Details

analyze1.2s (18.9%)

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)

sample63.0ms (1%)

Algorithm

1×

intervals

Results

28.0ms	64×	body	1024	valid
14.0ms	146×	body	128	valid
10.0ms	38×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify20.0ms (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 → 1

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%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 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 61 to 46 computations (24.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))

rewrite140.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

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:

18.0ms	(/.f64 x (tan.f64 B))
15.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
12.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 2478 to 880 computations (64.5% saved)

series80.0ms (1.3%)

Error

0.1b

Counts

3 → 27

Calls

3 calls:

36.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
25.0ms	(/.f64 x (tan.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 892 to 583 computations (34.6% saved)

simplify106.0ms (1.7%)

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

172 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	1891
1	500	1829
2	2064	1801
3	4885	1801
4	5080	1801

prune86.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	6	68

Error

0.0b

Counts

68 → 6

Alt Table

Status	Error	Program
	27.4b	(/.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))))
	18.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	36.5b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
▶	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	0.2b	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))
	32.5b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))

Compiler

Compiled 945 to 483 computations (48.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 1 (tan.f64 B))
0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

rewrite178.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

44×	`add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`

Counts

4 → 194

Calls

4 calls:

14.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
13.0ms	(/.f64 1 (sin.f64 B))
13.0ms	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
13.0ms	(/.f64 1 (tan.f64 B))

Compiler

Compiled 3003 to 1829 computations (39.1% saved)

series217.0ms (3.4%)

Error

0.0b

Counts

4 → 33

Calls

4 calls:

131.0ms	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
32.0ms	(/.f64 1 (sin.f64 B))
27.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
10.0ms	(/.f64 1 (tan.f64 B))

Compiler

Compiled 1191 to 810 computations (32% saved)

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
440×	`cancel-sign-sub-inv_binary64`
206×	`unswap-sqr_binary64`
175×	`associate-l_binary64`
173×	`associate-r_binary64`

Counts

227 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	2416
1	578	2186
2	2391	2165
3	4636	2165
4	4937	2165

prune58.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Error

0.0b

Counts

120 → 7

Alt Table

Status	Error	Program
	27.4b	(/.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))))
	18.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	36.5b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
✓	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	0.2b	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))
▶	0.2b	(/.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (sin.f64 B))
	32.3b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))

Compiler

Compiled 1557 to 845 computations (45.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B))
0.1b	(/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B))
0.1b	(/.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (sin.f64 B))

rewrite144.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
12×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

3 → 125

Calls

3 calls:

57.0ms	(/.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (sin.f64 B))
13.0ms	(/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B))
9.0ms	(fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B))

Compiler

Compiled 2354 to 338 computations (85.6% saved)

series143.0ms (2.2%)

Error

0.0b

Counts

3 → 36

Calls

3 calls:

55.0ms	(/.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (sin.f64 B))
43.0ms	(/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B))
29.0ms	(fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B))

Compiler

Compiled 1332 to 822 computations (38.3% saved)

simplify127.0ms (2%)

Algorithm

1×	egg-herbie

Rules

863×	`fma-def_binary64`
482×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
138×	`associate-r_binary64`
125×	`associate-l_binary64`

Counts

161 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2849
1	559	2641
2	2181	2513
3	4506	2513
4	4957	2513

prune86.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Error

Counts

108 → 8

Alt Table

Status	Error	Program
	27.4b	(/.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))))
	18.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	36.5b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
✓	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.2b	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))
✓	0.2b	(/.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (sin.f64 B))
	1.4b	(/.f64 (/.f64 (/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (tan.f64 B)) (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B)))
	32.3b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))

Compiler

Compiled 1766 to 543 computations (69.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
0.1b	(/.f64 (tan.f64 B) (sin.f64 B))
0.2b	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))
0.2b	(/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x))

rewrite179.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

62×	`add-cube-cbrt_binary64`
24×	`add-exp-log_binary64`
24×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`

Counts

4 → 192

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
15.0ms	(/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x))
14.0ms	(/.f64 (tan.f64 B) (sin.f64 B))
13.0ms	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))

Compiler

Compiled 3812 to 900 computations (76.4% saved)

series152.0ms (2.4%)

Error

Counts

4 → 48

Calls

4 calls:

46.0ms	(/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x))
45.0ms	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))
26.0ms	(-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)
11.0ms	(/.f64 (tan.f64 B) (sin.f64 B))

Compiler

Compiled 1885 to 1322 computations (29.9% saved)

simplify204.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

330×	`fma-neg_binary64`
319×	`cancel-sign-sub-inv_binary64`
180×	`associate-r_binary64`
163×	`times-frac_binary64`
159×	`unswap-sqr_binary64`

Counts

240 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	338	4346
1	834	4034
2	3292	3901
3	4969	3897
4	5014	3897

prune65.0ms (1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	110	8	118

Error

Counts

118 → 8

Alt Table

Status	Error	Program
	27.4b	(/.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))))
	18.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	36.5b	(neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
	0.2b	(/.f64 1 (/.f64 (tan.f64 B) (-.f64 (/.f64 (tan.f64 B) (sin.f64 B)) x)))
	0.2b	(/.f64 (/.f64 (fma.f64 (sin.f64 B) (neg.f64 x) (tan.f64 B)) (tan.f64 B)) (sin.f64 B))
	1.4b	(/.f64 (/.f64 (/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (tan.f64 B)) (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (cbrt.f64 (sin.f64 B)))
	32.3b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))))

Compiler

Compiled 1941 to 781 computations (59.8% saved)

regimes574.0ms (8.9%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Compiler

Compiled 7928 to 5530 computations (30.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-mul-1_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	14	16
2	20	14
3	32	14
4	39	14
5	43	14
6	44	14
7	42	14

end1.0ms (0%)

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

sample2.4s (37.7%)

Algorithm

1×

intervals

Results

1.1s	2334×	body	1024	valid
398.0ms	3951×	body	128	valid
333.0ms	1138×	body	512	valid
111.0ms	572×	body	256	valid
14.0ms	157×	body	128	invalid
5.0ms	5×	body	2048	valid
1.0ms	3×	body	1024	invalid

Compiler

Compiled 158 to 106 computations (32.9% 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

analyze1.2s (18.9%)

sample63.0ms (1%)

simplify20.0ms (0.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite140.0ms (2.2%)

series80.0ms (1.3%)

simplify106.0ms (1.7%)

prune86.0ms (1.3%)

localize10.0ms (0.1%)

rewrite178.0ms (2.8%)

series217.0ms (3.4%)

simplify119.0ms (1.8%)

prune58.0ms (0.9%)

localize9.0ms (0.1%)

rewrite144.0ms (2.3%)

series143.0ms (2.2%)

simplify127.0ms (2%)

prune86.0ms (1.3%)

localize10.0ms (0.2%)

rewrite179.0ms (2.8%)

series152.0ms (2.4%)

simplify204.0ms (3.2%)

prune65.0ms (1%)

regimes574.0ms (8.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.4s (37.7%)

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