Details

analyze924.0ms (8.4%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample213.0ms (1.9%)

Algorithm

1×

intervals

Results

33.0ms	27×	body	2048	valid
19.0ms	62×	body	1024	valid
9.0ms	141×	body	128	valid
4.0ms	1×	body	4096	valid
4.0ms	20×	body	512	valid
1.0ms	5×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

297×	`fma-def_binary64`
157×	`fma-neg_binary64`
50×	`cancel-sign-sub-inv_binary64`
37×	`associate-/l*_binary64`
33×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

prune3.0ms (0%)

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

12.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	13.5b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))

Compiler

Compiled 88 to 48 computations (45.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
✓	0.2b	(*.f64 (PI.f64) l)
✓	3.1b	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
✓	28.2b	(tan.f64 (*.f64 (PI.f64) l))

series151.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

92.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
43.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
14.0ms	(tan.f64 (*.f64 (PI.f64) l))
2.0ms	(*.f64 (PI.f64) l)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 82

Calls

4 calls:

7.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
4.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
3.0ms	(*.f64 (PI.f64) l)
1.0ms	(tan.f64 (*.f64 (PI.f64) l))

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
624×	`fma-def_binary64`
610×	`associate-/l*_binary64`
223×	`fma-neg_binary64`
147×	`cancel-sign-sub-inv_binary64`

Counts

142 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	3051
1	478	2877
2	1544	2771
3	4922	2768
4	4881	2768

prune233.0ms (2.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	127	16	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	129	16	145

Error

9.5b

Counts

145 → 16

Alt Table

Status	Error	Program
	48.5b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (.f64 (.f64 (PI.f64) l) (.f64 (PI.f64) l)) (+.f64 (.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	13.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	38.3b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))
	9.8b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	12.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))) (*.f64 F F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) F) (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	52.8b	(neg.f64 (/.f64 (sin.f64 (.f64 (PI.f64) l)) (.f64 (cos.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	12.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 (PI.f64)) l))) (*.f64 F F)))
	17.4b	(*.f64 l (-.f64 (PI.f64) (/.f64 (PI.f64) (pow.f64 F 2))))
	27.5b	(-.f64 (.f64 (PI.f64) l) (exp.f64 (log.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	12.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	28.3b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
▶	9.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	12.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) l))) (.f64 F F)))
	38.3b	(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) l)) (sqrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	38.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) l)) (sqrt.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))

Compiler

Compiled 3826 to 1165 computations (69.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
	0.2b	(*.f64 (PI.f64) l)
✓	0.5b	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	28.2b	(tan.f64 (*.f64 (PI.f64) l))

series106.0ms (1%)

Counts

2 → 48

Calls

2 calls:

59.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
46.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

rewrite108.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

405×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
195×	`add-cube-cbrt_binary64`
47×	`associate-/r*_binary64`

Counts

2 → 236

Calls

2 calls:

42.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
3.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

simplify508.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-neg_binary64`
352×	`*-commutative_binary64`
291×	`fma-def_binary64`
278×	`associate-/r/_binary64`
242×	`unswap-sqr_binary64`

Counts

284 → 341

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	280	8467
1	586	7416
2	1805	7073
3	2193	7067
4	2824	7067
5	4081	6913
6	4484	6901
7	4978	6901
8	4894	6901

prune1.0s (9.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	394	7	401
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	400	17	417

Error

9.5b

Counts

417 → 17

Alt Table

Status	Error	Program
	10.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) (pow.f64 (cbrt.f64 F) 2)) (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 F))))))
	48.5b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (.f64 (.f64 (PI.f64) l) (.f64 (PI.f64) l)) (+.f64 (.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	13.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	10.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 l (cbrt.f64 (PI.f64))))) F))))
	9.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))) (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))) (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
	28.3b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	12.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))) (*.f64 F F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) F) (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	52.8b	(neg.f64 (/.f64 (sin.f64 (.f64 (PI.f64) l)) (.f64 (cos.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	37.4b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
	17.4b	(*.f64 l (-.f64 (PI.f64) (/.f64 (PI.f64) (pow.f64 F 2))))
	38.3b	(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) l)) (sqrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l)))) F))))
	12.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
▶	9.8b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) (/.f64 1 F)))
	13.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))))
	12.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) l))) (.f64 F F)))

