Details

analyze3.5s (21.2%)

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)

sample286.0ms (1.7%)

Algorithm

1×

intervals

Results

141.0ms	96×	body	1024	valid
109.0ms	58×	body	2048	valid
12.0ms	51×	body	512	valid
6.0ms	5×	body	4096	valid
5.0ms	31×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify86.0ms (0.5%)

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

prune2.0ms (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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.1b	(-.f64 x (tan.f64 x))
✓	1.1b	(-.f64 x (sin.f64 x))

series18.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite22.0ms (0.1%)

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:

7.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
3.0ms	(-.f64 x (sin.f64 x))

simplify104.0ms (0.6%)

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 → 152

Iterations

Useful iterations: 2 (0.0ms)

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

prune72.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	4	153

Error

0.0b

Counts

153 → 4

Alt Table

Status	Error	Program
	46.2b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 (fma.f64 1 x (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))))
	30.4b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.4b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
▶	30.2b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 3218 to 921 computations (71.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
	1.1b	(-.f64 x (tan.f64 x))
	1.1b	(-.f64 x (sin.f64 x))

series18.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
8.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 204

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
7.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))

simplify185.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

643×	`times-frac_binary64`
434×	`fma-def_binary64`
272×	`distribute-rgt-in_binary64`
239×	`div-sub_binary64`
233×	`distribute-lft-in_binary64`

Counts

228 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	6694
1	576	6207
2	1867	6034
3	4735	6028
4	5371	6028

prune160.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	324	4	328

Error

0.0b

Counts

328 → 4

Alt Table

Status	Error	Program
	46.2b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 (fma.f64 1 x (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))))
▶	30.4b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.4b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	30.2b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 7726 to 2240 computations (71% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.1b	(/.f64 1 (cos.f64 x))
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
✓	1.5b	(+.f64 (/.f64 1 (cos.f64 x)) -1)

series56.0ms (0.3%)

Counts

4 → 32

Calls

4 calls:

24.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
14.0ms	(/.f64 1 (cos.f64 x))
10.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
6.0ms	(/.f64 (sin.f64 x) x)

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
41×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 138

Calls

4 calls:

22.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
13.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
4.0ms	(/.f64 1 (cos.f64 x))
4.0ms	(/.f64 (sin.f64 x) x)

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

443×	`fma-def_binary64`
410×	`associate-*l/_binary64`
341×	`associate-/l*_binary64`
334×	`distribute-rgt-in_binary64`
312×	`associate-*r/_binary64`

Counts

170 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	2417
1	573	2236
2	1485	2213
3	4391	2213
4	4980	2213

prune169.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	215	4	219

Error

0.0b

Counts

219 → 4

Alt Table

Status	Error	Program
	46.2b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 (fma.f64 1 x (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))))
✓	30.4b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
▶	33.4b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	30.2b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 4519 to 2458 computations (45.6% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 9/40 (.f64 x x))
✓	0.3b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	16.1b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series14.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
4.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
3.0ms	(.f64 9/40 (.f64 x x))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
4.0ms	(.f64 9/40 (.f64 x x))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-neg_binary64`
399×	`associate-+r+_binary64`
379×	`associate-+l+_binary64`
320×	`fma-def_binary64`
300×	`times-frac_binary64`

Counts

88 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1147
1	199	1072
2	668	980
3	2038	980
4	4543	969
5	4942	969

prune55.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	81	4	85

Error

0.0b

Counts

85 → 4

Alt Table

Status	Error	Program
✓	30.2b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
	33.4b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
	46.2b	(/.f64 (-.f64 x (sin.f64 x)) (+.f64 (fma.f64 1 x (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))))
✓	30.4b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))

Compiler

Compiled 1580 to 1145 computations (27.5% saved)

regimes119.0ms (0.7%)

Accuracy

Total 0.0b remaining (38.4%)

Threshold costs 0.0b (38.4%)

Counts

33 → 3

Compiler

Compiled 937 to 615 computations (34.4% saved)

bsearch93.0ms (0.6%)

Steps

Iters	Range		Point
9	3.5509424094744937e-9	0.21010183126687135	0.0294829394400758
9	-172.9036424740226	-0.00038194101173499374	-0.03251857343197739

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	64
1	31	64
2	39	64
3	43	64
4	45	64
5	45	64

end2.0ms (0%)

Compiler: Compiled 43 to 25 computations (41.9% saved)

sample11.3s (68%)

Algorithm

1×

intervals

Results

7.0s	1991×	body	2048	valid
2.4s	3053×	body	1024	valid
613.0ms	1490×	body	512	valid
256.0ms	101×	body	4096	valid
253.0ms	747×	body	256	valid
95.0ms	618×	body	128	valid

Compiler

Compiled 127 to 75 computations (40.9% saved)

Details

analyze3.5s (21.2%)

sample286.0ms (1.7%)

simplify86.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0%)

series18.0ms (0.1%)

rewrite22.0ms (0.1%)

simplify104.0ms (0.6%)

prune72.0ms (0.4%)

localize8.0ms (0%)

series18.0ms (0.1%)

rewrite45.0ms (0.3%)

simplify185.0ms (1.1%)

prune160.0ms (1%)

localize18.0ms (0.1%)

series56.0ms (0.3%)

rewrite50.0ms (0.3%)

simplify101.0ms (0.6%)

prune169.0ms (1%)

localize14.0ms (0.1%)

series14.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify74.0ms (0.4%)

prune55.0ms (0.3%)

regimes119.0ms (0.7%)

bsearch93.0ms (0.6%)

simplify7.0ms (0%)

end2.0ms (0%)

sample11.3s (68%)

Profiling