Details

analyze739.0ms (9.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample1.8s (21.9%)

Results

762.0ms	2011×	body	1024	valid
493.0ms	4683×	body	128	valid
285.0ms	1017×	body	512	valid
107.0ms	539×	body	256	valid
3.0ms	6×	body	2048	valid

Compiler

Compiled 50 to 26 computations (48% saved)

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

678×	`unsub-neg_binary64`
627×	`times-frac_binary64`
565×	`div-sub_binary64`
547×	`fma-def_binary64`
526×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	19	22
2	30	22
3	47	22
4	94	22
5	137	22
6	211	22
7	437	22
8	928	22
9	1718	22
10	3074	22
11	3861	22
12	4442	22
13	4822	22

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))

Compiler

Compiled 92 to 45 computations (51.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
✓	0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

series94.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

62.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
13.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
9.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
11×	`pow1_binary64`

Counts

4 → 102

Calls

4 calls:

5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
2.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)

simplify94.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

588×	`cancel-sign-sub-inv_binary64`
342×	`fma-def_binary64`
323×	`fma-neg_binary64`
287×	`associate-l_binary64`
237×	`associate-r_binary64`

Counts

150 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3084
1	360	2781
2	960	2730
3	3123	2721
4	5035	2721

prune241.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	144	15	159
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	15	161

Error

0.0b

Counts

161 → 15

Alt Table

Status	Error	Program
	0.4b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
	0.8b	(.f64 (/.f64 (+.f64 1 (tan.f64 x)) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (-.f64 1 (tan.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))))
	1.6b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	1.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.5b	(*.f64 (/.f64 (+.f64 1 (tan.f64 x)) (hypot.f64 1 (tan.f64 x))) (/.f64 (-.f64 1 (tan.f64 x)) (hypot.f64 1 (tan.f64 x))))
	0.4b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (expm1.f64 (log1p.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
▶	0.4b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))

Compiler

Compiled 4146 to 1999 computations (51.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.2b	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.2b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

series112.0ms (1.4%)

Counts

2 → 24

Calls

2 calls:

63.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
49.0ms	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 77

Calls

2 calls:

9.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
2.0ms	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-neg_binary64`
627×	`distribute-rgt-in_binary64`
383×	`cancel-sign-sub-inv_binary64`
244×	`associate-l_binary64`
234×	`fma-def_binary64`

Counts

101 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	280	2128
2	767	2112
3	2212	2112
4	4886	2112
5	5267	2112

prune386.0ms (4.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	198	15	213

Error

0.0b

Counts

213 → 15

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
	0.8b	(.f64 (/.f64 (+.f64 1 (tan.f64 x)) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (-.f64 1 (tan.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))))
	1.6b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.5b	(*.f64 (/.f64 (+.f64 1 (tan.f64 x)) (hypot.f64 1 (tan.f64 x))) (/.f64 (-.f64 1 (tan.f64 x)) (hypot.f64 1 (tan.f64 x))))
	0.4b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(expm1.f64 (log1p.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))
	0.4b	(.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.4b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	1.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))

Compiler

Compiled 5365 to 2758 computations (48.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 1 (tan.f64 x))
✓	0.2b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
✓	0.2b	(-.f64 1 (tan.f64 x))
✓	0.2b	(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))

series116.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

67.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
36.0ms	(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
7.0ms	(-.f64 1 (tan.f64 x))
6.0ms	(+.f64 1 (tan.f64 x))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

211×	`*-un-lft-identity_binary64`
204×	`times-frac_binary64`
159×	`add-sqr-sqrt_binary64`
99×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`

Counts

4 → 234

Calls

4 calls:

11.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
4.0ms	(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
3.0ms	(-.f64 1 (tan.f64 x))
2.0ms	(+.f64 1 (tan.f64 x))

simplify272.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
497×	`times-frac_binary64`
388×	`distribute-rgt-in_binary64`
341×	`distribute-lft-in_binary64`
259×	`fma-neg_binary64`

Counts

282 → 308

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	9358
1	672	8993
2	2255	8597
3	4653	8597
4	4963	8597
5	4911	8597

prune531.0ms (6.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	301	7	308
Fresh	9	4	13
Picked	1	0	1
Done	1	0	1
Total	312	11	323

