Details

analyze2.2s (20.7%)

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample176.0ms (1.6%)

Algorithm

1×

intervals

Results

108.0ms	75×	body	1024	valid
24.0ms	134×	body	128	valid
16.0ms	33×	body	512	valid
5.0ms	14×	body	256	valid
2.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

105×	`fma-def_binary64`
66×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
11×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize130.0ms (1.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
✓	0.1b	(/.f64 x (tan.f64 B))
✓	0.1b	(/.f64 1 (sin.f64 B))

rewrite116.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
231×	`*-un-lft-identity_binary64`
222×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

3 → 295

Calls

3 calls:

35.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 1 (sin.f64 B))
5.0ms	(/.f64 x (tan.f64 B))

series441.0ms (4.1%)

Counts

3 → 52

Calls

3 calls:

226.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
190.0ms	(/.f64 x (tan.f64 B))
24.0ms	(/.f64 1 (sin.f64 B))

simplify782.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

908×	`fma-def_binary64`
454×	`times-frac_binary64`
255×	`fma-neg_binary64`
182×	`associate-/l/_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

347 → 612

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	11199
1	749	7806
2	1775	6080
3	4356	6080
4	4828	6080
5	4996	6080
6	4788	6080

prune608.0ms (5.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	603	9	612
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	605	9	614

Error

0.0b

Counts

614 → 9

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 x (sin.f64 B))) (cos.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	32.3b	(-.f64 (exp.f64 (neg.f64 (log.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	31.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	10.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	29.2b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	16.8b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 11909 to 3732 computations (68.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 1 (tan.f64 B))
✓	0.2b	(*.f64 x (/.f64 1 (tan.f64 B)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 115

Calls

3 calls:

13.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
13.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
6.0ms	(/.f64 1 (tan.f64 B))

series450.0ms (4.2%)

Counts

3 → 60

Calls

3 calls:

212.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
177.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
60.0ms	(/.f64 1 (tan.f64 B))

simplify260.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-neg_binary64`
690×	`fma-def_binary64`
330×	`associate-+l+_binary64`
308×	`associate-l_binary64`
263×	`associate-r_binary64`

Counts

175 → 285

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	178	2673
1	426	2347
2	1219	2210
3	3953	2177
4	4671	2175
5	4892	2175

prune408.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	343	1	344
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	344	9	353

Error

0.0b

Counts

353 → 9

Alt Table

Status	Error	Program
	29.2b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	32.3b	(-.f64 (exp.f64 (neg.f64 (log.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	31.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	10.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	16.8b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 4411 to 2469 computations (44% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite64.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
13×	`fma-neg_binary64`

Counts

3 → 105

Calls

3 calls:

31.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
12.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
5.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

series268.0ms (2.5%)

Counts

3 → 52

Calls

3 calls:

123.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
119.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
26.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

simplify232.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
430×	`times-frac_binary64`
324×	`fma-neg_binary64`
322×	`associate-*r/_binary64`
318×	`associate-*l/_binary64`

Counts

157 → 243

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	3051
1	468	2821
2	1527	2620
3	4356	2587
4	4697	2587
5	4880	2587

prune347.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	358	3	361
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	362	8	370

Error

Counts

370 → 8

Alt Table

Status	Error	Program
	31.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	10.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(-.f64 (pow.f64 (sin.f64 B) -1) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	26.2b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
	16.8b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

Compiler

Compiled 4571 to 1714 computations (62.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`unpow-prod-down_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`fma-neg_binary64`

Counts

2 → 50

Calls

2 calls:

9.0ms	(-.f64 (pow.f64 (sin.f64 B) -1) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
3.0ms	(pow.f64 (sin.f64 B) -1)

series136.0ms (1.3%)

Counts

2 → 36

Calls

2 calls:

114.0ms	(-.f64 (pow.f64 (sin.f64 B) -1) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
22.0ms	(pow.f64 (sin.f64 B) -1)

simplify145.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

530×	`fma-def_binary64`
474×	`associate-l_binary64`
420×	`associate-r_binary64`
276×	`associate-*l/_binary64`
250×	`associate-*r/_binary64`

Counts

86 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1630
1	322	1497
2	1042	1382
3	4239	1382
4	4909	1382

prune294.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	269	8	277

Error

Counts

277 → 8

Alt Table

Status	Error	Program
	31.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	10.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(-.f64 (pow.f64 (sin.f64 B) -1) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	26.2b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
	16.8b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))

Compiler

Compiled 3885 to 1461 computations (62.4% saved)

regimes906.0ms (8.5%)

Accuracy

Total 0.1b remaining (88.4%)

Threshold costs 0.1b (88.4%)

Compiler

Compiled 6961 to 4560 computations (34.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`distribute-neg-frac_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	14	14
2	20	14
3	25	14
4	28	14
5	29	14
6	28	14

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample2.5s (23.6%)

Algorithm

1×

intervals

Results

1.2s	2300×	body	1024	valid
462.0ms	4023×	body	128	valid
326.0ms	1132×	body	512	valid
112.0ms	540×	body	256	valid
16.0ms	164×	body	128	invalid
6.0ms	5×	body	2048	valid

Compiler

Compiled 169 to 108 computations (36.1% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Details

analyze2.2s (20.7%)

sample176.0ms (1.6%)

simplify37.0ms (0.4%)

prune7.0ms (0.1%)

localize130.0ms (1.2%)

rewrite116.0ms (1.1%)

series441.0ms (4.1%)

simplify782.0ms (7.3%)

prune608.0ms (5.7%)

localize19.0ms (0.2%)

rewrite46.0ms (0.4%)

series450.0ms (4.2%)

simplify260.0ms (2.4%)

prune408.0ms (3.8%)

localize17.0ms (0.2%)

rewrite64.0ms (0.6%)

series268.0ms (2.5%)

simplify232.0ms (2.2%)

prune347.0ms (3.3%)

localize19.0ms (0.2%)

rewrite17.0ms (0.2%)

series136.0ms (1.3%)

simplify145.0ms (1.4%)

prune294.0ms (2.8%)

regimes906.0ms (8.5%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample2.5s (23.6%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14