Details

analyze1.3s (8.9%)

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)

sample3.1s (20.6%)

Results

1.4s	2108×	body	1024	valid
839.0ms	4638×	body	128	valid
466.0ms	965×	body	512	valid
183.0ms	540×	body	256	valid
4.0ms	5×	body	2048	valid

Compiler

Compiled 50 to 26 computations (48% saved)

simplify125.0ms (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

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))

Compiler

Compiled 92 to 45 computations (51.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
✓	0.3b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

series212.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

144.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
24.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
22.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
20.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite189.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

433×	`log-prod_binary64`
381×	`prod-diff_binary64`
236×	`egg-rr`
196×	`fma-def_binary64`
157×	`expm1-udef_binary64`

Counts

4 → 236

Calls

4 calls:

173.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
173.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
173.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
173.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	44
1	180	44
2	2351	44
3	4971	44
0	0	0
1	0	0

simplify167.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
542×	`associate-l_binary64`
461×	`unswap-sqr_binary64`
457×	`associate-r_binary64`
342×	`cancel-sign-sub-inv_binary64`

Counts

284 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	868
1	132	864
2	326	858
3	936	856
4	3585	856
5	4667	856
6	4878	856
7	4953	856

prune1.1s (7.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	296	12	308
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	298	12	310

Error

0.0b

Counts

310 → 12

Alt Table

Status	Error	Program
	0.8b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.6b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2)))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	0.6b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2)))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	32.5b	(/.f64 (fma.f64 (.f64 (neg.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) 1) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	0.5b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.7b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
▶	0.5b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))))))

Compiler

Compiled 11553 to 6802 computations (41.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1))
	0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
✓	0.5b	(pow.f64 (tan.f64 x) 4)
✓	1.5b	(fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)

series116.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

41.0ms

(fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)

40.0ms

(-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1))

35.0ms

(pow.f64 (tan.f64 x) 4)

rewrite109.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

484×	`log-prod_binary64`
300×	`prod-diff_binary64`
205×	`fma-def_binary64`
204×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`

Counts

3 → 90

Calls

3 calls:

106.0ms

(-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1))

106.0ms

(pow.f64 (tan.f64 x) 4)

106.0ms

(fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	243	27
2	2776	27
3	5345	27
0	0	0
1	0	0

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary64`
669×	`fma-neg_binary64`
666×	`associate-l_binary64`
546×	`associate-r_binary64`
354×	`times-frac_binary64`

Counts

126 → 116

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	525
1	121	523
2	301	521
3	929	519
4	4177	495
5	4874	495
6	4944	495

prune880.0ms (5.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	185	13	198

Error

0.0b

Counts

198 → 13

Alt Table

Status	Error	Program
	0.9b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) 3)))
	0.7b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))))
	0.8b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.6b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2)))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	0.6b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2)))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	32.5b	(/.f64 (fma.f64 (.f64 (neg.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) 1) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	0.5b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
▶	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
	0.5b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 6))) (+.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (tan.f64 x) 4))) -1)))
	0.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))))))

Compiler

Compiled 7002 to 4308 computations (38.5% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.2b	(/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.5b	(fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
✓	48.8b	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))

series965.0ms (6.5%)

Counts

4 → 48

Calls

4 calls:

413.0ms	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))
284.0ms	(fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
149.0ms	(/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
119.0ms	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))

rewrite160.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
215×	`fma-def_binary64`
193×	`log-div_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`

Counts

4 → 155

Calls

4 calls:

153.0ms	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))
153.0ms	(/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
153.0ms	(fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
153.0ms	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	101
1	261	77
2	2758	68
3	5020	68
0	0	0
1	0	0

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-neg_binary64`
730×	`fma-def_binary64`
677×	`cancel-sign-sub-inv_binary64`
305×	`times-frac_binary64`
187×	`neg-mul-1_binary64`

