)

regimes2.2s (7.7%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Compiler

Compiled 11128 to 8624 computations (22.5% saved)

bsearch287.0ms (1%)

Steps

Iters	Range		Point
8	3.5002673822567855e-06	0.0033015066052798896	0.003263911912299716
9	-486175378.59057677	-3.249062292476843	-16872814.748516325

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	57	84
1	57	84

end0.0ms (0%)

sample10.2s (35.3%)

Algorithm

1×

intervals

Results

2.3s	2194×	body	1024	valid
941.0ms	4123×	body	128	valid
777.0ms	1089×	body	512	valid
275.0ms	585×	body	256	valid
164.0ms	713×	body	128	invalid
22.0ms	122×	body	128	nan
15.0ms	9×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 2849 to 2203 computations (22.7% saved)

Details

analyze3.3s (11.5%)

sample196.0ms (0.7%)

simplify426.0ms (1.5%)

prune16.0ms (0.1%)

localize51.0ms (0.2%)

rewrite417.0ms (1.4%)

series1.7s (6%)

simplify170.0ms (0.6%)

prune431.0ms (1.5%)

localize33.0ms (0.1%)

rewrite286.0ms (1%)

series1.8s (6.3%)

simplify172.0ms (0.6%)

prune413.0ms (1.4%)

localize34.0ms (0.1%)

rewrite787.0ms (2.7%)

series1.9s (6.5%)

simplify271.0ms (0.9%)

prune1.0s (3.5%)

localize41.0ms (0.1%)

rewrite408.0ms (1.4%)

series1.7s (5.9%)

simplify171.0ms (0.6%)

prune398.0ms (1.4%)

regimes2.2s (7.7%)

bsearch287.0ms (1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample10.2s (35.3%)

Profiling