Details

analyze1.8s (16.4%)

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)

sample8.2s (72.3%)

Results

5.0s	2067×	body	2048	valid
2.0s	3104×	body	1024	valid
589.0ms	1579×	body	512	valid
199.0ms	766×	body	256	valid
185.0ms	131×	body	4096	valid
97.0ms	609×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`fma-def_binary64`
421×	`div-sub_binary64`
332×	`times-frac_binary64`
157×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	75	14
5	130	14
6	260	14
7	543	14
8	1322	14
9	2479	14
10	3294	14
11	3659	14
12	3788	14
13	3815	14
14	3825	14
15	3829	14
16	3829	14

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

29.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 39 to 21 computations (46.2% saved)

localize6.0ms (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)))
✓	1.0b	(-.f64 x (tan.f64 x))
✓	1.0b	(-.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))

rewrite130.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`prod-diff_binary64`
336×	`egg-rr`
170×	`log1p-udef_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	26
1	170	26
2	2750	26

Stop Event

1×	node limit

Counts

3 → 336

Calls

3 calls:

116.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
116.0ms	(-.f64 x (tan.f64 x))
116.0ms	(-.f64 x (sin.f64 x))

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
295×	`fma-def_binary64`
275×	`sub-neg_binary64`
219×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	658
1	261	654
2	860	614
3	4331	602

Stop Event

1×	node limit

Counts

366 → 367

prune211.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	364	3	367
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	364	4	368

Error

Counts

368 → 4

Alt Table

Status	Error	Program
✓	29.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	46.1b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
▶	29.8b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
	33.9b	(+.f64 -1/2 (fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800)))

Compiler

Compiled 16669 to 4203 computations (74.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
✓	0.1b	(*.f64 (cos.f64 x) x)
✓	0.2b	(/.f64 (sin.f64 x) x)
✓	0.2b	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

series20.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

10.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))
5.0ms	(+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
3.0ms	(/.f64 (sin.f64 x) x)
3.0ms	(*.f64 (cos.f64 x) x)

rewrite56.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`log-prod_binary64`
372×	`prod-diff_binary64`
174×	`log1p-udef_binary64`
173×	`expm1-udef_binary64`
166×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	194	27
2	2737	27

Stop Event

1×	node limit

Counts

4 → 163

Calls

4 calls:

53.0ms	(+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
53.0ms	(*.f64 (cos.f64 x) x)
53.0ms	(/.f64 (sin.f64 x) x)
53.0ms	(/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x))

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

437×	`distribute-rgt-neg-in_binary64`
434×	`cancel-sign-sub-inv_binary64`
314×	`distribute-lft-neg-in_binary64`
270×	`unswap-sqr_binary64`
247×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	210
1	148	202
2	400	190
3	1354	190
4	3358	190

Stop Event

1×	node limit

Counts

181 → 190

prune101.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	190	4	194

Error

Counts

194 → 4

Alt Table

Status	Error	Program
✓	29.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	46.1b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
✓	29.8b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
▶	33.9b	(+.f64 -1/2 (fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800)))

Compiler

Compiled 3648 to 1500 computations (58.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800))
✓	0.1b	(*.f64 (pow.f64 x 4) -27/2800)
✓	0.1b	(*.f64 x 9/40)

series8.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800))
3.0ms	(*.f64 (pow.f64 x 4) -27/2800)
2.0ms	(*.f64 x 9/40)

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`log1p-expm1-u_binary64`
731×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
147×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	188	25
2	2024	25

Stop Event

1×	node limit

Counts

3 → 49

Calls

3 calls:

39.0ms	(fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800))
39.0ms	(*.f64 (pow.f64 x 4) -27/2800)
39.0ms	(*.f64 x 9/40)

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
666×	`fma-neg_binary64`
396×	`distribute-rgt-neg-in_binary64`
348×	`cancel-sign-sub-inv_binary64`
336×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	297
1	30	279
2	63	279
3	186	279
4	741	279
5	1822	279
6	3087	279
7	4831	279

Stop Event

1×	node limit

Counts

85 → 55

prune38.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	55	4	59

Error

Counts

59 → 4

Alt Table

Status	Error	Program
✓	29.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	46.1b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
✓	29.8b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
✓	33.9b	(+.f64 -1/2 (fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800)))

Compiler

Compiled 934 to 716 computations (23.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
✓	0.1b	(pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2)
	1.0b	(-.f64 x (tan.f64 x))
	1.0b	(-.f64 x (sin.f64 x))

series42.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

25.0ms	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
16.0ms	(pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2)

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

778×	`prod-diff_binary64`
194×	`log1p-udef_binary64`
108×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	231	20
2	3058	20

Stop Event

1×	node limit

Counts

2 → 89

Calls

2 calls:

49.0ms	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
49.0ms	(pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
220×	`associate-/l*_binary64`
185×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	243
1	149	243
2	507	226
3	3030	216

Stop Event

1×	node limit

Counts

97 → 103

prune89.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
✓	29.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	46.1b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) 2) (-.f64 x (tan.f64 x)))
✓	29.8b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1) (/.f64 (sin.f64 x) x))
✓	33.9b	(+.f64 -1/2 (fma.f64 x (.f64 x 9/40) (.f64 (pow.f64 x 4) -27/2800)))

Compiler

Compiled 4485 to 1636 computations (63.5% saved)

regimes110.0ms (1%)

Accuracy

Total 0.0b remaining (16.3%)

Threshold costs 0.0b (16.3%)

Counts

45 → 3

Compiler

Compiled 1180 to 834 computations (29.3% saved)

bsearch55.0ms (0.5%)

Steps

Iters	Range		Point
11	2.5126605943342024e-24	17.982048189299746	0.030434030350276232
10	-21457418873875.535	-0.006888136300654941	-0.028886751310159164

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (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	22	55
1	26	55
2	34	55
3	38	55
4	40	55

Stop Event

1×

saturated

end77.0ms (0.7%)

Compiler: Compiled 127 to 74 computations (41.7% saved)

Details

analyze1.8s (16.4%)

sample8.2s (72.3%)

simplify59.0ms (0.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series15.0ms (0.1%)

rewrite130.0ms (1.1%)

simplify45.0ms (0.4%)

prune211.0ms (1.9%)

localize9.0ms (0.1%)

series20.0ms (0.2%)

rewrite56.0ms (0.5%)

simplify32.0ms (0.3%)

prune101.0ms (0.9%)

localize7.0ms (0.1%)

series8.0ms (0.1%)

rewrite40.0ms (0.4%)

simplify43.0ms (0.4%)

prune38.0ms (0.3%)

localize9.0ms (0.1%)

series42.0ms (0.4%)

rewrite53.0ms (0.5%)

simplify26.0ms (0.2%)

prune89.0ms (0.8%)

regimes110.0ms (1%)

bsearch55.0ms (0.5%)

simplify3.0ms (0%)

end77.0ms (0.7%)

Profiling