Details

analyze976.0ms (9.5%)

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
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)

sample221.0ms (2.2%)

Algorithm

1×

intervals

Results

31.0ms	32×	body	2048	valid
21.0ms	59×	body	1024	valid
9.0ms	133×	body	128	valid
6.0ms	28×	body	512	valid
1.0ms	8×	body	128	invalid
1.0ms	4×	body	256	valid

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

prune4.0ms (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

17.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.3b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 (.f64 F F)) (tan.f64 (.f64 (PI.f64) l))))
▶	17.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))

Compiler

Compiled 88 to 48 computations (45.5% saved)

localize10.0ms (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)))
✓	0.3b	(*.f64 (PI.f64) l)
✓	3.5b	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
✓	30.2b	(tan.f64 (*.f64 (PI.f64) l))

series143.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

82.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
44.0ms	(-.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)

rewrite18.0ms (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:

6.0ms	(-.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))

simplify108.0ms (1.1%)

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

prune330.0ms (3.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	122	21	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	21	145

Error

13.3b

Counts

145 → 21

Alt Table

Status	Error	Program
	31.3b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	13.8b	(-.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)))
	46.9b	(/.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))))))
	17.8b	(-.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)))
	17.4b	(-.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)))
	27.7b	(-.f64 (.f64 (PI.f64) l) (exp.f64 (log.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	39.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 l)))) (.f64 F F)))
	17.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 (.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	38.6b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))
	27.3b	(-.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	17.8b	(-.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
▶	13.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F))
	17.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) l))) (.f64 F F)))
	13.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	13.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	37.7b	(/.f64 (-.f64 (.f64 (.f64 (PI.f64) l) (.f64 (PI.f64) l)) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 6)) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))
	41.9b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) l) (.f64 (PI.f64) l)) (.f64 (PI.f64) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	26.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	17.4b	(-.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)))
	17.3b	(-.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)))
	34.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F) (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))

Compiler

Compiled 4068 to 1283 computations (68.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) F)
✓	0.2b	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
	0.3b	(*.f64 (PI.f64) l)
	30.2b	(tan.f64 (*.f64 (PI.f64) l))

series109.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

62.0ms	(/.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) F)
46.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/l*_binary64`

Counts

2 → 102

Calls

2 calls:

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

simplify240.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

699×	`times-frac_binary64`
602×	`unswap-sqr_binary64`
440×	`associate-/l/_binary64`
422×	`associate-/l*_binary64`
359×	`associate-/r*_binary64`

Counts

150 → 164

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	191	3604
1	430	3466
2	986	3390
3	3679	3366
4	4197	3361
5	5141	3361

prune462.0ms (4.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	214	10	224
Fresh	7	13	20
Picked	1	0	1
Done	0	0	0
Total	222	23	245

Error

13.3b

Counts

245 → 23

Alt Table

Status	Error	Program
▶	13.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))))
	13.8b	(-.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)))
	31.3b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	36.0b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) F))
	46.9b	(/.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))))))
	17.8b	(-.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)))
	47.1b	(-.f64 (.f64 (PI.f64) l) (exp.f64 (-.f64 (log.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F)) (log.f64 F))))
	23.7b	(-.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) l))) (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F))
	13.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 l (cbrt.f64 (PI.f64))))) F) F))
	17.4b	(-.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)))
	27.7b	(-.f64 (.f64 (PI.f64) l) (exp.f64 (log.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	17.8b	(-.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	36.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 (tan.f64 (exp.f64 (log.f64 (.f64 (PI.f64) l)))) F) F))
	17.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) l))) (.f64 F F)))
	13.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	17.3b	(-.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)))
	38.4b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F))
	13.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (cbrt.f64 F)))))
	38.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (sqrt.f64 F)) (sqrt.f64 F)) F))
	13.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (.f64 (PI.f64) l)))) (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 F (/.f64 (cbrt.f64 (tan.f64 (.f64 (PI.f64) l))) (cbrt.f64 F)))))
	17.4b	(-.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)))
	13.6b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	34.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F) (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))

Compiler

Compiled 5809 to 1744 computations (70% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
	0.3b	(*.f64 (PI.f64) l)
✓	0.4b	(/.f64 1 (.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	30.2b	(tan.f64 (*.f64 (PI.f64) l))

series250.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

134.0ms	(/.f64 1 (.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
116.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

2 → 65

Calls

2 calls:

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

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

489×	`associate-l_binary64`
448×	`associate-r_binary64`
389×	`unswap-sqr_binary64`
386×	`associate-/l*_binary64`
386×	`times-frac_binary64`

Counts

113 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	2341
1	331	2161
2	1043	2083
3	4353	2083
4	5263	2083

prune292.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	152	5	157
Fresh	15	7	22
Picked	1	0	1
Done	0	0	0
Total	168	12	180