Error

0.0b

Counts

323 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (cbrt.f64 (+.f64 1 (tan.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (/.f64 1 (-.f64 1 (tan.f64 x)))))
	0.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))))
	8.1b	(/.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 1 (sqrt.f64 (-.f64 1 (tan.f64 x))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (sqrt.f64 (-.f64 1 (tan.f64 x)))))
▶	0.4b	(*.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1)))
	0.9b	(/.f64 (+.f64 1 (tan.f64 x)) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (*.f64 (cbrt.f64 (-.f64 1 (tan.f64 x))) (cbrt.f64 (-.f64 1 (tan.f64 x))))) (/.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (-.f64 1 (tan.f64 x))))))
	0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (cbrt.f64 (+.f64 1 (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (tan.f64 x))) (cbrt.f64 (-.f64 1 (tan.f64 x)))))) (/.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (-.f64 1 (tan.f64 x))))))
	0.5b	(log.f64 (exp.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))))
	0.4b	(expm1.f64 (log1p.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))
	0.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.8b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (.f64 (.f64 (cbrt.f64 (-.f64 1 (tan.f64 x))) (cbrt.f64 (-.f64 1 (tan.f64 x)))) (cbrt.f64 (-.f64 1 (tan.f64 x))))))

Compiler

Compiled 9741 to 5451 computations (44% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1)))
✓	0.2b	(/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1))
✓	0.2b	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.4b	(pow.f64 (tan.f64 x) 3)

series311.0ms (3.9%)

Counts

4 → 48

Calls

4 calls:

154.0ms	(*.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1)))
76.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1))
66.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
13.0ms	(pow.f64 (tan.f64 x) 3)

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`add-sqr-sqrt_binary64`
113×	`*-un-lft-identity_binary64`
100×	`times-frac_binary64`
57×	`add-cube-cbrt_binary64`
56×	`difference-of-squares_binary64`

Counts

4 → 211

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1)))
9.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
4.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1))
2.0ms	(pow.f64 (tan.f64 x) 3)

simplify254.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-def_binary64`
234×	`cancel-sign-sub-inv_binary64`
212×	`unswap-sqr_binary64`
209×	`fma-neg_binary64`
181×	`div-sub_binary64`

Counts

259 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	9599
1	825	8982
2	2818	8506
3	4359	8506
4	4966	8506
5	4918	8506

prune625.0ms (7.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	312	11	323

Error

0.0b

Counts

323 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (cbrt.f64 (+.f64 1 (tan.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (/.f64 1 (-.f64 1 (tan.f64 x)))))
	0.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))))
	8.1b	(/.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 1 (sqrt.f64 (-.f64 1 (tan.f64 x))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (sqrt.f64 (-.f64 1 (tan.f64 x)))))
✓	0.4b	(*.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (+.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1)))
	0.9b	(/.f64 (+.f64 1 (tan.f64 x)) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (*.f64 (cbrt.f64 (-.f64 1 (tan.f64 x))) (cbrt.f64 (-.f64 1 (tan.f64 x))))) (/.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (-.f64 1 (tan.f64 x))))))
	0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (cbrt.f64 (+.f64 1 (tan.f64 x)))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (tan.f64 x))) (cbrt.f64 (-.f64 1 (tan.f64 x)))))) (/.f64 (cbrt.f64 (+.f64 1 (tan.f64 x))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (-.f64 1 (tan.f64 x))))))
	0.5b	(log.f64 (exp.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))))
	0.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (-.f64 (.f64 1 1) (.f64 (tan.f64 x) (tan.f64 x))) (.f64 (fma.f64 (tan.f64 x) (+.f64 1 (tan.f64 x)) 1) (-.f64 1 (tan.f64 x)))))
	0.8b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (.f64 (.f64 (cbrt.f64 (-.f64 1 (tan.f64 x))) (cbrt.f64 (-.f64 1 (tan.f64 x)))) (cbrt.f64 (-.f64 1 (tan.f64 x))))))

Compiler

Compiled 12819 to 7820 computations (39% saved)

regimes1.9s (24%)

Accuracy

Total 0.2b remaining (74.4%)

Threshold costs 0.2b (74.4%)

Counts

404 → 1

Compiler

Compiled 42653 to 26309 computations (38.3% saved)

simplify3.0ms (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	9	22
1	16	22
2	22	22
3	26	22
4	28	22
5	26	22

end208.0ms (2.6%)

Compiler: Compiled 379 to 227 computations (40.1% saved)

Details

analyze739.0ms (9.2%)

sample1.8s (21.9%)

simplify91.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series94.0ms (1.2%)

rewrite16.0ms (0.2%)

simplify94.0ms (1.2%)

prune241.0ms (3%)

localize8.0ms (0.1%)

series112.0ms (1.4%)

rewrite17.0ms (0.2%)

simplify101.0ms (1.3%)

prune386.0ms (4.8%)

localize8.0ms (0.1%)

series116.0ms (1.4%)

rewrite48.0ms (0.6%)

simplify272.0ms (3.4%)

prune531.0ms (6.6%)

localize12.0ms (0.2%)

series311.0ms (3.9%)

rewrite60.0ms (0.7%)

simplify254.0ms (3.2%)

prune625.0ms (7.8%)

regimes1.9s (24%)

simplify3.0ms (0%)

end208.0ms (2.6%)

Profiling