Details

analyze2.0s (11.4%)

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)

sample6.7s (38.5%)

Results

2.5s	1024×	body	2048	valid
2.0s	1948×	body	1024	valid
1.1s	4263×	body	128	valid
461.0ms	672×	body	512	valid
321.0ms	42×	body	4096	valid
143.0ms	307×	body	256	valid
45.0ms	186×	body	128	invalid
8.0ms	6×	body	2048	invalid
5.0ms	4×	body	8192	exit

Compiler

Compiled 50 to 32 computations (36% saved)

simplify39.0ms (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

prune6.0ms (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

16.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	17.1b	(-.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)

localize13.0ms (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)
✓	4.0b	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
✓	28.8b	(tan.f64 (*.f64 (PI.f64) l))

series246.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

125.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
90.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
26.0ms	(tan.f64 (*.f64 (PI.f64) l))
5.0ms	(*.f64 (PI.f64) l)

rewrite34.0ms (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:

10.0ms	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
8.0ms	(/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))
5.0ms	(*.f64 (PI.f64) l)
2.0ms	(tan.f64 (*.f64 (PI.f64) l))

simplify195.0ms (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

prune354.0ms (2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	123	20	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	20	145

Error

12.6b

Counts

145 → 20

Alt Table

Status	Error	Program
	43.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 l)))) (.f64 F F)))
	17.7b	(-.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)))
	27.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 (log.f64 (exp.f64 (tan.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	13.1b	(+.f64 (.f64 (PI.f64) l) (.f64 (neg.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)))
▶	12.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))
	17.2b	(-.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)))
	12.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	51.7b	(neg.f64 (/.f64 (sin.f64 (.f64 (PI.f64) l)) (.f64 (cos.f64 (.f64 (PI.f64) l)) (.f64 F F))))
	45.6b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 6) (.f64 (.f64 (PI.f64) l) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	41.3b	(-.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)))
	42.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) l)) (sqrt.f64 (.f64 (PI.f64) l)))) (*.f64 F F)))
	45.0b	(exp.f64 (log.f64 (-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))))
	40.6b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)) (.f64 (.f64 l l) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	17.6b	(-.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)))
	17.2b	(-.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)))
	42.9b	(-.f64 (.f64 (PI.f64) l) (exp.f64 (-.f64 (log.f64 (tan.f64 (.f64 (PI.f64) l))) (log.f64 (*.f64 F F)))))
	42.7b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))
	42.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l))) (.f64 F F)))
	17.2b	(-.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)))
	37.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 (tan.f64 (cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)) (.f64 (.f64 l l) l)))) (*.f64 F F)))

Compiler

Compiled 3988 to 1277 computations (68% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))
✓	0.2b	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
	0.2b	(*.f64 (PI.f64) l)
	28.8b	(tan.f64 (*.f64 (PI.f64) l))

series248.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

162.0ms	(/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))
86.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

rewrite32.0ms (0.2%)

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-/r*_binary64`

Counts

2 → 102

Calls

2 calls:

8.0ms	(/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))
6.0ms	(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

simplify257.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-/r/_binary64`
433×	`fma-neg_binary64`
416×	`*-commutative_binary64`
410×	`cancel-sign-sub-inv_binary64`
401×	`associate-/r*_binary64`

Counts

150 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	3620
1	462	3460
2	1574	3372
3	3233	3342
4	4862	3342
5	4957	3342

prune558.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	12	7	19
Picked	1	0	1
Done	0	0	0
Total	228	13	241

Error

6.5b

Counts

241 → 13

Alt Table

Status	Error	Program
▶	12.9b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))))
	13.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (.f64 (/.f64 1 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (cbrt.f64 F))))))
	42.7b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)))
	22.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (cbrt.f64 (pow.f64 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) 3))))
	18.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (cbrt.f64 (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) 3)))))
	12.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	45.6b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 6) (.f64 (.f64 (PI.f64) l) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	17.6b	(-.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)))
	17.7b	(-.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)))
	17.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))))
	13.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (fma.f64 (/.f64 F l) (/.f64 F (PI.f64)) (fma.f64 (pow.f64 (PI.f64) 5) (.f64 (.f64 (pow.f64 l 5) (.f64 F F)) -2/945) (.f64 (.f64 F F) (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) -1/45)))))))
	41.3b	(-.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)))
	40.6b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)) (.f64 (.f64 l l) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))

Compiler

Compiled 5751 to 1976 computations (65.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l))))
	0.2b	(*.f64 (PI.f64) l)
✓	0.2b	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
	28.8b	(tan.f64 (*.f64 (PI.f64) l))

series323.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

167.0ms	(.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l))))
156.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
14×	`associate-r_binary64`

Counts

2 → 65

Calls

2 calls:

13.0ms	(.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l))))
5.0ms	(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))

simplify201.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-neg_binary64`
395×	`associate-/l*_binary64`
323×	`*-commutative_binary64`
284×	`unswap-sqr_binary64`
260×	`fma-def_binary64`