Compiler

Compiled 11335 to 3629 computations (68% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (/.f64 F (tan.f64 (.f64 (PI.f64) l)))) (/.f64 1 F))
✓	0.2b	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
✓	1.0b	(/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))
	28.2b	(tan.f64 (*.f64 (PI.f64) l))

series283.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

170.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
60.0ms	(.f64 (/.f64 1 (/.f64 F (tan.f64 (.f64 (PI.f64) l)))) (/.f64 1 F))
53.0ms	(/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`times-frac_binary64`
144×	`add-sqr-sqrt_binary64`
108×	`*-un-lft-identity_binary64`
99×	`add-exp-log_binary64`
97×	`add-cube-cbrt_binary64`

Counts

3 → 238

Calls

3 calls:

22.0ms	(.f64 (/.f64 1 (/.f64 F (tan.f64 (.f64 (PI.f64) l)))) (/.f64 1 F))
5.0ms	(/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))
3.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))

simplify194.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
784×	`fma-def_binary64`
573×	`associate-/l*_binary64`
372×	`associate-/l/_binary64`
351×	`associate-/r/_binary64`

Counts

310 → 369

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	6847
1	557	5949
2	1692	5875
3	4445	5871
4	5057	5871

prune723.0ms (6.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	382	5	387
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	391	13	404

Error

2.1b

Counts

404 → 13

Alt Table

Status	Error	Program
	48.5b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (.f64 (.f64 (PI.f64) l) (.f64 (PI.f64) l)) (+.f64 (.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	13.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) F) (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	52.8b	(neg.f64 (/.f64 (sin.f64 (.f64 (PI.f64) l)) (.f64 (cos.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	14.7b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 F (tan.f64 (.f64 (PI.f64) l))) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))) (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))))) (/.f64 1 F)))
	37.4b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
	17.4b	(*.f64 l (-.f64 (PI.f64) (/.f64 (PI.f64) (pow.f64 F 2))))
	9.8b	(-.f64 (.f64 (PI.f64) l) (.f64 (.f64 (/.f64 1 F) (/.f64 1 (/.f64 1 (tan.f64 (.f64 (PI.f64) l))))) (/.f64 1 F)))
	38.3b	(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) l)) (sqrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	2.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (+.f64 (.f64 1/3 (.f64 (PI.f64) (.f64 F l))) (+.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (.f64 (pow.f64 l 5) F))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (.f64 (pow.f64 l 3) F))))))) (/.f64 1 F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))) (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))) (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
	9.8b	(-.f64 (.f64 (PI.f64) l) (pow.f64 (.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) F) -1))
▶	2.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))))))) (/.f64 1 F)))

Compiler

Compiled 10680 to 4202 computations (60.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5))))))))
✓	1.0b	(pow.f64 (PI.f64) 3)
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	4.8b	(.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))))

series665.0ms (6.1%)

Counts

4 → 48

Calls

4 calls:

560.0ms	(/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5))))))))
105.0ms	(.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))))
0.0ms	(pow.f64 (PI.f64) 5)
0.0ms	(pow.f64 (PI.f64) 3)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5))))))))
3.0ms	(.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))))
1.0ms	(pow.f64 (PI.f64) 3)
1.0ms	(pow.f64 (PI.f64) 5)

simplify165.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

395×	`associate-/l*_binary64`
316×	`fma-def_binary64`
286×	`distribute-rgt-in_binary64`
273×	`distribute-lft-in_binary64`
265×	`unswap-sqr_binary64`

