Details

analyze1.8s (14.3%)

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)

sample9.0s (73.8%)

Results

5.5s	2030×	body	2048	valid
2.3s	3151×	body	1024	valid
613.0ms	1572×	body	512	valid
207.0ms	718×	body	256	valid
146.0ms	104×	body	4096	valid
114.0ms	681×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify84.0ms (0.7%)

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

29.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (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)))
✓	1.4b	(-.f64 x (tan.f64 x))
✓	1.5b	(-.f64 x (sin.f64 x))

series15.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

8.0ms	(/.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))

rewrite21.0ms (0.2%)

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)))
3.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify104.0ms (0.9%)

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

prune81.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	4	153

Error

0.0b

Counts

153 → 4

Alt Table

Status	Error	Program
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	29.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.8b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
▶	29.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 3172 to 909 computations (71.3% saved)

localize8.0ms (0.1%)

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))))
	1.4b	(-.f64 x (tan.f64 x))
	1.5b	(-.f64 x (sin.f64 x))

series12.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
5.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))

rewrite50.0ms (0.4%)

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:

15.0ms	(/.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)))

simplify196.0ms (1.6%)

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

prune136.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	323	1	324
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	323	5	328

Error

Counts

328 → 5

Alt Table

Status	Error	Program
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	29.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
	33.4b	(/.f64 1 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
	33.8b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	29.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 7708 to 2250 computations (70.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (cos.f64 x))
✓	0.2b	(/.f64 (sin.f64 x) x)
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
✓	2.0b	(+.f64 (/.f64 1 (cos.f64 x)) -1)

series26.0ms (0.2%)

Counts

4 → 32

Calls

4 calls:

9.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
9.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
5.0ms	(/.f64 1 (cos.f64 x))
3.0ms	(/.f64 (sin.f64 x) x)

rewrite29.0ms (0.2%)

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:

11.0ms	(*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1))
5.0ms	(+.f64 (/.f64 1 (cos.f64 x)) -1)
5.0ms	(/.f64 (sin.f64 x) x)
2.0ms	(/.f64 1 (cos.f64 x))

simplify92.0ms (0.8%)

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

prune127.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	215	5	220

Error

Counts

220 → 5

Alt Table

Status	Error	Program
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
▶	33.4b	(/.f64 1 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
	33.8b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	29.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 4501 to 2470 computations (45.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
✓	0.0b	(fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2))
✓	0.1b	(fma.f64 (*.f64 x x) -9/10 -2)

series9.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 1 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
3.0ms	(fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2))
2.0ms	(fma.f64 (*.f64 x x) -9/10 -2)

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 53

Calls

3 calls:

2.0ms	(/.f64 1 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
0.0ms	(fma.f64 (*.f64 x x) -9/10 -2)
0.0ms	(fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2))

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-neg_binary64`
603×	`fma-def_binary64`
453×	`div-sub_binary64`
359×	`cancel-sign-sub-inv_binary64`
285×	`times-frac_binary64`

Counts

89 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1731
1	222	1527
2	513	1521
3	1772	1517
4	4212	1517
5	5225	1517

prune75.0ms (0.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	107	5	112

Error

Counts

112 → 5

Alt Table

Status	Error	Program
✓	29.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.7b	(+.f64 1 (*.f64 (/.f64 (sin.f64 x) x) (+.f64 (/.f64 1 (cos.f64 x)) -1)))
✓	33.4b	(/.f64 1 (fma.f64 (pow.f64 x 4) -513/1400 (fma.f64 (*.f64 x x) -9/10 -2)))
	33.8b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	29.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))

Compiler

Compiled 2184 to 1652 computations (24.4% saved)

regimes104.0ms (0.8%)

Accuracy

Total 0.2b remaining (93.4%)

Threshold costs 0.2b (93.4%)

Counts

36 → 3

Compiler

Compiled 1082 to 772 computations (28.7% saved)

bsearch59.0ms (0.5%)

Steps

Iters	Range		Point
10	9.190145687768286e-5	113294488792.16826	4.99533306627316
8	-99.69361360461316	-0.026239293976662876	-0.09740715512336516

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	70
1	47	70
2	56	70
3	62	70
4	65	70
5	64	70

end96.0ms (0.8%)

Compiler: Compiled 164 to 118 computations (28% saved)

Details

analyze1.8s (14.3%)

sample9.0s (73.8%)

simplify84.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series15.0ms (0.1%)

rewrite21.0ms (0.2%)

simplify104.0ms (0.9%)

prune81.0ms (0.7%)

localize8.0ms (0.1%)

series12.0ms (0.1%)

rewrite50.0ms (0.4%)

simplify196.0ms (1.6%)

prune136.0ms (1.1%)

localize8.0ms (0.1%)

series26.0ms (0.2%)

rewrite29.0ms (0.2%)

simplify92.0ms (0.8%)

prune127.0ms (1%)

localize10.0ms (0.1%)

series9.0ms (0.1%)

rewrite5.0ms (0%)

simplify89.0ms (0.7%)

prune75.0ms (0.6%)

regimes104.0ms (0.8%)

bsearch59.0ms (0.5%)

simplify4.0ms (0%)

end96.0ms (0.8%)

Profiling