Details

analyze3.9s (23.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample497.0ms (3%)

Algorithm

1×

intervals

Results

360.0ms	65×	body	2048	valid
72.0ms	86×	body	1024	valid
31.0ms	61×	body	512	valid
8.0ms	4×	body	4096	valid
6.0ms	19×	body	256	valid
4.0ms	21×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

prune3.0ms (0%)

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

30.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	0.9b	(-.f64 x (tan.f64 x))
✓	0.9b	(-.f64 x (sin.f64 x))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

15.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
7.0ms	(-.f64 x (tan.f64 x))
7.0ms	(-.f64 x (sin.f64 x))

series52.0ms (0.3%)

Counts

3 → 30

Calls

3 calls:

21.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
21.0ms	(-.f64 x (tan.f64 x))
9.0ms	(-.f64 x (sin.f64 x))

simplify219.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune156.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	211	4	215
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	212	4	216

Error

Counts

216 → 4

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
▶	30.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	30.8b	(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x)))) (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (sin.f64 x) x))
	32.2b	(fma.f64 9/40 (*.f64 x x) -1/2)

Compiler

Compiled 3234 to 916 computations (71.7% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	0.9b	(-.f64 x (tan.f64 x))
	0.9b	(-.f64 x (sin.f64 x))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
25×	`times-frac_binary64`

Counts

1 → 46

Calls

1 calls:

21.0ms

(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

series55.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

54.0ms

(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

simplify176.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary64`
417×	`unswap-sqr_binary64`
355×	`times-frac_binary64`
239×	`associate-/l*_binary64`
207×	`sub-neg_binary64`

Counts

58 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1282
1	303	1232
2	772	1192
3	3133	1180
4	4898	1180
5	4976	1180

prune226.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	325	4	329

Error

Counts

329 → 4

Alt Table

Status	Error	Program
	30.9b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	30.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
▶	30.1b	(log.f64 (exp.f64 (*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))))
	32.2b	(fma.f64 9/40 (*.f64 x x) -1/2)

Compiler

Compiled 5252 to 1510 computations (71.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (exp.f64 (*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))))
✓	0.1b	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
	0.9b	(-.f64 x (tan.f64 x))
	0.9b	(-.f64 x (sin.f64 x))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`associate-r_binary64`
17×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 69

Calls

2 calls:

24.0ms	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
4.0ms	(log.f64 (exp.f64 (*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))))

series71.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

51.0ms	(log.f64 (exp.f64 (*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))))
20.0ms	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))

simplify178.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
377×	`times-frac_binary64`
338×	`associate-l_binary64`
318×	`associate-/l*_binary64`
313×	`associate-r_binary64`

Counts

93 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2214
1	375	2060
2	1184	1984
3	4587	1984
4	5118	1984

prune226.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	409	0	409
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	409	4	413

Error

Counts

413 → 4

Alt Table

Status	Error	Program
▶	30.9b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	30.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	30.1b	(log.f64 (exp.f64 (*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))))
	32.2b	(fma.f64 9/40 (*.f64 x x) -1/2)

Compiler

Compiled 4976 to 1972 computations (60.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(-.f64 x (tan.f64 x))
	0.9b	(-.f64 x (tan.f64 x))
	0.9b	(-.f64 x (sin.f64 x))
	0.9b	(-.f64 x (sin.f64 x))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune175.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1428	0	1428
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1428	4	1432

Error

Counts

1432 → 4

Alt Table

Status	Error	Program
✓	30.9b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	30.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	30.1b	(log.f64 (exp.f64 (*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))))
	32.2b	(fma.f64 9/40 (*.f64 x x) -1/2)

Compiler

Compiled 5532 to 1202 computations (78.3% saved)

regimes226.0ms (1.4%)

Accuracy

Total 0.1b remaining (64%)

Threshold costs 0.1b (64%)

Compiler

Compiled 1524 to 864 computations (43.3% saved)

bsearch88.0ms (0.5%)

Steps

Iters	Range		Point
9	1.5917922070283656e-6	2056.451616149925	0.003965314230899635
10	-176548.3900270325	-2.343531164785286e-6	-2.208632844132881

Compiler

Compiled 2 to 1 computations (50% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	96
1	55	96
2	71	96
3	79	96
4	83	96
5	81	96

end2.0ms (0%)

Compiler: Compiled 62 to 36 computations (41.9% saved)

sample10.0s (60.1%)

Algorithm

1×

intervals

Results

6.4s	1999×	body	2048	valid
2.1s	2998×	body	1024	valid
580.0ms	1527×	body	512	valid
184.0ms	728×	body	256	valid
170.0ms	104×	body	4096	valid
101.0ms	644×	body	128	valid

Compiler

Compiled 129 to 75 computations (41.9% saved)

Details

analyze3.9s (23.6%)

sample497.0ms (3%)

simplify103.0ms (0.6%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite42.0ms (0.3%)

series52.0ms (0.3%)

simplify219.0ms (1.3%)

prune156.0ms (0.9%)

localize27.0ms (0.2%)

rewrite30.0ms (0.2%)

series55.0ms (0.3%)

simplify176.0ms (1.1%)

prune226.0ms (1.4%)

localize22.0ms (0.1%)

rewrite37.0ms (0.2%)

series71.0ms (0.4%)

simplify178.0ms (1.1%)

prune226.0ms (1.4%)

localize19.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify48.0ms (0.3%)

prune175.0ms (1.1%)

regimes226.0ms (1.4%)

bsearch88.0ms (0.5%)

simplify11.0ms (0.1%)

end2.0ms (0%)

sample10.0s (60.1%)

Profiling