Details

analyze796.0ms (14.4%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
37.5%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
46.8%	53.1%	0.1%	10
46.8%	53.1%	0.1%	11
48.4%	51.5%	0.1%	12
48.4%	51.5%	0.1%	13
49.2%	50.7%	0.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample2.3s (41.9%)

Results

1.1s	2093×	body	1024	valid
629.0ms	4660×	body	128	valid
339.0ms	1022×	body	512	valid
112.0ms	478×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify14.0ms (0.3%)

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

prune3.0ms (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 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series91.0ms (1.6%)

Counts

4 → 56

Calls

4 calls:

42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
41.0ms	(/.f64 x (tan.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(sin.f64 B)

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
240×	`add-sqr-sqrt_binary64`
232×	`*-un-lft-identity_binary64`
223×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

4 → 304

Calls

4 calls:

19.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))
1.0ms	(sin.f64 B)

simplify332.0ms (6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
453×	`times-frac_binary64`
297×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`
182×	`associate-/l/_binary64`

Counts

360 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	13369
1	790	8583
2	1892	6789
3	4533	6789
4	4786	6789

prune308.0ms (5.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	356	9	365
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	358	9	367

Error

0.0b

Counts

367 → 9

Alt Table

Status	Error	Program
	8.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	27.4b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	31.4b	(/.f64 (-.f64 1 x) B)
	0.7b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	24.4b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))

Compiler

Compiled 12401 to 3937 computations (68.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series62.0ms (1.1%)

Counts

3 → 35

Calls

3 calls:

32.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
23.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
91×	`prod-diff_binary64`
91×	`add-cube-cbrt_binary64`

Counts

3 → 177

Calls

3 calls:

11.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
4.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))

simplify217.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

319×	`associate-/l/_binary64`
318×	`fma-neg_binary64`
292×	`associate-/r*_binary64`
287×	`cancel-sign-sub-inv_binary64`
231×	`distribute-rgt-neg-in_binary64`

Counts

212 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	6796
1	591	5509
2	2082	4195
3	4407	4192
4	4936	4192
5	4990	4192
6	4856	4192

prune225.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	261	8	269

Error

0.0b

Counts

269 → 8

Alt Table

Status	Error	Program
	8.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
✓	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	24.4b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
	34.6b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	0.2b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))

Compiler

Compiled 8530 to 2560 computations (70% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B))))
✓	0.1b	(expm1.f64 (log1p.f64 (sin.f64 B)))
	0.2b	(/.f64 x (tan.f64 B))
✓	0.2b	(log1p.f64 (sin.f64 B))

series212.0ms (3.8%)

Counts

3 → 36

Calls

3 calls:

203.0ms	(log1p.f64 (sin.f64 B))
7.0ms	(/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B))))
2.0ms	(expm1.f64 (log1p.f64 (sin.f64 B)))

rewrite5.0ms (0.1%)

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 → 55

Calls

3 calls:

2.0ms	(/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B))))
0.0ms	(log1p.f64 (sin.f64 B))
0.0ms	(expm1.f64 (log1p.f64 (sin.f64 B)))

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
533×	`distribute-rgt-neg-in_binary64`
425×	`distribute-lft-neg-in_binary64`
355×	`associate-l_binary64`
337×	`cancel-sign-sub-inv_binary64`

Counts

91 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	747
1	188	701
2	398	689
3	1023	679
4	2967	679
5	4512	679
6	4998	679
7	4907	679

prune121.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	141	8	149

Error

0.0b

Counts

149 → 8

Alt Table

Status	Error	Program
	8.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
✓	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	24.4b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
	34.6b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	0.2b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))

Compiler

Compiled 2575 to 1125 computations (56.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))
	0.2b	(/.f64 x (tan.f64 B))
✓	0.2b	(expm1.f64 (sin.f64 B))
✓	0.2b	(log1p.f64 (expm1.f64 (sin.f64 B)))

series12.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))
4.0ms	(expm1.f64 (sin.f64 B))
2.0ms	(log1p.f64 (expm1.f64 (sin.f64 B)))

rewrite5.0ms (0.1%)

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 → 55

Calls

3 calls:

2.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (sin.f64 B))))
0.0ms	(expm1.f64 (sin.f64 B))
0.0ms	(log1p.f64 (expm1.f64 (sin.f64 B)))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
563×	`distribute-rgt-neg-in_binary64`
458×	`distribute-lft-neg-in_binary64`
384×	`associate-l_binary64`
332×	`cancel-sign-sub-inv_binary64`

Counts

91 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	753
1	190	707
2	430	688
3	1061	684
4	3128	684
5	4580	684
6	4965	684

prune119.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	140	8	148

Error

Counts

148 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (sin.f64 B)))))) (/.f64 x (tan.f64 B)))
	8.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.7b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
✓	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	24.4b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
	34.6b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	0.2b	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))

Compiler

Compiled 2450 to 1051 computations (57.1% saved)

regimes254.0ms (4.6%)

Accuracy

Total 0.1b remaining (78.6%)

Threshold costs 0.1b (78.6%)

Counts

82 → 1

Compiler

Compiled 3991 to 2754 computations (31% saved)

simplify3.0ms (0.1%)

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	11	14
1	15	14
2	20	14
3	24	14
4	27	14
5	28	14
6	26	14

end115.0ms (2.1%)

Compiler: Compiled 170 to 109 computations (35.9% 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

analyze796.0ms (14.4%)

sample2.3s (41.9%)

simplify14.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series91.0ms (1.6%)

rewrite64.0ms (1.1%)

simplify332.0ms (6%)

prune308.0ms (5.6%)

localize9.0ms (0.2%)

series62.0ms (1.1%)

rewrite38.0ms (0.7%)

simplify217.0ms (3.9%)

prune225.0ms (4.1%)

localize10.0ms (0.2%)

series212.0ms (3.8%)

rewrite5.0ms (0.1%)

simplify103.0ms (1.9%)

prune121.0ms (2.2%)

localize10.0ms (0.2%)

series12.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify82.0ms (1.5%)

prune119.0ms (2.1%)

regimes254.0ms (4.6%)

simplify3.0ms (0.1%)

end115.0ms (2.1%)

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