Details

analyze2.1s (25.9%)

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)

sample264.0ms (3.2%)

Algorithm

1×

intervals

Results

160.0ms	134×	body	128	valid
64.0ms	75×	body	1024	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)

simplify39.0ms (0.5%)

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)

localize18.0ms (0.2%)

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))

rewrite103.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`

Counts

3 → 145

Calls

3 calls:

32.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
28.0ms	(/.f64 x (tan.f64 B))
26.0ms	(/.f64 1 (sin.f64 B))

series449.0ms (5.5%)

Counts

3 → 52

Calls

3 calls:

226.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
199.0ms	(/.f64 x (tan.f64 B))
24.0ms	(/.f64 1 (sin.f64 B))

simplify251.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
570×	`associate-/l/_binary64`
313×	`cancel-sign-sub-inv_binary64`
219×	`distribute-rgt-neg-in_binary64`
198×	`distribute-lft-neg-in_binary64`

Counts

197 → 269

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2272
1	500	2210
2	2064	2182
3	4885	2182
4	5080	2182

prune343.0ms (4.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	260	9	269
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	262	9	271

Error

Counts

271 → 9

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	26.4b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	18.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (cbrt.f64 (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
	10.7b	(-.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2))) (cbrt.f64 (/.f64 1 (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)))
	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 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 3660 to 1519 computations (58.5% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite116.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`

Counts

3 → 144

Calls

3 calls:

35.0ms	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
34.0ms	(/.f64 (tan.f64 B) (sin.f64 B))
31.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)

series196.0ms (2.4%)

Counts

3 → 60

Calls

3 calls:

119.0ms	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
56.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
20.0ms	(/.f64 (tan.f64 B) (sin.f64 B))

simplify149.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
475×	`fma-neg_binary64`
249×	`cancel-sign-sub-inv_binary64`
198×	`distribute-rgt-in_binary64`
154×	`distribute-rgt-neg-in_binary64`

Counts

204 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3000
1	572	2912
2	2254	2638
3	4597	2638
4	4939	2638

prune159.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	290	3	293
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	294	8	302

Error

Counts

302 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.2b	(/.f64 (-.f64 1 (*.f64 (cos.f64 B) x)) (sin.f64 B))
	26.4b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.2b	(*.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (/.f64 1 (tan.f64 B)))
	10.7b	(-.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶	0.2b	(/.f64 (-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 4115 to 1072 computations (73.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite94.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
22×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cbrt-cube_binary64`

Counts

4 → 184

Calls

4 calls:

38.0ms	(/.f64 (-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x) (tan.f64 B))
15.0ms	(*.f64 (sin.f64 B) (cos.f64 B))
14.0ms	(-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x)
14.0ms	(/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B)))

series139.0ms (1.7%)

Counts

4 → 64

Calls

4 calls:

89.0ms	(/.f64 (-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x) (tan.f64 B))
29.0ms	(-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x)
14.0ms	(/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B)))
6.0ms	(*.f64 (sin.f64 B) (cos.f64 B))

simplify144.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

396×	`fma-neg_binary64`
339×	`cancel-sign-sub-inv_binary64`
198×	`times-frac_binary64`
174×	`associate-r_binary64`
171×	`associate-l_binary64`

Counts

248 → 396

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	3205
1	705	3052
2	2992	2849
3	4814	2849
4	4914	2849

prune254.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	395	1	396
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	396	8	404

Error

Counts

404 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 (cos.f64 B) x)) (sin.f64 B))
	26.4b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.4b	(/.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B)))) 3) x) (tan.f64 B))
	0.2b	(*.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (/.f64 1 (tan.f64 B)))
✓	0.2b	(/.f64 (-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 6295 to 1785 computations (71.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cube-cbrt_binary64`
15×	`pow1_binary64`
12×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`

Counts

2 → 88

Calls

2 calls:

18.0ms	(/.f64 (-.f64 1 (*.f64 (cos.f64 B) x)) (sin.f64 B))
12.0ms	(*.f64 (cos.f64 B) x)

series74.0ms (0.9%)

Counts

2 → 28

Calls

2 calls:

48.0ms	(/.f64 (-.f64 1 (*.f64 (cos.f64 B) x)) (sin.f64 B))
25.0ms	(*.f64 (cos.f64 B) x)

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
207×	`fma-neg_binary64`
192×	`associate-/l/_binary64`
190×	`associate-/r/_binary64`
182×	`cancel-sign-sub-inv_binary64`

Counts

116 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	1563
1	443	1454
2	1754	1414
3	4738	1413
4	4997	1413

prune114.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	187	8	195

Error

Counts

195 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 (cos.f64 B) x)) (sin.f64 B))
	26.4b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 2)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.4b	(/.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B)))) 3) x) (tan.f64 B))
	0.2b	(*.f64 (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x) (/.f64 1 (tan.f64 B)))
✓	0.2b	(/.f64 (-.f64 (/.f64 (sin.f64 B) (*.f64 (sin.f64 B) (cos.f64 B))) x) (tan.f64 B))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 2376 to 1079 computations (54.6% saved)

regimes635.0ms (7.8%)

Accuracy

Total 0.1b remaining (89.1%)

Threshold costs 0.1b (89.1%)

Compiler

Compiled 7807 to 5451 computations (30.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`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	10	14
1	14	14
2	20	14
3	24	14
4	27	14
5	28	14
6	27	14

end1.0ms (0%)

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

sample2.3s (28.5%)

Algorithm

1×

intervals

Results

1.0s	2300×	body	1024	valid
412.0ms	4023×	body	128	valid
337.0ms	1132×	body	512	valid
102.0ms	540×	body	256	valid
15.0ms	164×	body	128	invalid
7.0ms	5×	body	2048	valid

Compiler

Compiled 151 to 103 computations (31.8% 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

analyze2.1s (25.9%)

sample264.0ms (3.2%)

simplify39.0ms (0.5%)

prune7.0ms (0.1%)

localize18.0ms (0.2%)

rewrite103.0ms (1.3%)

series449.0ms (5.5%)

simplify251.0ms (3.1%)

prune343.0ms (4.2%)

localize18.0ms (0.2%)

rewrite116.0ms (1.4%)

series196.0ms (2.4%)

simplify149.0ms (1.8%)

prune159.0ms (2%)

localize10.0ms (0.1%)

rewrite94.0ms (1.1%)

series139.0ms (1.7%)

simplify144.0ms (1.8%)

prune254.0ms (3.1%)

localize8.0ms (0.1%)

rewrite34.0ms (0.4%)

series74.0ms (0.9%)

simplify100.0ms (1.2%)

prune114.0ms (1.4%)

regimes635.0ms (7.8%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.3s (28.5%)

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