Error

2.2b

Counts

180 → 12

Alt Table

Status	Error	Program
	46.9b	(/.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))))))
	17.8b	(-.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)))
	13.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (cbrt.f64 F)))))
▶	2.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (+.f64 (.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))))))))))
	13.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (/.f64 1 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
	34.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F) (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	13.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	36.0b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) F))
	18.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (cbrt.f64 (pow.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) 3)))))
	17.8b	(-.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	38.4b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F))
	13.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (.f64 F (/.f64 1 (tan.f64 (.f64 (PI.f64) l)))))))

Compiler

Compiled 3865 to 1506 computations (61% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (PI.f64) 3)
✓	1.0b	(pow.f64 (PI.f64) 5)
✓	1.7b	(.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (+.f64 (.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))))))))
✓	5.5b	(.f64 F (+.f64 (.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)))))

series346.0ms (3.4%)

Counts

4 → 48

Calls

4 calls:

196.0ms	(.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (+.f64 (.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))))))))
150.0ms	(.f64 F (+.f64 (.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)

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
41×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 142

Calls

4 calls:

10.0ms	(.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (+.f64 (.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))))))))
9.0ms	(.f64 F (+.f64 (.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)))))
2.0ms	(pow.f64 (PI.f64) 3)
1.0ms	(pow.f64 (PI.f64) 5)

simplify244.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
595×	`fma-neg_binary64`
524×	`times-frac_binary64`
361×	`associate-r_binary64`
356×	`associate-l_binary64`

Counts

190 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	11505
1	630	8733
2	2556	6956
3	4647	6956
4	4954	6956

prune589.0ms (5.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	203	15	218

Error

0.4b

Counts

218 → 15

Alt Table

Status	Error	Program
	17.8b	(-.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)))
	50.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (/.f64 (.f64 F (-.f64 (.f64 (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)))) (.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5))) (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))))) (-.f64 (.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))))))))))
	46.9b	(/.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))))))
	17.8b	(-.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	56.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (/.f64 (.f64 F (+.f64 (pow.f64 (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3))) 3) (pow.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5))) 3))) (+.f64 (.f64 (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3))) (.f64 1/45 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)))) (-.f64 (.f64 (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5))) (.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)))) (.f64 (.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))))))))))))
	13.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (/.f64 1 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
	34.4b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F) (/.f64 (sqrt.f64 (tan.f64 (.f64 (PI.f64) l))) F)))
	13.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (/.f64 F (tan.f64 (.f64 (PI.f64) l)))))
	36.0b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F) F))
	18.7b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (cbrt.f64 (pow.f64 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))) 3)))))
	13.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 (/.f64 1 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (cbrt.f64 F)))))
	2.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (log.f64 (exp.f64 (.f64 F (+.f64 (.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))))))))))))
	2.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 (.f64 l F) 1/3) (.f64 F (+.f64 (.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))))))))))
	38.4b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) l) 3)) (/.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) F))
	13.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (.f64 F (/.f64 1 (tan.f64 (.f64 (PI.f64) l)))))))

Compiler

Compiled 17787 to 11116 computations (37.5% saved)

regimes2.1s (20.6%)

Accuracy

Total 2.1b remaining (79.2%)

Threshold costs 0b (0%)

Counts

219 → 1

Compiler

Compiled 36244 to 22396 computations (38.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	66
1	41	66
2	50	66
3	54	66
4	56	66
5	54	66

end1.0ms (0%)

Compiler: Compiled 43 to 28 computations (34.9% saved)

sample3.5s (34.5%)

Algorithm

1×

intervals

Results

1.2s	1817×	body	1024	valid
1.0s	1036×	body	2048	valid
319.0ms	4164×	body	128	valid
204.0ms	59×	body	4096	valid
146.0ms	634×	body	512	valid
43.0ms	290×	body	256	valid
13.0ms	180×	body	128	invalid
4.0ms	10×	body	8192	exit
4.0ms	8×	body	2048	invalid

Compiler

Compiled 601 to 383 computations (36.3% 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

analyze976.0ms (9.5%)

sample221.0ms (2.2%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series143.0ms (1.4%)

rewrite18.0ms (0.2%)

simplify108.0ms (1.1%)

prune330.0ms (3.2%)

localize8.0ms (0.1%)

series109.0ms (1.1%)

rewrite53.0ms (0.5%)

simplify240.0ms (2.3%)

prune462.0ms (4.5%)

localize8.0ms (0.1%)

series250.0ms (2.4%)

rewrite12.0ms (0.1%)

simplify88.0ms (0.9%)

prune292.0ms (2.8%)

localize24.0ms (0.2%)

series346.0ms (3.4%)

rewrite47.0ms (0.5%)

simplify244.0ms (2.4%)

prune589.0ms (5.7%)

regimes2.1s (20.6%)

simplify4.0ms (0%)

end1.0ms (0%)

sample3.5s (34.5%)

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