Counts

113 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	2274
1	334	2151
2	1202	2135
3	3443	2125
4	4726	2125
5	4942	2125

prune399.0ms (2.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	155	14	169

Error

2.9b

Counts

169 → 14

Alt Table

Status	Error	Program
	22.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (cbrt.f64 (pow.f64 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) 3))))
	41.6b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 1 (.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l))))))
	18.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (cbrt.f64 (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) 3)))))
	12.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	45.6b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 6) (.f64 (.f64 (PI.f64) l) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	10.8b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (fma.f64 (/.f64 F (.f64 (PI.f64) l)) F (fma.f64 (.f64 F (.f64 (pow.f64 (PI.f64) 5) (.f64 F (pow.f64 l 5)))) -2/945 (.f64 (.f64 F F) (-.f64 (.f64 (.f64 (PI.f64) l) -1/3) (.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)))))))))
	40.6b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)) (.f64 (.f64 l l) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))
	17.6b	(-.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)))
▶	3.4b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (.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))))))))))
	13.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (.f64 (/.f64 1 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (cbrt.f64 F))))))
	13.6b	(-.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 1 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))))
	17.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))))
	13.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (fma.f64 (/.f64 F l) (/.f64 F (PI.f64)) (fma.f64 (pow.f64 (PI.f64) 5) (.f64 (.f64 (pow.f64 l 5) (.f64 F F)) -2/945) (.f64 (.f64 F F) (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) -1/45)))))))
	41.3b	(-.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 4165 to 1633 computations (60.8% saved)

localize54.0ms (0.3%)

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)
✓	1.2b	(.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (.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))))))))
✓	3.7b	(.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)))))

series483.0ms (2.8%)

Counts

4 → 48

Calls

4 calls:

292.0ms	(.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (.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))))))))
190.0ms	(.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) 3)
0.0ms	(pow.f64 (PI.f64) 5)

rewrite100.0ms (0.6%)

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:

21.0ms	(.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (.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))))))))
19.0ms	(.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)))))
3.0ms	(pow.f64 (PI.f64) 3)
3.0ms	(pow.f64 (PI.f64) 5)

simplify465.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
595×	`fma-neg_binary64`
524×	`times-frac_binary64`
362×	`associate-r_binary64`
355×	`associate-l_binary64`

Counts

190 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	11505
1	630	8733
2	2557	6956
3	4648	6956
4	4955	6956

prune1.1s (6.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	205	15	220

Error

0.5b

Counts

220 → 15

Alt Table

Status	Error	Program
	22.6b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (cbrt.f64 (pow.f64 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) 3))))
	41.6b	(-.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 1 (.f64 F (/.f64 F (tan.f64 (.f64 (PI.f64) l))))))
	18.3b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (cbrt.f64 (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F) 3)))))
	13.0b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (fma.f64 (/.f64 F l) (/.f64 F (PI.f64)) (fma.f64 (pow.f64 (PI.f64) 5) (.f64 (.f64 (pow.f64 l 5) (.f64 F F)) -2/945) (.f64 (.f64 F F) (fma.f64 (.f64 (PI.f64) l) -1/3 (.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 l 3)) -1/45)))))))
	3.2b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (log1p.f64 (expm1.f64 (.f64 F (fma.f64 2/945 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)) (.f64 1/45 (pow.f64 (*.f64 (PI.f64) l) 3)))))))))))
	12.9b	(-.f64 (.f64 (PI.f64) l) (.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
	45.6b	(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) l) 3) (pow.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F)) 3)) (+.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) (.f64 F F))) 6) (.f64 (.f64 (PI.f64) l) (fma.f64 (PI.f64) l (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F))))))
	17.6b	(-.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)))
	13.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (.f64 (/.f64 1 (.f64 (cbrt.f64 F) (cbrt.f64 F))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (cbrt.f64 F))))))
	13.6b	(-.f64 (.f64 (.f64 (PI.f64) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 1 (.f64 F (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))))
	47.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (/.f64 (.f64 F (fma.f64 -4/893025 (.f64 (pow.f64 (PI.f64) 10) (pow.f64 l 10)) (.f64 1/2025 (pow.f64 (.f64 (PI.f64) l) 6)))) (-.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))))))))))
	54.5b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (.f64 F (-.f64 (/.f64 F (.f64 (PI.f64) l)) (fma.f64 (PI.f64) (.f64 1/3 (.f64 F l)) (/.f64 (.f64 F (fma.f64 8/843908625 (pow.f64 (.f64 (pow.f64 (PI.f64) 5) (pow.f64 l 5)) 3) (pow.f64 (.f64 1/45 (pow.f64 (.f64 (PI.f64) l) 3)) 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))))))))))))
	17.1b	(-.f64 (.f64 (PI.f64) l) (/.f64 1 (/.f64 F (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (.f64 (PI.f64) l)) F))))))
	41.3b	(-.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)))
	40.6b	(-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (PI.f64)) (.f64 (.f64 l l) l))) (/.f64 (tan.f64 (.f64 (PI.f64) l)) (*.f64 F F)))

Compiler

Compiled 17758 to 11093 computations (37.5% saved)

regimes2.9s (16.7%)

Accuracy

Total 1.8b remaining (77.2%)

Threshold costs 0b (0%)

Counts

214 → 1

Compiler

Compiled 34389 to 21325 computations (38% saved)

simplify7.0ms (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

end671.0ms (3.9%)

Compiler: Compiled 596 to 376 computations (36.9% 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

analyze2.0s (11.4%)

sample6.7s (38.5%)

simplify39.0ms (0.2%)

prune6.0ms (0%)

localize13.0ms (0.1%)

series246.0ms (1.4%)

rewrite34.0ms (0.2%)

simplify195.0ms (1.1%)

prune354.0ms (2%)

localize17.0ms (0.1%)

series248.0ms (1.4%)

rewrite32.0ms (0.2%)

simplify257.0ms (1.5%)

prune558.0ms (3.2%)

localize18.0ms (0.1%)

series323.0ms (1.9%)

rewrite26.0ms (0.2%)

simplify201.0ms (1.2%)

prune399.0ms (2.3%)

localize54.0ms (0.3%)

series483.0ms (2.8%)

rewrite100.0ms (0.6%)

simplify465.0ms (2.7%)

prune1.1s (6.1%)

regimes2.9s (16.7%)

simplify7.0ms (0%)

end671.0ms (3.9%)

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