Counts

203 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	975
1	155	975
2	419	967
3	1314	963
4	4262	963
5	4940	963

prune1.7s (11.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	305	2	307
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	308	12	320

Error

0.0b

Counts

320 → 12

Alt Table

Status	Error	Program
	0.9b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) 3)))
	0.7b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))))
	0.8b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
▶	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))) 0)
	0.6b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2)))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))) (fma.f64 (neg.f64 (log1p.f64 (expm1.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))) (/.f64 (tan.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
	0.5b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 6))) (+.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (tan.f64 x) 4))) -1)))
	0.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	32.5b	(/.f64 (fma.f64 (.f64 (neg.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) 1) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))))))

Compiler

Compiled 18896 to 10189 computations (46.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))
	0.2b	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.2b	(/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))

series153.0ms (1%)

Counts

1 → 12

Calls

1 calls:

153.0ms

(*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))

rewrite167.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

720×	`log1p-expm1-u_binary64`
720×	`expm1-log1p-u_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`
103×	`fma-neg_binary64`

Counts

1 → 50

Calls

1 calls:

165.0ms

(*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	154	17
2	1905	17
3	4974	17
4	4994	17
5	5007	17
0	0	0
1	0	0

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

611×	`unswap-sqr_binary64`
579×	`distribute-rgt-neg-in_binary64`
546×	`associate-l_binary64`
436×	`associate-r_binary64`
312×	`fma-def_binary64`

Counts

62 → 60

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	30	328
1	75	324
2	189	322
3	608	322
4	2983	234
5	4689	106
6	4978	106
7	4920	106

prune647.0ms (4.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	203	12	215

Error

0.0b

Counts

215 → 12

Alt Table

Status	Error	Program
	0.9b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) 3)))
	0.7b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))))
	0.8b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
✓	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (*.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))) 0)
	0.6b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2)))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (+.f64 1 (-.f64 (pow.f64 (tan.f64 x) 4) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1)))) (fma.f64 (neg.f64 (log1p.f64 (expm1.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))) (/.f64 (tan.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (tan.f64 x) 1))))
	0.5b	(/.f64 (-.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (fma.f64 (tan.f64 x) (tan.f64 x) 1) -1)) (+.f64 1 (fma.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (-.f64 1 (pow.f64 (tan.f64 x) 6))) (+.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (tan.f64 x) 4))) -1)))
	0.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	32.5b	(/.f64 (fma.f64 (.f64 (neg.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) 1) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))))))

Compiler

Compiled 6528 to 4043 computations (38.1% saved)

regimes3.0s (20.1%)

Accuracy

Total 0.2b remaining (77.3%)

Threshold costs 0.2b (77.3%)

Counts

487 → 1

Compiler

Compiled 66552 to 41493 computations (37.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`*-rgt-identity_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	19	24
2	22	24
3	23	24
4	21	24

end325.0ms (2.2%)

Compiler: Compiled 609 to 394 computations (35.3% saved)

Details

analyze1.3s (8.9%)

sample3.1s (20.6%)

simplify125.0ms (0.8%)

prune6.0ms (0%)

localize13.0ms (0.1%)

series212.0ms (1.4%)

rewrite189.0ms (1.3%)

simplify167.0ms (1.1%)

prune1.1s (7.3%)

localize28.0ms (0.2%)

series116.0ms (0.8%)

rewrite109.0ms (0.7%)

simplify100.0ms (0.7%)

prune880.0ms (5.9%)

localize29.0ms (0.2%)

series965.0ms (6.5%)

rewrite160.0ms (1.1%)

simplify103.0ms (0.7%)

prune1.7s (11.7%)

localize23.0ms (0.2%)

series153.0ms (1%)

rewrite167.0ms (1.1%)

simplify119.0ms (0.8%)

prune647.0ms (4.4%)

regimes3.0s (20.1%)

simplify2.0ms (0%)

end325.0ms (2.2%)

Profiling