Details

analyze1.4s (10.7%)

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)

sample72.0ms (0.6%)

Algorithm

1×

intervals

Results

33.0ms	73×	body	1024	valid
14.0ms	141×	body	128	valid
8.0ms	26×	body	512	valid
3.0ms	16×	body	256	valid

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify99.0ms (0.8%)

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

prune7.0ms (0.1%)

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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
✓	0.1b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

series266.0ms (2.1%)

Counts

4 → 48

Calls

4 calls:

178.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
36.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
26.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
25.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite34.0ms (0.3%)

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:

8.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
1.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)

simplify185.0ms (1.4%)

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 → 160

Iterations

Useful iterations: 3 (0.0ms)

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

prune429.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	147	13	160
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	13	162

Error

0.0b

Counts

162 → 13

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))))
	0.4b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(.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 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.9b	(.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))))
	0.5b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.5b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (tan.f64 x) (tan.f64 x)) 3)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))))))
	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	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))))
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.8b	(/.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))))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	17.9b	(exp.f64 (-.f64 (log1p.f64 (neg.f64 (.f64 (tan.f64 x) (tan.f64 x)))) (log1p.f64 (.f64 (tan.f64 x) (tan.f64 x)))))

Compiler

Compiled 4102 to 1962 computations (52.2% saved)

localize17.0ms (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)))

series317.0ms (2.5%)

Counts

4 → 48

Calls

4 calls:

188.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
95.0ms	(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
17.0ms	(-.f64 1 (tan.f64 x))
17.0ms	(+.f64 1 (tan.f64 x))

rewrite105.0ms (0.8%)

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:

23.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))
10.0ms	(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
7.0ms	(-.f64 1 (tan.f64 x))
5.0ms	(+.f64 1 (tan.f64 x))

simplify535.0ms (4.1%)

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

prune1.1s (8.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	309	12	321

Error

0.0b

Counts

321 → 12

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))) (cbrt.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))))) (cbrt.f64 (/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.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))
	0.9b	(.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))))
	0.5b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.5b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.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 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))))
	0.5b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (tan.f64 x) (tan.f64 x)) 3)) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))))))
	0.4b	(/.f64 (/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (+.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))))
	0.8b	(/.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))))) (cbrt.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)) (log.f64 (exp.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))))
	17.9b	(exp.f64 (-.f64 (log1p.f64 (neg.f64 (.f64 (tan.f64 x) (tan.f64 x)))) (log1p.f64 (.f64 (tan.f64 x) (tan.f64 x)))))

Compiler

Compiled 9817 to 5443 computations (44.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series295.0ms (2.3%)

Counts

4 → 48

Calls

4 calls:

191.0ms	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
43.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
40.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))
20.0ms	(*.f64 (sin.f64 x) (tan.f64 x))

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
33×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
11.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
10.0ms	(*.f64 (sin.f64 x) (tan.f64 x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))

simplify265.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-def_binary64`
328×	`associate-/r/_binary64`
242×	`cancel-sign-sub-inv_binary64`
210×	`distribute-rgt-neg-in_binary64`
202×	`exp-prod_binary64`

Counts

184 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	5019
1	570	4557
2	2019	4173
3	4435	4173
4	4896	4173

prune708.0ms (5.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	196	10	206

Error

0.0b

Counts

206 → 10

Alt Table

Status	Error	Program
	0.5b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 1 (cos.f64 x)) (.f64 (sin.f64 x) (tan.f64 x))))) (fma.f64 (neg.f64 (/.f64 1 (cos.f64 x))) (.f64 (sin.f64 x) (tan.f64 x)) (.f64 (/.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.9b	(.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))))
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))))
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.5b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	17.9b	(exp.f64 (-.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (log1p.f64 (.f64 (tan.f64 x) (tan.f64 x)))))
▶	0.3b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 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))))
	0.4b	(/.f64 (+.f64 1 (tan.f64 x)) (log.f64 (exp.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x))))))

Compiler

Compiled 6404 to 2365 computations (63.1% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))
✓	0.2b	(fma.f64 1 1 (neg.f64 (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))))
✓	0.2b	(/.f64 (tan.f64 x) (cos.f64 x))
✓	46.4b	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))

series243.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

121.0ms	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))
44.0ms	(fma.f64 1 1 (neg.f64 (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))))
41.0ms	(*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))
36.0ms	(/.f64 (tan.f64 x) (cos.f64 x))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
23×	`add-exp-log_binary64`

Counts

4 → 106

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))
6.0ms	(/.f64 (tan.f64 x) (cos.f64 x))
1.0ms	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))
1.0ms	(fma.f64 1 1 (neg.f64 (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))))

simplify198.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
427×	`associate-/l*_binary64`
376×	`times-frac_binary64`
368×	`associate-l_binary64`
318×	`associate-r_binary64`

Counts

154 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	2535
1	385	2219
2	1055	2099
3	3747	2099
4	4906	2099
5	4882	2099

prune1.5s (11.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	368	10	378

Error

0.0b

Counts

378 → 10

Alt Table

Status	Error	Program
	0.5b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 1 (cos.f64 x)) (.f64 (sin.f64 x) (tan.f64 x))))) (fma.f64 (neg.f64 (/.f64 1 (cos.f64 x))) (.f64 (sin.f64 x) (tan.f64 x)) (.f64 (/.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.9b	(.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))))
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))))
	0.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.5b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	17.9b	(exp.f64 (-.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (log1p.f64 (.f64 (tan.f64 x) (tan.f64 x)))))
✓	0.3b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 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))))
	0.5b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))

Compiler

Compiled 18493 to 7345 computations (60.3% saved)

regimes2.5s (19.3%)

Accuracy

Total 0.2b remaining (75.4%)

Threshold costs 0.2b (75.4%)

Counts

285 → 1

Compiler

Compiled 31274 to 18218 computations (41.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	13	22
2	15	22
3	16	22
4	15	22

end1.0ms (0%)

Compiler: Compiled 15 to 8 computations (46.7% saved)

sample2.5s (19.3%)

Algorithm

1×

intervals

Results

844.0ms	1954×	body	1024	valid
469.0ms	4613×	body	128	valid
310.0ms	966×	body	512	valid
99.0ms	463×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 392 to 212 computations (45.9% saved)

Details

analyze1.4s (10.7%)

sample72.0ms (0.6%)

simplify99.0ms (0.8%)

prune7.0ms (0.1%)

localize14.0ms (0.1%)

series266.0ms (2.1%)

rewrite34.0ms (0.3%)

simplify185.0ms (1.4%)

prune429.0ms (3.3%)

localize17.0ms (0.1%)

series317.0ms (2.5%)

rewrite105.0ms (0.8%)

simplify535.0ms (4.1%)

prune1.1s (8.7%)

localize22.0ms (0.2%)

series295.0ms (2.3%)

rewrite68.0ms (0.5%)

simplify265.0ms (2.1%)

prune708.0ms (5.5%)

localize37.0ms (0.3%)

series243.0ms (1.9%)

rewrite41.0ms (0.3%)

simplify198.0ms (1.5%)

prune1.5s (11.3%)

regimes2.5s (19.3%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.5s (19.3%)

Profiling