Details

analyze1.2s (17.5%)

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)

sample2.9s (43.2%)

Results

1.4s	2277×	body	1024	valid
762.0ms	4122×	body	128	valid
494.0ms	1250×	body	512	valid
170.0ms	599×	body	256	valid
25.0ms	156×	body	128	invalid
8.0ms	8×	body	2048	valid
1.0ms	3×	body	512	invalid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify14.0ms (0.2%)

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

prune4.0ms (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))

series93.0ms (1.4%)

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))
8.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(sin.f64 B)

rewrite58.0ms (0.9%)

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:

15.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))
1.0ms	(sin.f64 B)

simplify245.0ms (3.6%)

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

prune356.0ms (5.3%)

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
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	27.6b	(-.f64 (/.f64 1 (log.f64 (exp.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	31.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (sqrt.f64 (tan.f64 B))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
	31.5b	(-.f64 (/.f64 1 (sin.f64 B)) (exp.f64 (log.f64 (/.f64 x (tan.f64 B)))))
	17.5b	(-.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)))
	29.4b	(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (+.f64 (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))))
	12.3b	(/.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 (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 12531 to 4003 computations (68.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series69.0ms (1%)

Counts

3 → 52

Calls

3 calls:

29.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
25.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
16.0ms	(/.f64 x (sin.f64 B))

rewrite20.0ms (0.3%)

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:

6.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
5.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
2.0ms	(/.f64 x (sin.f64 B))

simplify146.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
414×	`fma-neg_binary64`
372×	`associate-/l*_binary64`
342×	`times-frac_binary64`
338×	`associate-*l/_binary64`

Counts

157 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2974
1	476	2749
2	1426	2544
3	4328	2511
4	4945	2511
5	4995	2511
6	4920	2511

prune177.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	221	10	231

Error

Counts

231 → 10

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	27.6b	(-.f64 (/.f64 1 (log.f64 (exp.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	31.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (sqrt.f64 (tan.f64 B))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
	29.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	12.3b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.f64 x (cos.f64 B)))) (.f64 (sin.f64 B) (sin.f64 B)))
	17.5b	(-.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 (/.f64 1 (sin.f64 B))) (cos.f64 B)))
	12.3b	(/.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 (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 4936 to 1853 computations (62.5% saved)

localize9.0ms (0.1%)

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))
✓	0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

series116.0ms (1.7%)

Counts

3 → 60

Calls

3 calls:

45.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
42.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
29.0ms	(/.f64 1 (tan.f64 B))

rewrite21.0ms (0.3%)

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:

6.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
6.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
3.0ms	(/.f64 1 (tan.f64 B))

simplify116.0ms (1.7%)

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 → 189

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

prune209.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	232	9	241

Error

Counts

241 → 9

Alt Table

Status	Error	Program
	27.6b	(-.f64 (/.f64 1 (log.f64 (exp.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	29.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
	17.5b	(-.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 (/.f64 1 (sin.f64 B))) (cos.f64 B)))
	28.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (log.f64 (exp.f64 (/.f64 1 (tan.f64 B))))))
	12.3b	(/.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 (sin.f64 B)) (cos.f64 B)))
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))

Compiler

Compiled 4559 to 2542 computations (44.2% saved)

localize8.0ms (0.1%)

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))
✓	0.3b	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))

series57.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

27.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
22.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
8.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

rewrite21.0ms (0.3%)

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:

7.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
5.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
3.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

simplify124.0ms (1.8%)

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 → 172

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

prune178.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	214	9	223

Error

Counts

223 → 9

Alt Table

Status	Error	Program
	27.6b	(-.f64 (/.f64 1 (log.f64 (exp.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	29.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
	17.5b	(-.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 (/.f64 1 (sin.f64 B))) (cos.f64 B)))
	28.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (log.f64 (exp.f64 (/.f64 1 (tan.f64 B))))))
	12.3b	(/.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 (sin.f64 B)) (cos.f64 B)))
	1.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))) (cbrt.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))

Compiler

Compiled 4516 to 1677 computations (62.9% saved)

regimes435.0ms (6.4%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

143 → 1

Compiler

Compiled 7654 to 5172 computations (32.4% saved)

simplify2.0ms (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

end155.0ms (2.3%)

Compiler: Compiled 210 to 133 computations (36.7% 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

analyze1.2s (17.5%)

sample2.9s (43.2%)

simplify14.0ms (0.2%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series93.0ms (1.4%)

rewrite58.0ms (0.9%)

simplify245.0ms (3.6%)

prune356.0ms (5.3%)

localize8.0ms (0.1%)

series69.0ms (1%)

rewrite20.0ms (0.3%)

simplify146.0ms (2.2%)

prune177.0ms (2.6%)

localize9.0ms (0.1%)

series116.0ms (1.7%)

rewrite21.0ms (0.3%)

simplify116.0ms (1.7%)

prune209.0ms (3.1%)

localize8.0ms (0.1%)

series57.0ms (0.8%)

rewrite21.0ms (0.3%)

simplify124.0ms (1.8%)

prune178.0ms (2.6%)

regimes435.0ms (6.4%)

simplify2.0ms (0%)

end155.0ms (2.3%)

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