Counts

157 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	6350
1	517	5645
2	1852	5615
3	4920	5615
4	4886	5615

prune437.0ms (4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	168	14	182

Error

1.9b

Counts

182 → 14

Alt Table

Status	Error	Program
	2.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (fma.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) (.f64 2/945 (*.f64 (pow.f64 (pow.f64 (PI.f64) (sqrt.f64 5)) (sqrt.f64 5)) (pow.f64 l 5)))))))) (/.f64 1 F)))
	4.5b	(-.f64 (.f64 (PI.f64) l) (.f64 (expm1.f64 (log1p.f64 (/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 l F)) (.f64 (fma.f64 1/45 (pow.f64 (.f64 (PI.f64) l) 3) (.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))) F)))))) (/.f64 1 F)))
	48.5b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (.f64 (.f64 (PI.f64) l) (.f64 (PI.f64) l)) (+.f64 (.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) (.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	13.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) l)) (cbrt.f64 (.f64 (PI.f64) l))) (cbrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) F) (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	52.8b	(neg.f64 (/.f64 (sin.f64 (.f64 (PI.f64) l)) (.f64 (cos.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	14.7b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 F (tan.f64 (.f64 (PI.f64) l))) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))) (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))))) (/.f64 1 F)))
	37.4b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
	17.4b	(*.f64 l (-.f64 (PI.f64) (/.f64 (PI.f64) (pow.f64 F 2))))
	9.8b	(-.f64 (.f64 (PI.f64) l) (.f64 (.f64 (/.f64 1 F) (/.f64 1 (/.f64 1 (tan.f64 (.f64 (PI.f64) l))))) (/.f64 1 F)))
	38.3b	(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) l)) (sqrt.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	9.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))) (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))) (cbrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
	2.7b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (log1p.f64 (expm1.f64 (.f64 (fma.f64 1/45 (pow.f64 (.f64 (PI.f64) l) 3) (.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))) F)))))) (/.f64 1 F)))
	9.8b	(-.f64 (.f64 (PI.f64) l) (pow.f64 (.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) F) -1))

Compiler

Compiled 9807 to 5851 computations (40.3% saved)

regimes2.3s (21.2%)

Accuracy

Total 1.0b remaining (42.3%)

Threshold costs 1.0b (42.3%)

Counts

300 → 1

Compiler

Compiled 51632 to 31862 computations (38.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	62
1	41	62
2	55	62
3	64	62
4	69	62
5	70	62
6	68	62

end1.0ms (0%)

Compiler: Compiled 41 to 28 computations (31.7% saved)

sample2.6s (24%)

Algorithm

1×

intervals

Results

957.0ms	1026×	body	2048	valid
570.0ms	1853×	body	1024	valid
269.0ms	4111×	body	128	valid
147.0ms	42×	body	4096	valid
138.0ms	680×	body	512	valid
43.0ms	288×	body	256	valid
11.0ms	166×	body	128	invalid
3.0ms	7×	body	2048	invalid
1.0ms	2×	body	8192	exit

Compiler

Compiled 483 to 271 computations (43.9% saved)

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20

Details

analyze924.0ms (8.4%)

sample213.0ms (1.9%)

simplify22.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series151.0ms (1.4%)

rewrite19.0ms (0.2%)

simplify107.0ms (1%)

prune233.0ms (2.1%)

localize8.0ms (0.1%)

series106.0ms (1%)

rewrite108.0ms (1%)

simplify508.0ms (4.6%)

prune1.0s (9.3%)

localize9.0ms (0.1%)

series283.0ms (2.6%)

rewrite56.0ms (0.5%)

simplify194.0ms (1.8%)

prune723.0ms (6.6%)

localize26.0ms (0.2%)

series665.0ms (6.1%)

rewrite22.0ms (0.2%)

simplify165.0ms (1.5%)

prune437.0ms (4%)

regimes2.3s (21.2%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.6s (24%)

Profiling

Iter	Nodes	Cost
0	11	23
1	25	20
2	50	20
3	121	20
4	181	20
5	247	20
6	321	20
7	384	20
8	470	20
9	483	20
10	509	20
11	462	20